This document proposes a kernel spectral matched filter for target detection in hyperspectral imagery. It begins with an overview of linear matched filtering and introduces the concept of implementing algorithms in kernel feature spaces. It then defines a nonlinear matched filter model in a kernel feature space, which is equivalent to a nonlinear matched filter in the original input space. Finally, it derives an expression for the kernel spectral matched filter by rewriting the matched filter defined in the kernel feature space in terms of kernel functions using the kernel trick. Simulation results on hyperspectral imagery show the kernel spectral matched filter outperforms the conventional linear matched filter.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
Call for paper 2012, hard copy of Certificate, research paper publishing, where to publish research paper,
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Diagnosis of Faulty Sensors in Antenna Array using Hybrid Differential Evolut...IJECEIAES
In this work, differential evolution based compressive sensing technique for detection of faulty sensors in linear arrays has been presented. This algorithm starts from taking the linear measurements of the power pattern generated by the array under test. The difference between the collected compressive measurements and measured healthy array field pattern is minimized using a hybrid differential evolution (DE). In the proposed method, the slow convergence of DE based compressed sensing technique is accelerated with the help of parallel coordinate decent algorithm (PCD). The combination of DE with PCD makes the minimization faster and precise. Simulation results validate the performance to detect faulty sensors from a small number of measurements.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
Call for paper 2012, hard copy of Certificate, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJCER, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, research and review articles, IJCER Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathematics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer review journal, indexed journal, research and review articles, engineering journal, www.ijceronline.com, research journals,
yahoo journals, bing journals, International Journal of Computational Engineering Research, Google journals, hard copy of Certificate,
journal of engineering, online Submission
Diagnosis of Faulty Sensors in Antenna Array using Hybrid Differential Evolut...IJECEIAES
In this work, differential evolution based compressive sensing technique for detection of faulty sensors in linear arrays has been presented. This algorithm starts from taking the linear measurements of the power pattern generated by the array under test. The difference between the collected compressive measurements and measured healthy array field pattern is minimized using a hybrid differential evolution (DE). In the proposed method, the slow convergence of DE based compressed sensing technique is accelerated with the help of parallel coordinate decent algorithm (PCD). The combination of DE with PCD makes the minimization faster and precise. Simulation results validate the performance to detect faulty sensors from a small number of measurements.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation
of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a
49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation
of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a
49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization
problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular
choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation
of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of
nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective
approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a
49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In
the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery
is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry
out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
Enhanced Mobile Node Tracking With Received Signal Strength in Wireless Senso...IOSR Journals
Abstract : Node localization is important parameter in WSN. Node localization is required to report origin of
events which makes it one of the important challenges in WSN. Received signal strength (RSS) is used to
calculate distance between mobile node and reference node. The position of the mobile node is calculated using
multilateration algorithm (MA). Extended Kalman filter (EKF) is utilized to estimate the actual position. In this
paper, the implementation and enhancement of a tracking system based on RSS indicator with the aid of an
Extended Kalman Filter (EKF) is described and an adaptive filter is derived.
Keywords - Extended Kalman filter (EKF), mobile node tracking, multilateration algorithm (MA), received
signal strength (RSS), Wireless sensor networks (WSN)
Enhanced Mobile Node Tracking With Received Signal Strength in Wireless Senso...IOSR Journals
Node localization is important parameter in WSN. Node localization is required to report origin of
events which makes it one of the important challenges in WSN. Received signal strength (RSS) is used to
calculate distance between mobile node and reference node. The position of the mobile node is calculated using
multilateration algorithm (MA). Extended Kalman filter (EKF) is utilized to estimate the actual position. In this
paper, the implementation and enhancement of a tracking system based on RSS indicator with the aid of an
Extended Kalman Filter (EKF) is described and an adaptive filter is derived.
MULTI RESOLUTION LATTICE DISCRETE FOURIER TRANSFORM (MRL-DFT)csandit
In many imaging applications, including sensor arrays, MRI and CT,data is often sampled on
non-rectangular point sets with non-uniform density. Moreover, in image and video processing,
a mix of non-rectangular sampling structures naturally arise. Multirate processing typically
utilizes a normalized integer indexing scheme, which masks the true physical dimensions of the
points. However, the spatial correlation of such signals often contains important
information.This paper presents a theory of signals defined on regular discrete sets called
lattices, and presents an associated form of a finite Fourier transform denoted here as
multiresolution lattice discrete Fourier transform (MRL-DFT). Multirate processing techniques
such as decimation, interpolation and polyphase representations are presented in a context
which preserves the true spatial dimensions of the sampling structure.Moreover, the polyphase
formulation enables systematic representation and processing for sampling patterns with
variable spatial density, and provides a framework for developing generalized FFT and
regridding algorithms.
Using Subspace Pursuit Algorithm to Improve Performance of the Distributed Co...Polytechnique Montreal
This paper applies a compressed algorithm to improve the spectrum sensing performance of cognitive radio technology.
At the fusion center, the recovery error in the analog to information converter (AIC) when reconstructing the
transmit signal from the received time-discrete signal causes degradation of the detection performance. Therefore, we
propose a subspace pursuit (SP) algorithm to reduce the recovery error and thereby enhance the detection performance.
In this study, we employ a wide-band, low SNR, distributed compressed sensing regime to analyze and evaluate the
proposed approach. Simulations are provided to demonstrate the performance of the proposed algorithm.
Mimo radar detection in compound gaussian clutter using orthogonal discrete f...ijma
This paper proposes orthogonal Discrete Frequency Coding Space Time Waveforms (DFCSTW) for
Multiple Input and Multiple Output (MIMO) radar detection in compound Gaussian clutter. The proposed
orthogonal waveforms are designed considering the position and angle of the transmitting antenna when
viewed from origin. These orthogonally optimized show good resolution in spikier clutter with Generalized
Likelihood Ratio Test (GLRT) detector. The simulation results show that this waveform provides better
detection performance in spikier Clutter.
Expert system design for elastic scattering neutrons optical model using bpnnijcsa
In present paper, a proposed expert system is designed to obtain a trained formulae for the optical model
parameters used in elastic scattering neutrons of light nuclei for (7Li), at energy range between [(1) to
(20)] MeV. A simple algorithm has used to design this expert system, while a multi-layer backwardpropagation
neural network (BPNN) is applied for training and testing the data used in this model. This
group of formulae may get a simple expert system occurring from governing formulae model, and predicts
the critical parameters usually resulted from the complicated computer coding methods. This expert system
may use in nuclear reactions yields in both fission and fusion nature who gives more closely results to the
real model.
Classification of Iris Data using Kernel Radial Basis Probabilistic Neural N...Scientific Review SR
Radial Basis Probabilistic Neural Network (RBPNN) has a broader generalized capability that been
successfully applied to multiple fields. In this paper, the Euclidean distance of each data point in RBPNN is
extended by calculating its kernel-induced distance instead of the conventional sum-of squares distance. The
kernel function is a generalization of the distance metric that measures the distance between two data points as the
data points are mapped into a high dimensional space. During the comparing of the four constructed classification
models with Kernel RBPNN, Radial Basis Function networks, RBPNN and Back-Propagation networks as
proposed, results showed that, model classification on Iris Data with Kernel RBPNN display an outstanding
performance in this regard
1000 words, 2 referencesBegin conducting research now on your .docxvrickens
1000 words, 2 references
Begin conducting research now on your company/client. After brainstorming on your company’s industry and after your preliminary research information-gathering techniques, create a research profile proposal to deliver to your company’s management that includes the following:
State the specific research goal for the proposal.
What is the company’s current business problem?
Who is the company’s competition?
Establish your population sample for researching customer attitudes and behaviors about the company and product.
Identify the steps in the research process.
.
1000 words only due by 5314 at 1200 estthis is a second part to.docxvrickens
1000 words only due by 5/3/14 at 12:00 est
this is a second part to this assignment due at a different time
Part 1
Your fast-food franchise has been cleared for business in all 4 countries (United Arab Emirates, Israel, Mexico, and China). You now have to start construction on your restaurants. The financing is coming from the United Arab Emirates, the materials are coming from Mexico and China, the engineering and technology are coming from Israel , and the labor will be hired locally within these countries by your management team from the United States. You invite all of the players to the headquarters in the United States for a big meeting to explain the project and get to know one another. The people seem to be staying with their own groups and not mingling.
What is the cultural phenomenon at play here (what is it called/ term)?
How do you explain the lack of intercultural communication and interaction?
What do you know about these cultures—specifically their economic, political, educational, and social systems—that could help you in getting them together?
What are some of the contrasting cultural values of these countries?
You are concerned about some of the language barriers as you start the meeting, particularly the fact that the United States is a low-context country, and some of the countries present are high-context countries. Furthermore, you only speak English, and you do not have an interpreter present.
How will this affect the presentation?
What are some of the issues you should be concerned about regarding verbal and nonverbal language for this group?
What strategy would you use to begin to have everyone develop a relationship with each other that will help ease future negotiations, development, and implementation?
.
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Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
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Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
ARRAY FACTOR OPTIMIZATION OF AN ACTIVE PLANAR PHASED ARRAY USING EVOLUTIONARY...jantjournal
Evolutionary algorithms (EAs) have the potential to handle complex, multi-dimensional optimization problems in the field of phased array. Out of different EAs, particle swarm optimization (PSO) is a popular choice. In a phased array, antenna element failure is a common phenomenon and this leads to degradation of the array factor (AF) pattern, primarily in terms of increased side lobe levels (SLLs), displacement of nulls and reduction in the null depths. The recovery of a degraded pattern using a cost and time-effective approach is on demand. In this context, an attempt made to obtain an optimized AF pattern after fault in a 49 elements quasi-circular aperture equilateral triangular grid active planar phased array using PSO. In the paper, multiple cases on recovery are discussed having a maximum 20% element failure. Each recovery is also further evaluated by different statistical analyses. A dedicated software tool was developed to carry out the work presented in this paper.
Enhanced Mobile Node Tracking With Received Signal Strength in Wireless Senso...IOSR Journals
Abstract : Node localization is important parameter in WSN. Node localization is required to report origin of
events which makes it one of the important challenges in WSN. Received signal strength (RSS) is used to
calculate distance between mobile node and reference node. The position of the mobile node is calculated using
multilateration algorithm (MA). Extended Kalman filter (EKF) is utilized to estimate the actual position. In this
paper, the implementation and enhancement of a tracking system based on RSS indicator with the aid of an
Extended Kalman Filter (EKF) is described and an adaptive filter is derived.
Keywords - Extended Kalman filter (EKF), mobile node tracking, multilateration algorithm (MA), received
signal strength (RSS), Wireless sensor networks (WSN)
Enhanced Mobile Node Tracking With Received Signal Strength in Wireless Senso...IOSR Journals
Node localization is important parameter in WSN. Node localization is required to report origin of
events which makes it one of the important challenges in WSN. Received signal strength (RSS) is used to
calculate distance between mobile node and reference node. The position of the mobile node is calculated using
multilateration algorithm (MA). Extended Kalman filter (EKF) is utilized to estimate the actual position. In this
paper, the implementation and enhancement of a tracking system based on RSS indicator with the aid of an
Extended Kalman Filter (EKF) is described and an adaptive filter is derived.
MULTI RESOLUTION LATTICE DISCRETE FOURIER TRANSFORM (MRL-DFT)csandit
In many imaging applications, including sensor arrays, MRI and CT,data is often sampled on
non-rectangular point sets with non-uniform density. Moreover, in image and video processing,
a mix of non-rectangular sampling structures naturally arise. Multirate processing typically
utilizes a normalized integer indexing scheme, which masks the true physical dimensions of the
points. However, the spatial correlation of such signals often contains important
information.This paper presents a theory of signals defined on regular discrete sets called
lattices, and presents an associated form of a finite Fourier transform denoted here as
multiresolution lattice discrete Fourier transform (MRL-DFT). Multirate processing techniques
such as decimation, interpolation and polyphase representations are presented in a context
which preserves the true spatial dimensions of the sampling structure.Moreover, the polyphase
formulation enables systematic representation and processing for sampling patterns with
variable spatial density, and provides a framework for developing generalized FFT and
regridding algorithms.
Using Subspace Pursuit Algorithm to Improve Performance of the Distributed Co...Polytechnique Montreal
This paper applies a compressed algorithm to improve the spectrum sensing performance of cognitive radio technology.
At the fusion center, the recovery error in the analog to information converter (AIC) when reconstructing the
transmit signal from the received time-discrete signal causes degradation of the detection performance. Therefore, we
propose a subspace pursuit (SP) algorithm to reduce the recovery error and thereby enhance the detection performance.
In this study, we employ a wide-band, low SNR, distributed compressed sensing regime to analyze and evaluate the
proposed approach. Simulations are provided to demonstrate the performance of the proposed algorithm.
Mimo radar detection in compound gaussian clutter using orthogonal discrete f...ijma
This paper proposes orthogonal Discrete Frequency Coding Space Time Waveforms (DFCSTW) for
Multiple Input and Multiple Output (MIMO) radar detection in compound Gaussian clutter. The proposed
orthogonal waveforms are designed considering the position and angle of the transmitting antenna when
viewed from origin. These orthogonally optimized show good resolution in spikier clutter with Generalized
Likelihood Ratio Test (GLRT) detector. The simulation results show that this waveform provides better
detection performance in spikier Clutter.
Expert system design for elastic scattering neutrons optical model using bpnnijcsa
In present paper, a proposed expert system is designed to obtain a trained formulae for the optical model
parameters used in elastic scattering neutrons of light nuclei for (7Li), at energy range between [(1) to
(20)] MeV. A simple algorithm has used to design this expert system, while a multi-layer backwardpropagation
neural network (BPNN) is applied for training and testing the data used in this model. This
group of formulae may get a simple expert system occurring from governing formulae model, and predicts
the critical parameters usually resulted from the complicated computer coding methods. This expert system
may use in nuclear reactions yields in both fission and fusion nature who gives more closely results to the
real model.
Classification of Iris Data using Kernel Radial Basis Probabilistic Neural N...Scientific Review SR
Radial Basis Probabilistic Neural Network (RBPNN) has a broader generalized capability that been
successfully applied to multiple fields. In this paper, the Euclidean distance of each data point in RBPNN is
extended by calculating its kernel-induced distance instead of the conventional sum-of squares distance. The
kernel function is a generalization of the distance metric that measures the distance between two data points as the
data points are mapped into a high dimensional space. During the comparing of the four constructed classification
models with Kernel RBPNN, Radial Basis Function networks, RBPNN and Back-Propagation networks as
proposed, results showed that, model classification on Iris Data with Kernel RBPNN display an outstanding
performance in this regard
Similar to International Journal of Computer Vision 71(2), 127–141, 2007.docx (20)
1000 words, 2 referencesBegin conducting research now on your .docxvrickens
1000 words, 2 references
Begin conducting research now on your company/client. After brainstorming on your company’s industry and after your preliminary research information-gathering techniques, create a research profile proposal to deliver to your company’s management that includes the following:
State the specific research goal for the proposal.
What is the company’s current business problem?
Who is the company’s competition?
Establish your population sample for researching customer attitudes and behaviors about the company and product.
Identify the steps in the research process.
.
1000 words only due by 5314 at 1200 estthis is a second part to.docxvrickens
1000 words only due by 5/3/14 at 12:00 est
this is a second part to this assignment due at a different time
Part 1
Your fast-food franchise has been cleared for business in all 4 countries (United Arab Emirates, Israel, Mexico, and China). You now have to start construction on your restaurants. The financing is coming from the United Arab Emirates, the materials are coming from Mexico and China, the engineering and technology are coming from Israel , and the labor will be hired locally within these countries by your management team from the United States. You invite all of the players to the headquarters in the United States for a big meeting to explain the project and get to know one another. The people seem to be staying with their own groups and not mingling.
What is the cultural phenomenon at play here (what is it called/ term)?
How do you explain the lack of intercultural communication and interaction?
What do you know about these cultures—specifically their economic, political, educational, and social systems—that could help you in getting them together?
What are some of the contrasting cultural values of these countries?
You are concerned about some of the language barriers as you start the meeting, particularly the fact that the United States is a low-context country, and some of the countries present are high-context countries. Furthermore, you only speak English, and you do not have an interpreter present.
How will this affect the presentation?
What are some of the issues you should be concerned about regarding verbal and nonverbal language for this group?
What strategy would you use to begin to have everyone develop a relationship with each other that will help ease future negotiations, development, and implementation?
.
1000 words with refernceBased on the American constitution,” wh.docxvrickens
1000 words with refernce
Based on the American “constitution,” which internal and external stakeholders, in the policy making process, possess “constitutional legitimacy” for their role in making public policy? Do entities with explicit power have more influence than those entities with implied powers in making public policy? Should they? Why or why not?
1000 words with reference
Accountability and ethical conduct are important concepts in public administration. In Tennessee, recent political stakeholders and some bureaucratic stakeholders have been caught up in various scandals (Operation Tennessee Waltz, Operation Rocky Top etc.). Based on the readings, what could Tennessee do to make political and bureaucratic functionaries more accountable?
.
10.1. In a t test for a single sample, the samples mean.docxvrickens
10.1. In a
t
test for a single sample
,
the sample
'
s mean is
c
o
m
par
ed to the
population
.
10.2. When we use a paired-samples
t
test to compare the pret
es
t and
p
ostt
est
scores for a group of 45 people, the degrees of freedom
(
df
)
ar
e _____.
10.3. If we conduct a
t
test for independent samples
,
and
n1
=
32 and
n2
=
35,
the degrees of freedom
(df)
are
_____.
10.4
.
A researcher wants to study the effect of college education on p
eo
p
le's
earning by comparing the annual salaries of a randomly
-
selecte
d g
ro
up
of 100 college graduates to the annual salaries of 100 randoml
y-selected
group of people whose highest level of education is high
schoo
l.
To
compare the mean annual salaries of the two groups
,
th
e resea
r
cher
should use a
t
test for
______.
10.5. A training coordinator wants to determine the effectiveness
of a program
that makes extensive use of educational technology when t
raining new
employees. She compares the scores of her new emplo
yees who
completed the training on a nationally-normed test to th
e
me
a
n
s
c
ore of
all
those in the country who took the same test.
The a
p
pro
p
riate
statistical test the training coordinator should use for h
er analysis
i
s the
t
test for ______.
10
.
6. As part of the process to develop two parallel forms o
f a q
u
es
t
io
nn
aire
,
the persons creating the questionnaire may admin
i
st
e
r b
o
th
f
or
ms to a
group of students, and then use a
t
test for ______ s
a
mpl
es
t
o com
p
are
the mean scores on the two forms
.
Circle the
correct
answer:
10.7. A difference
o
f 4 points between two
homogeneous group
s
is lik
e
ly to
be
more/less
statistically significant than the
s
ame
d
i
ffe
r
e
n
ce (of 4
points) between two
heterogeneous
groups
,
when all fou
r g
r
o
up
s are
taking completing the same survey and have appro
x
im
a
tel
y t
h
e same
number of subjects.
10.8. A difference of 3 points on a 100-item test taken b
y t
w
o g
rou
ps is likely to be
more/less
statistically significant than a difference of 3 po
i
nt
s on a 30-item test taken by the sa
m
e
t
w
o g
r
oups.
10.9 When
a
t
test for paired samples is u
s
ed to
c
ompare th
e
p
re
t
est an
d
the posttest
means
,
the number of pretest scores i
s
the
same as/different than
the number of
po
s
t-t
e
st scor
e
s.
10.10. W
hen
w
e
w
ant to compar
e w
h
e
th
e
r female
s
' scor
es
on th
e
G
MAT are
di
fferent f
rom males' scores
,
we should use a
t
test for
paired samples/independen
t
samples
.
10
.11 In studi
e
s
w
h
e
re the alte
r
nati
ve (
r
es
ear
c
h
)
h
y
poth
es
i
s
i
s
directiona
l
,
t
h
e critical va
lu
es
for
a
one tailed test/two-tailed test
should b
e us
ed t
o
d
e
t
erm
i
ne the
l
e
vel o
f
signi
fi
cance (i
.
e.
,
the
p
va
lue).
10.12 W
h
e
n
t
h
e
alt
e
rnati
ve
h
y
poth
e
si
s
is: H
A
: u1=u2
,
the c
ri
ti
ca
l
v
alu
es for
one
tailed test/
two-tailed
test
should b
e
u
se.
100 WORDS OR MOREConsider your past experiences either as a studen.docxvrickens
100 WORDS OR MORE
Consider your past experiences either as a student, early child care professional, or teacher. Describe a creative episode similar to the two boys who found a frog in the text (Creativity and the Arts with Young Children, p.309), when the teacher (maybe you) seized the opportunity (the teachable moment) to inspire the children to branch out using their imagination, creativity, and interests. Why do you think this was such a memorable moment?
WHAT WAS OBSERVED?
Two boys were exploring the outdoors and found a small frog. The teacher recognized their high interest and determined that this was an appropriate topic for a study. Their experience in nature provided the interest and stimulus for a long-term project on frogs. The teacher demonstrated her belief that this study could not only include informational learning but also be enriched by the use of the arts. She didn't know a lot about frogs, so she joined the children in looking for information about them. Stories provided the content for the drama about frogs, and the music selection encouraged listening and moving to the “frog music.” A group mural was created through the collaboration of several children, who created visual representations of the frog's environment. Another group of children investigated building a habitat for the frog in their classroom aquarium. All of the children were involved in active learning and used methods that matched their interests. At the conclusion of the study, the children shared their learning by making a giant book about frogs, creating a song about frogs, and demonstrating the development of the frog aquarium that emulated its outdoor environment. Finally, they returned the frog to its home, which led to their understanding that it needed to live in its natural habitat.
.
1000 to 2000 words Research Title VII of the Civil Rights Act of.docxvrickens
1000 to 2000 words
Research Title VII of the Civil Rights Act of 1964 and discuss why it is so significant.
Your paper should discuss the state of race relations in the United States prior to the Civil Rights Act of 1964. It should also discuss the political environment that led to the passing of the Civil Rights Act of 1964. Additionally, please include a response to the following in your analysis:
What is the purpose of this law?
What groups does it protect? What groups does it not protect?
How were the Jim Crow laws tested during this time period?
What is the U.S. Supreme Court case
Plessy v. Ferguson
about? Is the rule established in the Plessy case still the rule today?
.
1000 word essay MlA Format.. What is our personal responsibility tow.docxvrickens
1000 word essay MlA Format.. What is our personal responsibility toward the natural world, toward what we term our natural resources? Use one of these readings and interpet it to the question reflecting your answer. Add perentheses when using quotes.
“May’s Lion” (Le Guin)
“Deer Among Cattle” (Dickey)
“Meditation at Oyster River” (Roethke)
“The Call of the Wild” (Snyder)
“Eco-Defense” (Abbey)
“The Present” (Dillard)
“Time and the Machine” (Huxley)
Mending wall(Frost)
.
100 wordsGoods and services that are not sold in markets.docxvrickens
100 words
Goods and services that are not sold in markets, such as food produced and consumed at home and some household articles, are generally not included in GDP.
How might the absence of these values mislead one when comparing the economic well-being of the United States and India?
What other items are not included in GDP and how might their exclusion impact policy?
.
100 word responseChicago style citingLink to textbook httpbo.docxvrickens
100 word response
Chicago style citing
Link to textbook: http://books.google.com/books?id=zutRiJJMBQYC&printsec=frontcover#v=onepage&q&f=false
Article is attached
The overwhelming similarities between the articles are perception of identity through self-focus or self-identity through culture. Mulvaney tells us “truth is socially constructed through language and other symbol systems” (Mulvaney, 222). And as an example, it was just such self-focus that landed Galileo in jail by asserting that the universe was sun-centered as opposed to earth centered. The people of that time had socially constructed their own truths based on their perceptions of that time, although we now know that both were incorrect. It was from this perception of correctness that power was assumed and asserted by the majority, which in this case led to Galileo’s arrest (Mulvaney 2004).
Jandt touches on an interesting fact regarding existentialism, the idea of the “other” and the idea that both the observer and the observed are changed in the process. He states, “that the observer is not independent of the observed; the observed is in some sense “created” or changed or both by the act of observation” (Jandt, 212). It is from this dynamic that Jandt speaks of that we can see the formation of societal roles, i.e. the roles of those in positions of power and those in a subservient roles.
The interesting culmination of the information from all three articles is that the process is not a stagnant one, but rather one that can, and often times does change. Through introspective analysis, asking ourselves the question “Who am I?” we can embrace our cultural differences and through the acceptance of our individual qualities can take back some of the power that was perhaps lost (Jandt, 210). For example, take the labels “Feminist” and “Gay” along with “queer” and “Chicano,” which were certainly negative when created, have been transformed into positive labels embraced by those within each perspective community (Jandt 2004).
Works Cited
Jandt, Fred E., Dolores V. Tanno. "Decoding Domination, Encoding Self-Determination - Intercultural Comminication Research Process." In Intercultural Communication: A Global Reader, by Fred E. Jandt, 205 - 221. Thousand Oaks, CA: Sage Publications, Inc., 2004.
Mulvaney, Becky Michelle. "Gender Differences in Communication - An Intercultural Experience." In Intercultural Communication - A Global Reader, by Fred E. Jandt, 221 - 229. Thousand Oaks, CA: Sage Publications, Inc., 2004.
.
100 word response to the followingBoth perspectives that we rea.docxvrickens
100 word response to the following:
Both perspectives that we read referenced Hofstede’s work. Merrit and Helmreich focused closely on Hofstede’s principles of individualism and power distance. They studied how American flight crews differed in these areas from Asian flight crews. The American flight crews proved to have much more individualism than the Asian, although power distance perceptions were mixed between pilots and flight attendants, with the flight attendants perceiving more power distance than the pilots (in Jandt, 2004). Aldridge also focused on individualism and power distance, with regards to the American culture. It is Aldridge’s thesis that it is the idea of the “natural rights of man” that underpins American culture (in Jandt, 2004, p.94). The natural rights of man are a value that is espoused by a culture with high individuality and low power distance. If man has natural rights, then he is an independent being, and in order to value all men, we must have a lower perception of the distance between those of high status and those with lower status.
I enjoyed both perspectives. I felt that the aviation study was very strong, as they were careful to make sure that they accounted for cultural differences in their measurements. I agree with the authors that although they confirmed some sociological theories and demonstrated that flight crews tend to follow their cultural norms, the study is likely skewed. In order to understand how different flight crews behave from standard Asian social norms, the surveys would have to be done from an Asian perspective and even then, there is not just one Asian culture, so that should be taken into account. We likely miss many of the subtle differences between Asian flight crews and their home culture, by not having a sensitive test to that culture.
My main complaint about Aldridge’s perspective is a lack of strong comparison to other cultures. I felt that the argument that American culture is strong based on our belief in natural human rights would have been better served by showing more comparison to other cultures that also espouse this value and/or to cultures that clearly do not. The comparison to Nazi culture was a start, but one that gets kind of old after a while, and is not a culture that is as current as I would prefer in a comparison.
Readings:
Texbook: Jandt, Fred E. (editor) Intercultural Communication: A Global Reader. Thousand Oaks, CA: Sage. 2004
“Human Factors on the Flight Deck: The Influence of National Culture,” Merritt and Helmreich, Jandt pages 13-27
“What is the Basis of American Culture,” Aldridge, Jandt pages 84-98
100 word response to the following
The perspectives learned this week relate to the evolution of human beings and their ability to evolve and survive. As it was state in Aldridge’s readings human beings have the capability to communicate and this ability makes them superior, than animals. All human beings came from the same land and eventually with th.
100 word response to the followingThe point that Penetito is tr.docxvrickens
100 word response to the following:
The point that Penetito is trying to make is that it is important for indigenous cultures to survive. He uses the case of the education of the Maori in New Zealand as an example to exhibit the declining influence of the culture because of the influence of the more dominant British culture. Penetito strengthens his argument by referencing problems that come with colonization and the negative on natives, most notably, the educational system. By attacking this one issue and using facts about the culture to enrich the discussion helps to focus his message that cultures being dominated is a bad thing. The Maori educational system has been moulded to fit the mainstream framework rather than a Maori one (Jandt, 2004, p. 173) and this creates many of the problems and contributes to the extinction of culture. He could use other examples of how colonizing countries leads to the destruction of less important areas of indigiounous cultures such as dress, language, or food in order to strengthen his arguments about the educational systems. The lack of attention in the educational field is having lasting effects on Maoris living in New Zealand and any more information he could use to support this would be important to know. Also examples of educational systems in other colonized countries, to compare and contrast them to New Zealand's would also help to influence readers. He references a report done by the Ministry of Maori Development which states that, "disparities between Maori and non-Maori in a variety of economic sectors such as employment and income" (Jandt, 2004, p. 181). The Maori are just an example of one culture that is fighting for survival out of many. The problem is that through colonization, diversity dwindles. Penetito's writing is valid for all endangered languages because all cultures can use it as a template and useful knowledge for preserving their cultures before they are completely gone.
Textbook: Jandt, F. (2004). Intercultural Communication:A Global Reader. Thousand Oaks, CA: Sage Publications Inc.
---------------------------------------------------------------------------------------------------------------------------
100 word response to the following:
I would like to ask a provocative question, or two.
Given that all of the indigenous languages in the USA are on the brink of extinction, should there be federal funding to protect these languages and these cultures?
Along the same lines, what do you think of English-only initiatives? Do these aid or hurt American culture?
http://www.endangeredlanguages.com/
.
100 word response to the folowingMust use Chicago style citing an.docxvrickens
100 word response to the folowing:
Must use Chicago style citing and the textbook: Jandt, Fred E. (editor) Intercultural Communication: A Global Reader. Thousand Oaks, CA: Sage. 2004. Part I Cultural Values
Culture has many different meanings anywhere from historical perspectives to behavioral perspectives to different traditions that have been passed down from generations to generations.
Levi Strauss was interested in structuralism which he defined as “the search for unusual harmonies” (pg 1 Jandt). “There are many more human cultures than human races”, human cultures are counted by the thousands and human races are divided up by units.
The collaboration between cultures is trying to compare the old world with the new world. “No society is intrinsically cumulative. Cumulative history is the way of life of cultures and how they get a long together. All cultural contributions are divided into two groups; isolated acquisitions or features, the features are important but at the same time they are limited. The second group is systemized contributions which is how each society has chosen to express human aspirations. According to Strauss the true contribution of a culture is its difference from others.
Geert Hostede looks at business cultures and states that culture may be divided into four categories symbols, heroes, rituals and values. “Understanding people means understanding their background from which their present and future behavior can be predicted”. There are also four national cultural differences: 1.power distance-the population from equal to extremely unequal 2. Individualism -people have learned to act as individuals rather than in a group 3.masculinity- assertiveness or masculine values prevail over the feminine ones 4.uncertainty avoidance- people in a country prefer structured over unstructured situations.
References:
Jandt, E. Fred. Intercultural Communications. Thousand Oaks; Sage Publications. 2004. Print.
100 word response to the folowing:
Must use Chicago style citing and the textbook: Jandt, Fred E. (editor) Intercultural Communication: A Global Reader. Thousand Oaks, CA: Sage. 2004 Part I Cultural Values
Our culture is something that has been ingrained in us from an early age, and is largely unconscious. Levi-Strauss says that while certain biological traits were selected for us in the beginning of evolution, as soon as culture came into being, those biological traits were influenced by the dynamics of culture (Jandt, p. 6). Essentially, we are not able to separate ourselves from culture, and to do so would be to ruin what is wonderful and unique about each culture. According to Hofstede, all cultures have their processes, and their values. While things like symbols and rituals in a culture vary greatly, he says; “Values represent the deepest level of culture. (Jandt, p. 9)”
Because culture is deeply ingrained in us, all of the variants that Levi-Strauss and Hofstede discussed must be taken in account when dealing wit.
100 word response using textbook Getlein, Mark. Living with Art, 9t.docxvrickens
100 word response using textbook: Getlein, Mark. Living with Art, 9th Ed., New York: McGraw-Hill, 2010. Citing in MLA Format:
Between the Baroque and Rococo era, according to Getlein in Living with Art 2010, Rococo is a development and extension of the baroque style. Rococo is not only a play on the word baroque, but also French for rocks and shells. Rococo is known for its ornate style and several points of contrast. Baroque on the other hand was an art of cathedrals and palaces (Getlein p. 397). The Mirror Room of the Amailienburg in Nymphenburg is a great example of the Rococo style of art with its gentle pastels, overall intimacy, multiple mirrors and its illusion of the sky and with that baroque is large in scale and rococo is lighter. According to Getlein p. 398, Rococo architecture first originated in France but was soon exported, some examples of this type of art are found in Germany. Hall of mirrors on page 392 by Charles Le Brun is an example of baroque art, it is a more intense piece of work that is more vibrant and energetic vice the lighter decoration s used in The Mirror Room.
100 word response using textbook: Getlein, Mark. Living with Art, 9th Ed., New York: McGraw-Hill, 2010. Citing in MLA Format:
The Renaissance covered the period from 1400 to 1600, which brought numerous changes that included new techniques in art, the way art was viewed, and how people viewed themselves. The term renaissance means "rebirth" and it refers to the renewal of interest in Roman and Greek cultures. During the period scholars who called themselves humanists believed in the pursuit of knowledge and striving to reach their full creative and intellectual potential. This new way of thinking had many impacts for art during this period. Artists became interested in observing the natural world and studied new techniques on how to accurately depict it. Various techniques were developed such as the effect of light known as chiaroscuro; noting that distant objects appeared smaller than nearer ones they developed linear perspective; seeing how detail and colored blurred with distance, they developed atmospheric perspective. (Getlein page 361) The nude also reappeared in art, for the body was one of God's most noble creations; an example of this can be seen in figure 16.8 the statue of David, by the artist Michelangelo. (Getlein page 368) The primary difference between the Renaissance and the prior period of time was that artists were no longer viewed craftsmen, they were now recognized as intellectuals. (Getlein page 362)
The Northern Renaissance developed more gradually than in Italy. Northern artists did not live among the ruins of Rome nor did they share the Italians’ sense of a personal link to the creators of the Classical past; thus affecting the focus and characteristics between the two cultures. (Getlein page 374) Renaissance artists in northern Europe focused more on small details of the visible world, such as decoration or the outer appearanc.
100 word response to the following. Must cite properly in MLA.Un.docxvrickens
100 word response to the following. Must cite properly in MLA.
Unlike the Egyptian culture that created statues of themselves as gods and pharaohs. Muslims did not worship false idols or statues so no pictures or statues or gods are present in their mosques. According to Geitlein (2010), “The Qur’an contains a stern warning against the worship of idols, and in time this led to a doctrine forbidding images of animate beings in religious contexts” (p. 410). Instead the Muslims of the Islam culture used geometry and plants to design buildings, like the Egyptian pyramids, Muslims built beautiful mosques with grand designs. Islam became a world religion, like Christians, they needed a place of worship and prayer. They also used fine textiles, sun dried brick, and ceramics to create their designs. An example would be the popular Cordoba mosque of Spain. A lot of mosques use the arch and dome technique like that of the Romans and Byzantine architecture. Arabic script also became popular and appeared inside the mosque temples. Islam used calligraphy as art and to illustrate writing. Egyptians were also big on scripting but theirs was called hieroglyphics, which not only had letters, but pictures were a big part of their writing system as well. The Egyptians didn’t technically worship false idols at all times, at some times they had statues created of themselves but there wasn’t really a religion in Egypt until the one god religion began there. Egypt gave you a visual of the life and world of Egypt, Islam leaves it more up to the imagination with no pictures of what any of the past history looked like.
References
Getlein, Mark. Living With Art. 9th ed. New York: McGraw-Hill, 2010. Print.
100 word response to the following. Must cite properly in MLA:
Realism was a mid to late 19th century movement in which artist should represent the world at it is regardless of artistic and social understandings. Realist were seeking to free art from social regulation and depicting how society shapes the lives of people (Little, page 80).
In his Fur Traders Descending the Missouri, American-born George Caleb Bingham a self taught artist and the first major painter to live and work west of the Mississippi River illustrates the realism of life for a French trapper and his son on the Missouri River hunting from a dugout canoe. The painting is simple to understand, it represents the calmness of a time to me when life was simple.
Abstract Expressionism was a movement that got its start following World War TWO. Developed in New York and often referred to as the New York School or Action Painting it is characterized to depict universal emotions. Additionally this was the first American movement to gain international recognition (Little, page 122).
Jackson Pollock’s perfected Abstract Expressionism through his “drip technique”, a technique in which you apply paint to a canvas on the floor indirectly from a brush. Pollock the youngest of five boys in a family that moved a.
100 original, rubric, word count and required readings must be incl.docxvrickens
100% original, rubric, word count and required readings must be included
This is 3 assignments in one. The final is all the assignments from M1A2- M5A2
The assignments are highlighted in yellow and the rubics are in red and attached for M3A2 and M5A2
Assignment 2: LASA 1—Preliminary Strategy Audit
The end result of this course is developing a strategy audit. In this module, you will outline and draft a preliminary framework for your final product. This provides you with the opportunity to get feedback before a final submission.
In
Module 1
, you reviewed the instructions for the capstone strategy audit assignment and grading rubric due in
Module 5
. By now, you have completed the following steps:
Identified the organization for your report
Interviewed at least one key mid-level or senior-level manager
Created a market position analysis
Conducted an external environmental scan in preparation of your final report and presentation
In this assignment, you will generate a preliminary strategy audit in preparation for your final course project.
Prepare a report that includes the following:
In preparation for your course project, prepare the preliminary strategy audit using the tools and framework you have focused on so far including the following:
Analysis of the company value proposition, market position, and competitive advantage
External environmental scan/five forces analysis
Identify the most important (5–7) strategic issues facing the organization or business unit.
You may modify the strategic issues in your final report based on the additional analysis you will conduct in the next module as well as the feedback you receive on this paper from your instructor.
Keep in mind that it is important to look at the strategic issue(s) from more than just one perspective in the business unit or company—speak to or research the issue from more than one angle to offer a 360-degree approach that does not cause more problems or issues.
Strategic issues arise from a mismatch between internal capabilities and external trends such that important opportunities are not being pursued or significant external threats are not being addressed under the current strategy.
Include a preliminary set of recommended tactics for improving your company’s strategic alignment and operating performance.
You may modify these recommendations in your final report based on the additional analysis you will conduct in the next module as well as the feedback you receive on this paper from your instructor.
Keep in mind that recommendations can include, but are not limited to, tactics in marketing, branding, alliances, mergers and acquisitions, integration, product development, diversification or divestiture, and globalization. If you recommend your company to go global, you must include a supply chain analysis and an analysis of your firm’s global capabilities.
Write your report as though you are a consultant to your company and are addressing the executive officers of this comp.
100 or more wordsFor this Discussion imagine that you are speaki.docxvrickens
100 or more words
For this Discussion imagine that you are speaking to a group of parents or early childcare professionals. Identify the characteristics of the group so that your readers know who is being addressed. Explain to the group why play is so important to children, including:
How and what children learn through play
Give examples of how they can encourage and support play for children
.
10. (TCOs 1 and 10) Apple, Inc. a cash basis S corporation in Or.docxvrickens
10.
(TCOs 1 and 10) Apple, Inc. a cash basis S corporation in Orange, Texas, formerly was a C corporation. Apple has the following assets and liabilities on January 1, 2010, the date the S election is made:
Adjusted Basis
Fair Market Value
Cash
$200,000
$200,000
Accounts receivable
-0-
$105,000
Equipment
$110,000
$100,000
Land
$1,800,000
$2,500,000
Accounts payable
-0-
$110,000
During 2010, Apple collects the accounts receivable and pays the accounts payable. The land is sold for $3 million, and taxable income for the year is $590,000. What is Apple's built-in gains tax?
(Points : 5)
.
10-12 slides with Notes APA Style ReferecesThe prosecutor is getti.docxvrickens
10-12 slides with Notes APA Style Refereces
The prosecutor is getting feedback from local law enforcement officers explaining that they are discouraged from making arrests in cases of domestic violence and child abuse. They claim that they have been either not making arrests in domestic violence situations or arresting both parties when they go out on a call. It seems that abused women often go back to the abusers, and children who get removed from the homes where they have been abused often return after removal. These occurrences have been especially demoralizing to law enforcement.
One of your jobs in working as a victim witness assistant is to help educate law enforcement on the nature and behaviors involved in domestic violence and child abuse. The prosecutor’s office has decided that you should present each of these topics for the next training session:
Topic 1: Domestic violence:
Your goal is to educate law enforcement to use best practices in the investigation of domestic abuse cases. Include the following topics:
How to approach a domestic violence situation when responding to an emergency call
when the parties should be separated
how to interview parties
what information needs to be in the report and why
how best to help a victim
what laws protect victims, including the use of protection orders
why victims return to abusers
length of time it may take to stay away from their abusers
Arrests
the legal standard needed to make an arrest in a domestic violence case
What evidence should be collected at the arrest?
Are dual arrests effective law enforcement?
how to assist domestic violence victims
reluctant victims
help for victims
Topic 2: Child Abuse:
Your goal will be to educate law enforcement about the dynamics of abuse and neglect cases. Include the following topics:
signs of child abuse and categories (physical, sexual, emotional)
difference between abuse and neglect
legal description of neglect
use of guardian
ad litems
the legal standards that must be met in removal from the home
termination of parental rights
requirements of Indian Child Welfare Act (ICWA)
role of court-appointed special advocates (CASA) in child abuse and neglect cases
role of social services in abuse and neglect cases
For more information on creating PowerPoint Presentations, please visit the Microsoft Office Applications Lab.
.
10-12 page paer onDiscuss the advantages and problems with trailer.docxvrickens
10-12 page paer on
Discuss the advantages and problems with trailers for temporary housing, the issues for FEMA, and recommendations for improvements to the housing program. Discuss how Public Assistance was used in New York for Hurricane Sandy recovery, and why this was so different than previous housing policies.
.
10. Assume that you are responsible for decontaminating materials in.docxvrickens
10. Assume that you are responsible for decontaminating materials in a large hospital.
How would you sterilize each of the following? Briefly justify your answers.
a. A mattress used by a patient with bubonic plague
b. Intravenous glucose-saline solutions
c. Used disposable syringe
d. Tissues taken from patients
.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Delivering Micro-Credentials in Technical and Vocational Education and TrainingAG2 Design
Explore how micro-credentials are transforming Technical and Vocational Education and Training (TVET) with this comprehensive slide deck. Discover what micro-credentials are, their importance in TVET, the advantages they offer, and the insights from industry experts. Additionally, learn about the top software applications available for creating and managing micro-credentials. This presentation also includes valuable resources and a discussion on the future of these specialised certifications.
For more detailed information on delivering micro-credentials in TVET, visit this https://tvettrainer.com/delivering-micro-credentials-in-tvet/
2. capable of generating nonlinear decision boundaries.
The kernel version of the linear spectral matched filter is
implemented and simulation results on hyperspectral
imagery show that the kernel spectral matched filter
outperforms the conventional linear matched filter.
Keywords: Matched filter· hyperspectral· kernel· nonlinear
detection· target detection
1. Introduction
Target detection using linear matched filtering is a well-
known approach in detecting objects of interest in hy-
perspectral imagery (Manolakis et al., 2000; Robey et
al., 1992; Kraut and Scharf, 1999; Kraut et al., 2001;
Chang, 2003; Van Veen and Buckley, 1988; Johnson
and Dudgeon, 1993; Capon, 1969). Typically, the tar-
get spectral signature is obtained from a spectral library
or from a set of training data, which is used in con-
junction with the correlation (covariance) matrix of the
data as the spectral matched filter. However, the linear
spectral matched filter detector (MFD) does not ex-
ploit the higher order statistical correlations between
the spectral bands since it is based only on the sec-
ond order statistics. Therefore, its performance is not
optimal for non-Gaussian data. Furthermore, the deci-
sion boundaries obtained by the conventional MFD is
linear, which is not optimal for non-Gaussian data. The
motivation behind designing the nonlinear matched fil-
ter is to obtain nonlinear decision boundaries as well
as exploiting the higher order statistical correlation be-
tween the spectral bands for non-Gaussian data in order
to improve the performance of the conventional linear
matched filter. Spectral MFDs are based on the assump-
tion of a linear model where the spectral signature of
3. the target and the background covariance matrix are as-
sumed to be known. A nonlinear spectral matched filter
can easily be developed by defining a matched filter like
model in a feature space of high dimensionality. How-
ever, to implement such a nonlinear matched filter in
the feature space may not be computationally tractable
due to the high dimensionality of the feature space.
Recently, using the ideas of kernel-based learning
theory it has been shown in Müller et al. (2001),
Schölkopf et al. (1999), Ruiz and Lopez-de Teruel
128 Kwon and Nasrabadi
(2001), Kwon and Nasrabadi (2004), Baudat and
Anouar (2000), Kwon and Nasrabadi (2005) that a
number of linear algorithms can easily be extended
to nonlinear versions by implementing them in terms
of kernel functions, thus avoiding the implementation
of the algorithm in the feature space. The input data
is in fact implicitly mapped into a kernel feature space
where the algorithm is then implemented in terms of
certain kernels such as the Mercer kernels (Schölkopf
and Smola, 2002).
In this paper, we introduce a kernel-based spectral
matched filter in the feature space and drive an expres-
sion for its kernel version. We define a matched filter
in a kernel feature space, which is equivalent to a non-
linear matched filter in the original input space. The
matched filter problem is first formulated in a particu-
lar kernel feature space, which is implicitly generated
by a nonlinear mapping associated with a kernel func-
tion. The matched filter expression derived in that fea-
4. ture space is then rewritten in terms of the vector dot
products form and by using the so called kernel trick,
see (12) in Section 2.2, it is converted in terms of the
kernel function. We refer to this process as kernelizing
the expression for the nonlinear matched filter and the
resulting matched filter is called the kernel-based spec-
tral matched filter detector (KMFD). Using the kernel
trick idea we avoid implementing the algorithm in the
high dimensional feature space. Furthermore, we do not
need to know the explicit expression for the nonlinear
map that produced the kernel feature space. However,
an appropriate kernel function with dot product prop-
erty (Mercer kernel) needs to be selected, which has
a particular nonlinear mapping associated with it that
models the data implicitly in the kernel feature space.
This paper is organized as follows. Section 2 intro-
duces the linear matched filter and the idea of kernel
trick when using Mercer kernels. In Section 3 the non-
linear matched filter is described, which is reformu-
lated in terms of the kernel function to obtain the ker-
nel matched filter. Performance of the kernel matched
filter on hyperspectral imagery is provided in Section
4 and conclusions are given in Section 5.
2. Preliminaries: Linear Matched Filter,
Introduction to Kernel Feature Space and
Kernel Trick
2.1. Linear Matched Filter
In this section, we introduce the concept of linear spec-
tral matched filter. The constrained least squares ap-
proach is used to derive the linear matched filter. Let the
input spectral signal x be x = [x (1), x (2), . . . , x ( J )]T
5. consisting of J spectral bands. We can model each
spectral observation as a linear combination of the tar-
get spectral signature and noise
x = as + n, (1)
where a is an attenuation constant (target abundance
measure). When a = 0 no target is present and
when a > 0 target is present, vector s = [s(1),
s(2), . . . , s( J )]T contains the spectral signature of the
target and vector n contains the additive background
clutter noise.
We can design a linear matched filter w = [w(1),
w(2), . . . , w( J )]T such that the desired target sig-
nal s is passed through while the average filter out-
put energy is minimized. Define X to be a J ×
N matrix of the N reference pixels obtained from
the test input image. Let each observation spectral
pixel to be represented as a column in the sample
matrix X
X = [x1 x2 · · · xN ]. (2)
The output of the filter for the input xi is given by
y(xi ) = wT xi = xTi w. (3)
The average output power of the filter for the reference
data X is given by
1
N
N∑
6. i =1
y(xi )
2 = wT
(
1
N
N∑
i =1
xi x
T
i
)
w = wT R
̂ w, (4)
where the R
̂ is the estimated correlation matrix of the
reference data. This constrained filter design is equiv-
alent to a constrained least squares minimization prob-
lem, as was shown in Scharf (1991), Van Veen and
Buckley (1988), Harsanyi (1993), Chang (2003), which
is given by
min
w
{wT R
̂ w} subject to sT w = 1 (5)
where minimization of minw{wT R
̂ w} ensures the back-
ground clutter noise is suppressed by the filter w and
the constrain condition sT w = 1 makes sure that the
filter gives an output of unity when a target is detected.
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Kernel Spectral Matched Filter for Hyperspectral Imagery 129
The solution to this quadratic minimization problem is
given by
w = R
̂
−1s
sT R
̂ −1s
(6)
where correlation matrix R
̂ is usually estimated
from the input image. The expression (6) is referred
to as the minimum variance distortionless response
(MVDR) beamformer in the array processing litera-
ture (Van Veen and Buckley, 1988; Johnson and Dud-
geon, 1993). More recently, the same expression was
derived in the hyperspectral target detection literature
and was called the constrained energy minimization
(CEM) filter or the spectral correlation-based matched
filter (Harsanyi, 1993; Chang, 2003). The output of the
linear correlation-based matched filter for a test input
r, given the estimated correlation matrix, is given by
y(r) = wT r = s
T R
̂ −1r
8. sT R
̂ −1s
. (7)
If the mean of the observation data is removed (cen-
tered) a similar expression is obtained for the centered
data which is given by
yr = wT r =
sT Ĉ−1r
sT Ĉ−1s
(8)
where Ĉ represents the estimated covariance matrix
for the centered reference image data. In the above
derivation of the correlation-based matched filter no
assumption was made about the distribution of the ad-
ditive noise n in the linear model (1). However, if n
is assumed to be a Gaussian random noise distributed
as N (0, C), it has been shown in Robey et al. (1992)
and Kraut and Scharf (1999) that using the Generalized
Likelihood Ratio Test (GLRT) a similar expression to
(8), as in MVDR or CEM, can be obtained for the es-
timated abundance measure â given by
â = s
T C−1r
sT C−1s
. (9)
It should be noted that C is now the expected covari-
ance matrix of the background noise only and does not
include any target data. When the estimated covari-
ance matrix Ĉ of the background data is used in (9)
this filter is referred to as the adaptive matched filter
9. (Robey et al., 1992) in the signal processing literature
or Capon method (Capon, 1969) in the array processing
literature. In Robey et al. (1992) it was shown that the
CFAR behavior of this filter is given by
α(r) = |s
T Ĉ−1r|2
sT Ĉ−1s
(10)
which is proportional to the estimated squared magni-
tude of the output matched filter referred in Kraut et al.
(2001) as the signal-to-noise ratio (SNR).
In this paper, we only present the experimental re-
sults for the linear correlation-based matched filter
given by the expression (7). Similar results are obtained
by using (8) for the centered data.
2.2. Kernel Feature Space and Kernel Trick
In this subsection an introduction to kernel feature
map and kernel learning is provided, which is used
in the next section to convert a nonlinear version of
the matched filter into its corresponding kernel format.
Suppose the input hyperspectral data is represented by
the data space (X ⊆ RJ ) and F be a nonlinear fea-
ture space associated with X by a nonlinear mapping
function φ
φ : X → F,
x �→ φ(x), (11)
where x is an input vector in X , which is mapped into
10. a potentially much higher dimensional feature space.
Any linear algorithm can be remodeled in this high
dimensional feature space by replacing the original in-
put data x with the mapped data φ(x). Implementing
any linear algorithm (e.g., matched filter) in the feature
space is equivalent to performing a nonlinear version
of that algorithm (i.e., nonlinear matched filter) in the
original data space. Due to the high dimensionality of
the feature space F it is computationally not feasible to
implement the algorithm in the feature space. However,
in the kernel-based learning algorithms the task is first
formulated in terms of dot products in the feature space
and then the kernel trick (12) is used to implement the
dot products in terms of kernel functions (Schölkopf
and Smola, 2002). The kernel representation for the dot
products in F (known as the kernel trick) is expressed
as
k(xi , x j ) = 〈φ(xi ), φ(x j )〉
= φ(xi ) · φ(x j ), (12)
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130 Kwon and Nasrabadi
where k is a positive definite kernel, such as a Mercer
kernel (Schölkopf and Smola, 2002).
Using this kernel trick allows us to implicitly com-
pute the dot products in F without mapping the input
vectors into F; therefore, in the kernel-based learn-
ing methods, the mapping φ does not need to be iden-
tified. However, an appropriate kernel has to be de-
fined, which has a nonlinear mapping associated with
it. Equation (12) shows that the dot products in F can
be avoided and replaced with a kernel, which can be
easily calculated without identifying the nonlinear map
φ. Experimental results for three different kernels are
reported in this paper. The three kernels are
(i) the Gaussian Radial Bases Function kernel (RBF
kernel): k(x, y) = exp( −‖x−y‖2
c
),
(ii) spectral angle-based kernel: k(x, y) = x·y‖x‖‖y‖ , and
(iii) polynomial kernel: k(x, y) = ((x · y) + θ )d
where c represents the width of the Gaussian RBF ker-
nel, d is a positive integer, and θ ≥ 0 is a constant. See
Schölkopf and Smola (2002) for more detailed infor-
mation about the properties of kernels and kernel-based
learning theory.
13. 3. Nonlinear Matched Filter and Kernel
Matched Filter
In this section, we show how to formulate a kernel
version of the linear matched filter. This is achieved by
modeling the data in a kernel feature space where the
corresponding linear matched filter in the feature space
is equivalent to a nonlinear matched filter in the input
space. We then show how to implement the nonlinear
matched filter in terms of the kernel function.
3.1. Introduction to Nonlinear Matched Filter
Consider a linear model of the input data in a kernel
feature space given by
φ(x) = aφ φ(s) + nφ , (13)
where φ is a nonlinear mapping associated with a ker-
nel function, aφ is an attenuation constant (target abun-
dance measure), the high dimensional vector φ(s) con-
tains the spectral signature of the target in the feature
space, and vector nφ contains the additive noise in the
feature space. The above linear model (13) in the fea-
ture space is not the same as the nonlinearly mapped
version of the additive model given in (1). However,
this linear model in the feature space is equivalent to a
specific nonlinear model in the input space. Therefore,
defining a matched filter using the linear model (13) is
the same as developing a nonlinear matched filter for a
specific nonlinear model in the input space.
Using the constrained least squares approach that
was explained in the previous section it can easily be
shown that the equivalent correlation-based matched
14. filter wφ in the feature space is given by
wφ =
R
̂ −1φ φ(s)
φ(s)T R
̂ −1φ φ(s)
, (14)
where R
̂ φ is the estimated correlation of pixels in the
feature space. The estimated correlation matrix is given
by
R
̂ φ =
1
N
Xφ Xφ
T (15)
where Xφ = [φ(x1) φ(x2) . . . φ(xN )] is a matrix
whose columns are the mapped input reference data
in the feature space. The matched filter in the feature
space (14) is equivalent to a nonlinear matched filter in
the input space and its output for the input φ(r) is given
by
y(φ(r)) = wTφ φ(r) =
φ(s)T R
̂ −1φ φ(r)
φ(s)T R
̂ −1φ φ(s)
. (16)
Due to the high dimensionality of the feature space
the expression (16) is not tractable. Therefore, we can-
not directly implement it in the feature space. We need
15. to first convert this expression in terms of the dot prod-
ucts of the input vectors in the feature space. The kernel
trick is then used to convert the dot products in the fea-
ture space in terms of the kernel functions.
3.2. Kernel Matched Filter
In this subsection, we show how to kernelize the
matched filter in the feature space. The estimated back-
ground correlation matrix can be represented by its
eigenvalue decomposition or so called spectral decom-
position (Strang, 1986) given by
R
̂ φ = Vφ �Vφ T , (17)
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Kernel Spectral Matched Filter for Hyperspectral Imagery 131
Figure 1. Two-dimensional toy data sets: (a) A Gaussian
mixture and (b) nonlinearly mapped data.
Figure 2. Contour and surface plots of MSD and KMSD: (a)
MFD on the data shown in Fig. 1(a), (b) KMFD on the data
shown in Fig. 1(a),
(c) MFD on the data shown in Figs. 1(b) and (d) KMFD on the
data shown in Fig. 1(b).
where � is a diagonal matrix consisting of the nonzero
eigenvalues of R
̂ φ and Vφ is a matrix whose columns
are the eigenvectors of R
̂ φ in the feature space. The
eigenvector matrix is represented by
Vφ = [v1φ v2φ · · · vNφ ], (18)
where N is the maximum number of eigenvectors with
nonzero eigenvalue.
The sample correlation (covariance) matrix in the
feature space is rank deficient because the number of
samples are usually much less than the dimensional-
ity of the feature space. Therefore, the inverse of R
̂ φ
cannot be obtained and we have to resort to the pseudo-
inverse of the sample correlation matrix, which is the
minimum length least squares solution for the inverse
sample correlation matrix (see p. 450 in Strang, 1986).
The pseudo-inverse of the estimated background cor-
17. relation matrix can be written in terms of its eigen-
value decomposition or singular value decomposition
(Strang, 1986) as
R
̂ #φ = Vφ �−1Vφ T . (19)
Furthermore, the diagonal matrix �−1 can be replaced
with a truncated version of �−1 by only including
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132 Kwon and Nasrabadi
Figure 3. Sample band images (48th) from the HYDICE and
mine images. (a) Desert Radiance II image, (b) Forest Radiance
I image and (c)
mine image.
the eigenvalues that are above a small threshold in
order to obtain what is called the effective rank of
the matrix (see p. 445 in Strang, 1986). Truncation
18. of the diagonal matrix �−1 will numerically provide
a more stable pseudo-inverse since, due to round-off
errors, it is not easy to identify the true non-zero
eigenvalues.
Each eigenvector v
j
φ in the feature space, as shown
in Schölkopf et al. (1999), can be expressed as a linear
combination of the input reference vectors in the feature
space given by
v
j
φ =
N∑
i =1
λ j
−1/2
β
j
i φ(xi ) = Xφβ j λ j −1/2, (20)
where the expansion coefficient vectors β j =
(β
j
1 , β
j
2 , . . . , β
19. j
N )
T , for j = 1, . . . , N1, N1 ≤ N , are
the eigenvectors with nonzero eigenvalues of the ker-
nel (Gram) matrix K(X, X) as shown in Appendix I,
K(X, X) = (K)i j is an N × N matrix whose entries
are the dot products k(xi , x j ) =< φ(xi ), φ(x j ) > for
xi , x j ∈ X; and λ j , j = 1, . . . , N1, N1 ≤ N are the
corresponding nonzero eigenvalues associated with the
eigenvectors. For all the eigenvectors Vφ in the feature
space we have
Vφ = XφB�−1/2, (21)
where B = [β1 β2 . . . β N1 ]. Substituting (21) into
(19) yields
R
̂ #φ = XφB�−2BT XTφ . (22)
Inserting Eq. (22) into (16) it can be rewritten as
y(φ(r)) =
φ(s)T XφB�−2BT XTφ φ(r)
φ(s)T XφB�−2BT XTφ φ(s)
. (23)
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21. Kernel Spectral Matched Filter for Hyperspectral Imagery 133
Figure 4. Examples of spectral curves from various regions in
the Forest Radiance I image: (a) tree, (b) grass, (c) shadow, and
(d) target regions.
In general, the spectral curves show a wide range of spectral
variability. Especially, the target spectral curves are remarkably
different in a local
region.
The dot product term φ(s)T Xφ in the feature space can
be represented in terms of the kernel function, which is
referred to as its empirical kernel map (Schölkopf and
Smola, 2002)
φ(s)T Xφ = (k(x1, s), k(x2, s), . . . , k(xN , s))
= kT (X, s) = kTs . (24)
Similarly ,
φ(r)T Xφ = (k(x1, r), k(x2, r), . . . , k(xN , r))
= kT (X, r) = kTr . (25)
Also using the properties of the Kernel Principal Com-
ponent Analysis (PCA) as shown in Appendix I, we
have the relationship
K−2 = 1
N 2
B�−2BT . (26)
Substituting (24), (25), and (26) into (23) the kernelized
22. version of the matched filter is given by
y(kr) =
k(X, s)T K−2k(X, r)
k(X, s)T K−2k(X, s)
= k
T
s K
−2kr
kTs K
−2ks
, (27)
which can now be implemented with no knowledge of
the mapping function φ. The only requirement is a good
choice for the kernel function k.
In the expression (27) the inverse K−2 may not be
numerically stable if the background spectral samples
are not independent. Therefore, the pseudo-inverse of
K is used, which is based on eigenvalue decomposition
in (42) where eigenvectors with non-zero eigenvalues
are used. In the experimental section, expression (42) is
used to obtain the pseudo-inverse of K where only the
eigenvectors with eigenvalues above a small threshold
are kept. A similar procedure has been used in Ruiz
and Lopez-de Teruel (2001) to obtain a stable pseudo-
inverse of the Gram matrix by discarding the lowest
eigenvalues that are below 10−5. The number of eigen-
vectors that are kept will determine the effective rank
of the matrix K.
In the derivation of the correlation-based kernel
23. matched filter we assumed that the data was not cen-
tered in the feature space. To obtain covariance-based
kernel matched filter, expression (8), we need to cen-
ter the data by removing the sample mean in the
feature space. However, removing the sample mean
is not computationally tractable in the feature space
due to the high dimensionality of F. Therefore, the
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134 Kwon and Nasrabadi
Figure 5. Examples of spectral curves from various regions in
the Desert Radiance II image: (a) vegetation, (b) dirt road, (c)
soil, and (d) target
regions. The target spectral curves are also characterized by a
wide range of spectral variability.
kernel matrix K needs to be properly centered, as shown
in Schölkopf and Smola (2002). The effect of center-
ing on the kernel matched filter can be incorporated by
25. replacing the uncentered Xφ with the centered Xφ −μφ
(where μφ = 1N
∑N
i =1 φ(xi ) is the mean of the refer-
ence input data) in the estimation of the centered cor-
relation (covariance) matrix expression (15) as well as
(24) and (25) for the empirical kernel mappings of the
target and input data, respectively. The resulting cen-
tered K
̂ is shown in Schölkopf and Smola (2002) to be
given by
K
̂ = (K − 1N K − K1N + 1N K1N ), (28)
where the elements of the N × N matrix (1N )i j = 1/N .
The properly centered kernel matched filter output for
(27) corresponding to the kernel version of (8) is now
given by
y(k̂ r) =
k̂ Ts K
̂
−2k̂ r
k̂ Ts K
̂
−2k̂ s
, (29)
where k̂ Ts = kTs − 1N
∑N
i =1 k(xi , s)�1 and k̂ Tr = kTr −
1
N
26. ∑N
i =1 k(xi , r)�1, which are obtained by replacing Xφ
with Xφ − μφ in (24), and (25), respectively. The col-
umn vector �1 denotes an N-dimensional vector with all
its components equal to 1.
Furthermore, the CFAR behavior of the kernel
matched filter (29) is given by
α(k̂ r) =
|k̂ Ts K
̂ −2k̂ r|2
k̂ Ts K
̂
−2k̂ s
. (30)
4. Simulation Results
In this section, we implemented both the proposed
KMFD described by (27) and the conventional MFD
described by (10) on simulated data as well as real
hyperspectral imagery. We implemented KMFD with
three kernel functions, each kernel function being as-
sociated with a different feature space. The three dif-
ferent kernels used were (i) the Gaussian RBF kernel,
exp(
−‖x−y‖2
30
), (ii) spectral angle-based kernel,
x·y
27. ‖x‖‖y‖ ,
and (iii) 5th order polynomial kernel, ((x · y) + 1)5.
The simulated data consists of two illustrative two-
dimensional toy data sets; a Gaussian mixture, as
shown in Fig. 1(a), and a nonlinearly mapped data
shown in Fig. 1(b). In Fig. 1 data points for the desired
target were represented by the star-shaped symbol and
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Kernel Spectral Matched Filter for Hyperspectral Imagery 135
Figure 6. Detection results for the Desert Radiance II image
using the kernel matched filter detectors (KMFD) and the
matched filter detector
(MFD): (a) KMFD with the Gaussian RBF kernel, (b) KMFD
with the polynomial kernel, (c) KMFD with the spectral angle-
based kernel, and
(d) MFD in the original input domain.
the background points were represented by the circles.
In Fig. 1(b) the two-dimensional data points x = (x , y)
for each class was obtained by nonlinearly mapping the
original Gaussian mixture data points x0 = (x0, y0) in
Fig. 1(a). All the data points in Fig. 1(a) were nonlin-
early mapped by x = (x , y) = (x0, x 20 + y0), therefore,
the second component of each data point is nonlinearly
28. related to its first component.
Figure 2 shows contour and surface plots of the con-
ventional MFD and KMFD on the toy data sets as
shown in Fig. 1. For both data sets, the contours gen-
erated by KMFD are highly nonlinear and naturally
follow the dispersion of the data, thus successfully sep-
arating the two classes, as opposed to the linear con-
tours obtained by MSD. For both the Gaussian mixture
and nonlinearly mapped data, KMFD clearly provided
significantly improved discrimination over the conven-
tional MFD.
The real hyperspectral images are from a HY-
DICE (HYperspectral Digital Imagery Collection
136 Kwon and Nasrabadi
Figure 7. Detection results for the Forest Radiance I image
using the kernel matched filter detectors (KMFDs) and the
matched filter detector
(MFD): (a) KMFD with the Gaussian RBF kernel, (b) KMFD
with the polynomial kernel, (c) KMFD with the spectral angle-
based kernel and
(d) MFD in the original input domain.
Experiment) sensor and a mine detection sensor. The
HYDICE imaging sensor generates 210 bands across
the whole spectral range (0.4–2.5 μm). But we only
use 150 bands by discarding water absorption and low
SNR bands; the spectral bands used are the 23rd–
101st, 109th–136th, and 152nd–194th. The hyperspec-
29. tral mine image consists of 70 bands over the spectral
range of 8–11.5 μm which includes the long-wave in-
frared (LWIR) band. Two HYDICE images from the
Desert Radiance II data collection and the Forest Ra-
diance I data collection, and the mine image were used
to test both the kernel-based and conventional matched
filter detectors. The Desert Radiance II (DR-II) image
contains 6 military targets located in the dirt road; the
Forest Radiance I (FR-I) image includes total of 14
military targets along the tree line; and the hyperspec-
tral mine image contains a total of 33 surface mines,
as shown in the sample band images in Fig. 3. While
spectral curves from various regions of different mate-
rials (or terrain types) show somewhat different spectral
Kernel Spectral Matched Filter for Hyperspectral Imagery 137
Figure 8. Detection results for the mine image using the kernel
matched filter detectors (KMFDs) and the matched filter
detector (MFD): (a)
KMFD with the Gaussian RBF kernel, (b) KMFD with the
polynomial kernel kernel, (c) KMFD with the spectral angle-
based kernel kernel and
(d) MFD in the original input domain.
characteristics, even in a local region of the same ma-
terial types they show a wide range of spectral variabil-
ity (especially for targets and vegetation), thus making
target detection a challenging task, as shown in Figs. 4
and 5.
All the pixel vectors in a test image are first normal-
30. ized by a constant, which is a maximum value obtained
from all the spectral components of the spectral vec-
tors in the corresponding test image, so that the entries
of the normalized pixel vectors fit into the interval of
spectral values between zero and one. The rescaling of
pixel vectors was mainly performed to effectively uti-
lize the dynamic range of Gaussian RBF kernel. The
rescaling does not affect the performance of KMFDs
or MFD when the other two kernel functions are used.
4.1. Algorithm Implementation
Background statistics—the kernel matrix K
̂ and the
correlation matrix R
̂ —are globally estimated for the
kernel-based and conventional implementation of the
138 Kwon and Nasrabadi
Figure 9. ROC curves obtained from the detection results for the
Desert Radiance II image shown in Fig. 6.
Figure 10. ROC curves obtained from the detection results for
the Forest Radiance I image shown in Fig. 7.
matched filter detectors, respectively. Global estima-
tion must be performed prior to detection and normally
needs a large amount of data samples to successfully
represent all the background types present in a given
data set. In this paper, we use a large number of spectral
vectors obtained from a given test image that best rep-
resent the spectral characteristics of the background. A
well-known data clustering algorithm, k-means (Jain
31. et al., 1999), is used on the spectral vectors in order to
generate a significantly less number of spectral vectors
Kernel Spectral Matched Filter for Hyperspectral Imagery 139
Figure 11. ROC curves obtained from the detection results for
the mine image shown in Fig. 8.
(centroids) from which appropriate background statis-
tics are estimated. The number of the representative
spectral vectors obtained from the k-means procedure
was set to 300 in the experiment. The correlation and
kernel matrices were obtained from these 300 spectral
vectors. In all the experiments the same target spectral
signature s is obtained by averaging the target samples
collected from one of the targets in the test image. For
both the DR-II and FR-I images it is the left most target.
Since a relatively small set of the background sam-
ples was used to represent the background statistics of
the given test images, the kernel matrix K
̂ and the cor-
relation matrix R
̂ need to be regularized in order to
obtain a numerically stable pseudo-inverse. In this pa-
per, in order to regularize both K
̂ and R
̂ the eigenvalues
decomposition of each of the two matrices is first per-
formed. The eigenvectors with large eigenvalues con-
vey more relevant information to the prior knowledge
of the background than the ones with very small eigen-
values that could represent sensor noise. The regular-
ized versions of K
̂ and R
̂ are obtained by discarding
all the eigenvalues below a small threshold, 10−5. In
our experimental results we did not have to regularize
the correlation matrix since the number of the back-
ground data was sufficient to obtain the correct inverse.
32. However, in the case of inverse Gram matrix the small
eigenvalues were always discarded.
4.2. Performance Comparison
The receiver operating characteristics (ROC) curves
representing detection probability Pd versus false
alarm rates N f were generated to provide quantitative
performance comparison as well as qualitative perfor-
mance comparison. For ROC curves generation, based
on the ground truth information for the HYDICE im-
ages, we obtain the coordinates of all the rectangular
target regions. Each target was considered to be de-
tected if at least one pixel within the corresponding
target region was detected at a given false alarm rate.
Pd and N f are defined as
Pd := Nhi tNt and N f :=
Nmi ss
Nt ot
, (31)
where Nhi t represents the number of targets detected
given a certain threshold; Nt represents the total num-
ber of targets in the hyperspectral image; Nmi ss rep-
resents the number of background pixels detected as
targets; and Nt ot represents the total number of pixels
in the hyperspectral image. Pd becomes one only when
all the targets are detected.
Figures 6–8 show the detection results for the DR-
II, FR-I and mine images using KMFD with the three
different kernels and correlation-based MFD, respec-
tively. The corresponding ROC curves for the detection
33. Anonymous
Highlight
140 Kwon and Nasrabadi
results are shown in Fig. 9–11. For the DR-II image, as
shown in Fig. 9, KMFD with any choice of the three
kernels clearly outperformed the conventional MFD at
almost every false alarm rate. For the FR-I image the
background structure is much more complex than that
of DR-I. It includes the tree area where most irregular
illumination effects occur, the long shadowy transition
and the region filled mostly with grass. KMFD using
any choice of the kernels still showed improved de-
tection results over the conventional MFD for both the
FR-I and the mine images, as shown in Figs. 10 and
11, respectively.
5. Conclusions
We have extended the conventional matched filter de-
tector to a nonlinear version by implicitly mapping the
input data into a much higher dimensional feature space
in order to make use of high-order nonlinear correla-
tions between the spectral bands of a hyperspectral im-
age. The expression of the nonlinear matched filter de-
tector in the feature space, which is basically intractable
due to high (potentially infinite) dimensionality, is con-
verted in terms of kernels using the kernel eigenvector
representation as well as the kernel trick to derive a
tractable algorithmic expression.
KMFD, the kernel counterpart of MFD, was im-
plemented with several different kernels, each with
34. different characteristics. In general, KMFD with all
the kernels showed a superior detection performance
when compared to the conventional MFD for the HY-
DICE and mine images tested in this paper. The detec-
tion results show that the kernel-based nonlinear detec-
tion method is quite suitable for identifying underlying
structures of complex data such as hyperspectral data,
thus they are more powerful in discriminating targets
of interest.
Appendix I: Kernel PCA
In this Appendix, we present derivation of Kernel PCA
and its properties providing the relationship between
the correlation (covariance) matrix and the correspond-
ing Gram (centered) matrix. Our goal is to prove (26).
To drive the Kernel PCA consider the estimated back-
ground clutter correlation matrix in the feature space
and assume that the input data is not centered . The
estimated correlation matrix in the feature space is
given by
R
̂ φ =
1
N
Xφ X
T
φ . (32)
The PCA eigenvectors are computed by solving the
eigenvalue problem
λvφ = R
̂ φ vφ
35. = 1
N
N∑
i =1
φ(xi )φ(xi )
T vφ
= 1
N
N∑
i =1
〈φ(xi ), vφ 〉φ(xi ), (33)
where vφ is an eigenvector in F with a corresponding
nonzero eigenvalue λ. Equation (33) indicates that each
eigenvector vφ with corresponding λ �= 0 are spanned
by φ(x1), . . . , φ(xN )—i.e.
vφ =
N∑
i =1
λ
−1/2
βi φ(xi ) = λ−1/2Xφβ, (34)
where Xφ = [ φ(x1) φ(x2) . . . φ(xN ) ] and β =
(β1, β2, . . . , βN )
T . Substituting (34) into (33) and mul-
36. tiplying with φ(xn )
T , n = 1, . . . , N , yields
λ
N∑
i =1
βi < φ(xn ), φ(xi ) >
= 1
N
N∑
i =1
βi φ(xn )φ(xi )φ(xi )
T
N∑
i =1
φ(xi )
= 1
N
N∑
i =1
βi 〈φ(xn ),
N∑
j =1
φ(x j )〈φ(x j ), φ(xi )〉〉,
37. for all n = 1, . . . , N . (35)
We denote by K = K(X, X) = (K)i j the N ×
N kernel matrix whose entries are the dot products
〈φ(xi ), φ(x j )〉. Equation (35) can now be rewritten as
N λβ = Kβ, (36)
where β turn out to be the eigenvectors with nonzero
eigenvalues of the kernel matrix K. Therefore, the
Gram matrix can be written in terms of its eigenvector
decomposition as
K = B�BT , (37)
Kernel Spectral Matched Filter for Hyperspectral Imagery 141
where B = [β1 β2 . . . β N ] are the eigenvectors of the
kernel matrix and � is a diagonal matrix with diagonal
values equal to the eigenvalues of the kernel matrix
K. Similarly, from the definition of PCA in the feature
space (33) the estimated background correlation matrix
is decomposed as
R
̂ φ = Vφ �Vφ T , (38)
where Vφ = [v1φ v2φ . . . vNφ ] and � is a diagonal ma-
trix with its diagonal elements being the eigenvalues of
Ĉφ . From (33) and (36) the eigenvalues of the correla-
tion matrix � in the feature space and the eigenvalues
of the kernel matrix � are related by
� = 1
38. N
�. (39)
Substituting (39) into (37) we obtain the relationship
K = N B�BT , (40)
where N is a constant representing the total num-
ber of background clutter samples, which can be
ignored.
The sample correlation matrix in the feature space is
rank deficient, therefore, its inverse cannot be obtained
but its pseudo-inverse can be written as (Strang, 1986)
R
̂ #φ = Vφ �−1Vφ T = XφB�−2BT Xφ T . (41)
The maximum number of eigenvectors in the pseudo-
inverse is equal to the number of non-zero eigenvalues
(or the number of independent data samples), which
cannot be exactly determined due to round-off er-
ror in the calculations. Therefore, the effective rank
(Strang, 1986) is determined by only including the
eigenvalues that are above a small threshold. Simi-
larly, the inverse Gram matrix K−1 can also be written
as
K−1 = 1
N
B�−1BT . (42)
If the data samples are not independent then the pseudo-
inverse of the Gram matrix has to be used, which is the
same as (42) except only the eigenvectors with eigen-
values above a small threshold are included in order
39. to obtain a numerically stable inverse. Using (42) it is
obvious that the squared inverse Gram matrix can also
be written as
K−2 = 1
N 2
B�−2BT . (43)
Acknowledgment
The authors would like to thank the anonymous review-
ers for their insightful comments and suggestions that
helped us to improve the quality of our paper.
References
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detec-
tor is a scale invariant-invariant GLRT. IEEE Trans. Signal Pro-
cess., 47(9):2538–2541.
Kraut, S., Scharf, L.L., and McWhorter, T. 2001. Adaptive
subspace
detectors. IEEE Trans. Signal Process., 49(1):208–216.
Kwon, H. and Nasrabadi, N.M. 2004. Kernel-based subpixel
target
detection in hyperspectral images. In Proc. of IEEE Joint
Confer-
ence on Neural Networks, Budapest, Hungary, pp. 717–722.
Kwon, H. and Nasrabadi, N.M. 2005. Kernel RX-algorithm: A
non-
linear anomaly detector for hyperspectral imagery. IEEE Trans.
Geosci. Remote Sensing, 43(2):388–397.
Manolakis, D., Shaw, G., and Keshava, N. 2000. Comparative
analy-
sis of hyperspectral adaptive matched filter detector. In Proc.
41. SPIE,
vol. 4049, pp. 2–17.
Müller, K.-R., Mika, S., Rätsch, G., Tsuda, K., and Schölkopf,
B.
2001. An introduction to kernel-based learning algorithms.
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Trans. Neural Networks., 2:181–202.
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Schölkopf, B. and Smola, A.J. 2002. Learning with Kernels. The
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College of Administrative and Financial Sciences
MGT 312
Assignment 3
Deadline: 30/11/2019 @ 23:59
Course Name: Decision Making and Problem Solving
Student’s Name:
Course Code: MGT 312
Student’s ID Number:
Semester: I
CRN:
Academic Year: 1440/1441 H
For Instructor’s Use only
Instructor’s Name:
Students’ Grade: Marks Obtained/Out of
Level of Marks: High/Middle/Low
Instructions – PLEASE READ THEM CAREFULLY
· The Assignment must be submitted on Blackboard (WORD
format only) via allocated folder.
· Assignments submitted through email will not be accepted.
· Students are advised to make their work clear and well
presented, marks may be reduced for poor presentation. This
43. includes filling your information on the cover page.
· Students must mention question number clearly in their
answer.
· Late submission will NOT be accepted.
· Avoid plagiarism, the work should be in your own words,
copying from students or other resources without proper
referencing will result in ZERO marks. No exceptions.
· All answered must be typed using Times New Roman (size 12,
double-spaced) font. No pictures containing text will be
accepted and will be considered plagiarism).
· Submissions without this cover page will NOT be accepted.
Course Learning Outcomes-Covered
CLO Number
Course Learning Outcome
10
Develop numerical skills required for quantitative decisions in
complex situations. (4.1)
13
Create a Decision Making and Problem Solving worksheet
document. (4.5)
14
Utilize technological tools and graphics as an aid to give visual
display to decision making data. (4.6)
15
Identify organized alternatives and select among
possible alternative to evaluate business options. (2.10)
Critical Thinking Questions: (Marks
05)
1. You are planning to start an online marketing for your KSA
based restaurant chain named as “Al-Mataam.”
a. Create a mind map to identify the essential procedures to
carry out an Internet marketing for “Al-Mataam”. [Note: Mind
map must be up to three levels]
44. b. Develop a decision tree to help your online customer to
determine what meal to buy from “Al-Mataam”. You may use
any attribute you wish (cost, calories,) type of food (Veg, Non-
Veg (chicken, Mutton, beef, or Fish)) Regional Food (Arabian,
India, Turkish, Chinese, etc).
c. As a CEO of “Al-Mataam” you have to hire a Restaurant
Manager for its Riyadh location. You have shortlisted the
following five candidates with their skill set.
Yousuf
Amal
John
Ahmad
Julie
Experience in Year
Experience of Restaurant
5
2
3
0
1
Knowledge of service industry
5
4
4
5
3
Business Development Experience
1
3
2
4
4
46. Kernel Matched Signal Detectors for Hyperspectral Target
Detection
Heesung Kwon and Nasser M. Nasrabadi
U.S. Army Research Laboratory, 2800 Powder Mill Rd.,
Adelphi, MD 20783-1197
Abstract
In this paper, we compare several detection algorithms that
are based on spectral matched (subspace) filters. Nonlin-
ear (kernel) versions of these spectral matched (subspace)
detectors are also discussed and their performance is com-
pared with the linear versions. These kernel-based detec-
tors exploit the nonlinear correlations between the spec-
tral bands that are ignored by the conventional detectors.
Several well-known matched detectors, such as matched
subspace detector, orthogonal subspace detector, spectral
matched filter and adaptive subspace detector (adaptive co-
sine estimator) are extended to their corresponding kernel
versions by using the idea of kernel-based learning theory.
In kernel-based detection algorithms the data is implicitly
mapped into a high dimensional kernel feature space by a
nonlinear mapping which is associated with a kernel func-
tion. The detection algorithm is then derived in the feature
space which is kernelized in terms of the kernel functions in
order to avoid explicit computation in the high dimensional
feature space. Experimental results based on simulated toy-
examples and real hyperspectral imagery show that the ker-
nel versions of these detectors outperform the conventional
47. linear detectors.
1 Introduction
Detecting signals of interest, particularly with wide signal
variability, in noisy environments has long been a challeng-
ing issue in various fields of signal processing. Among a
number of previously developed detectors, the well-known
matched subspace detector (MSD) [1], orthogonal subspace
detector (OSD) [1, 2], spectral matched filter (SMF) [3, 4],
and adaptive subspace detectors (ASD) also known as adap-
tive cosine estimator (ACE) [5, 6] have been widely used to
detect a desired signal (target).
Matched signal detectors, such as spectral matched fil-
ter and matched subspace detectors (whether adaptive or
non-adaptive), only exploit second order correlations, thus
completely ignoring nonlinear (higher order) spectral inter-
band correlations that could be crucial to discriminate be-
tween target and background. In this paper, our aim is to
introduce nonlinear versions of MSD, OSD, SMF and ASD
detectors which effectively exploits the higher order spec-
tral inter-band correlations in a high (possibly infinite) di-
mensional feature space associated with a certain nonlinear
mapping via kernel-based learning methods [7]. A nonlin-
ear mapping of the input data into a high dimensional fea-
ture space is often expected to increase the data separability
and reduce the complexity of the corresponding data struc-
ture. The nonlinear versions of a number of signal process-
ing techniques such as principal component analysis (PCA)
[8], Fisher discriminant analysis [9], linear classifiers [10],
and kernel-based anomaly detection [11] have already been
defined in a kernel space.
This paper is organized as follows. Section 2 provides
48. the background to the kernel-based learning methods and
kernel trick. Section 3 introduces a linear matched subspace
and its kernel version. The orthogonal subspace detector is
defined in Section 4 as well as its kernel version. In Section
5 we describe the conventional spectral matched filter ad its
kernel version in the feature space and reformulate the the
expression in terms of the kernel function using the kernel
trick. Finally, in Section 6 the adaptive subspace detector
and its kernel version are introduced. Performance com-
parison between the conventional and the kernel versions of
these algorithms is provided in Section 7 and conclusions
are given in Section 8.
2 Kernel-based Learning and Kernel
Trick
Suppose that the input hyperspectral data is represented by
the data space (
� � � �
) and � is a feature space associated
with
�
by a nonlinear mapping function �
� � � � � �
� � � � � (1)
where is an input vector in � which is mapped into a
potentially much higher – (could be infinite) – dimensional
feature space. Due to the high dimensionality of the feature
space � , it is computationally not feasible to implement any
algorithm directly in feature space. However, kernel-based
learning algorithms use an effective kernel trick given by
50. In this model the target pixel vectors are expressed as a lin-
ear combination of target spectral signature and background
spectral signature, which are represented by subspace target
spectra and subspace background spectra, respectively. The
hyperspectral target detection problem in a � -dimensional
input space is expressed as two competing hypotheses �
and � �
� � � � � � � � � (3)
� � � � � � � � � � � � � � � � � � � � � �
where � and � represent orthogonal matrices whose � -
dimensional column vectors span the target and background
subspaces, respectively; � and � are unknown vectors whose
entries are coefficients that account for the abundances of
the corresponding column vectors of � and � , respectively;�
represents Gaussian random noise ( � � � � ) distributed
as � ! � " # $ � ; and � � � � is a concatenated matrix of�
and � . The numbers of the column vectors of � and� , % &
and % ' , respectively, are usually smaller than �
( % & � % ' ( � ).
The generalized likelihood ratio test (GLRT) for the
model (3) was derived in [1], given as
) # � � � � * � $ + , - � �� * � $ + , . - � � / 01/ 2 3
(4)
where , - � � � * � � 4 � � * � � * is a projection ma-
trix associated with the % ' -dimensional background sub-
space ( � 5 ; , . - is a projection matrix associated with
the ( % ' & % ' � % & )-dimensional target-and-background
subspace ( � � 5
51. , . - � � � � � 6 � � 7 * 6 � � 7 � 4 � � � � � * 8 (5)
3.2 Linear MSD in the Feature Space and its
Kernel Version
The hyperspectral detection problem based on the target and
background subspaces can be described in the feature space� as
� � 9 � � � � � � : � : � � : � (6)� � 9 � � � � � �
: � : � � : � : � � :
� � : � : � � � :� : � � � : �
where � : and � : represent full-rank matrices whose
column vectors span target and background subspaces (� : 5
and ( � : 5 in � , respectively; � : and � : are un-
known vectors whose entries are coefficients that account
for the abundances of the corresponding column vectors of� :
and � : , respectively; � : represents Gaussian random
noise; and � � : � : � is a concatenated matrix of � :
and � : . Using a similar reasoning as described in the pre-
vious subsection, the GLRT of the hyperspectral detection
problem depicted by the model in (6) is given by
) # � � � � � � � � � � * � , ; 9 + , - 9 � � � � �� �
� � * � , ; 9 + , . 9 - 9 � � � � � � (7)
where , ; 9 represents an identity projection operator in � ;, - 9
� : � � *: � : � 4 � � *: � : � *: is a background
pro-
jection matrix; and , . 9 - 9 is a joint target-and-background
projection matrix in �
, . 9 - 9 � � : � : � � 6 � : � : 7 * 6 � : � : 7 � 4 � < (8)
� � : � : � *
� � : � : � � � *: � : � * : � :� *: � : � *: � : � 4
� � � * :� *: � 8
53. projection onto & $ is & %$ � � � � � % ! � � � � � �
where! � � � � � � and ! � � � � � � , referred to as the
empirical
kernel maps in the machine learning literature [7], are
column vectors whose entries are
" � ' � � � � for ' � � � � and' � � � � , respectively. Now
we can write
� � � % # $ # %$ � � � � ! � � � � � � % � � % !
� � � � � � � (12)
The projection onto the identity operator � � � % ( ) �
� � �
also needs to be kernelized which is given by
� � � % ( ) � � � � � � � � %
� � * * % %
� � � � � (13)
� ! � � � � � � � % * * % ! � � � � � � � �
where
� � �
� +
� and * is a matrix
whose columns are the eigenvectors ( , � , , � , . . . , , � � )
of the centered kernel matrix ! � � � � � � � � � = � ! � �
�
=
" � � � � � � � � � � � � � � � � + � � with nonzero
eigen-
values, normalized by the square root of their associ-
ated eigenvalues and ! � � � � � � � is a concatenated vector
! � � � � � � % ! � � � � � � % � % . To complete the
54. kernel-
ization process the denominator of (7) is given by
� � � % ( � � � � � � � � � � � %
& $ # $ � - (14)
. & %$ & $ & % $ # $# %$ & $ # % $ # $ /
0 � . & % $# % $ / � � �
�
! � � � � � � % � ! � � � � � � % � � -
. � % ! � � � � � � � � � % ! � � � � � � � �� % ! �
� � � � � � � � % ! � � � � � � � � /
0 � -
. � % ! � � � � � �� % ! � � � � � � / �
Finally, substituting (12), (14), and (14) into (7) the kernel-
ized GLRT is given by
1 � 2 � � ! � � � � � � � % * * % ! � � � � � � � 3
(15)! � � � � � � % � � % ! � � � � � � � 4
� ! � � � � � � � % * * % ! � � � � � � � 3
! � � � � � � % � ! � � � � � � % � � 5 0 �� -
. � % ! � � � � � �� % ! � � � � � � / � �
where 5 � � . � % ! � � � � � � � � � % ! � � � � � �
� �� % ! � � � � � � � � � % ! � � � � � � � � / �
In the above derivation (15) we assumed that the mapped
input data was centered in the feature space by removing
the sample mean. However, the original data is usually not
centered and the estimated mean in the feature space can not
55. be explicitly computed, therefore, the kernel matrices have
to be properly centered. The resulting centered 6! is shown
in [7] to be given by
6! � � ! 3 7 � ! 3 ! 7 � 8 7 � ! 7 � � � (16)
where the 9 - 9 matrix � 7 � � � � � : 4 9 . The empirical
kernel maps ! � � � � � � , ! � � � � � � , and ! � � � �
� � � have
also to be centered by removing their corresponding em-
pirical kernel map mean. (e.g. ;! � � � � � � � ! � � � � �
� 3�� < �� = �
" � � � � � � � � � � � � .)
4 OSP and Kernel OSP Algorithms
4.1 Linear spectral mixture model
The OSP algorithm [2] is based on maximizing the SNR
(signal-to-noise ratio) in the subspace orthogonal to the
background subspace and only depends on the noise
second-order statistics. It also does not provide any esti-
mate of the abundance measure for the desired end member
in the mixed pixel. A linear mixture model for pixel � con-
sisting of > spectral bands is described by
� � ? @ 8 A � (17)
where the � > - B � matrix ? represent B endmembers spec-
tra, @ is a � B - : � column vector whose elements are the co-
efficients that account for the proportions (abundances) of
each endmember spectrum contributing to the mixed pixel,
and A is an � > - : � vector representing an additive zero-
mean Gaussian noise with covariance matrix C � D and D is
the � > - > � identity matrix.
Assuming now we want to identify one particular signa-
ture (e.g. a military target) with a given spectral signatureE
57. spectra in the feature space and
� is an additive zero-mean
Gaussian noise with covariance matrix � � � � and � � is the
identity matrix in the feature space. The model (21) can
also be rewritten as
� � � � � � � � � � � � � � �
� � (22)
where � � � � represent the spectral signature of the desired
target in the feature space and the columns of � represent
the undesired background signatures in the feature space.
The output of the OSP classifier in the feature space is
given by�
� � � � � �
� � � � � � � � � �
� � � � � #� � � � � � � (23)
This output (23) is very similar to the numerator of (7). It
can easily be shown that the kernelized version of (23) is
given by� � � � � ! � " # $ � � �
% %
! � " # $ � � � � (24)! � " # � � �
& &
! � " # � � �
where " # � ' ( ) ( � � � � ( * + correspond to , input back-
ground spectral signatures and & � � - ) � - � � � � � � - *
. �
are the , / significant eigenvectors of the centered ker-
nel matrix (Gram matrix) ! � " # � " # � normalized by
the square root of their corresponding eigenvalues [8].
! � " # � � � and ! � " # � � � , are column vectors whose
en-
tries are
58. 0 � ( 1 � � � and 0 � ( 1 � � � for ( 1 2 " # , respectively." #
$ � " # 3 � and % is a matrix whose columns are the , / $
eigenvectors ( 4 ) , 4 � , . . . , 4 * . 5 ) of the centered kernel
ma-
trix ! � " # $ � " # $ � = � ! � 1 6 = 0 � ( 1 � ( 6 � � ( 1 � (
6 2 " # $ with
nonzero eigenvalues, normalized by the square root of their
associated eigenvalues. Also ! � " # $ � � � is the concate-
nated vector 7 ! � " # � � �
! � � � � �
8
and ! � " # $ � � �
is the concatenated vector 7 ! � " # � � �
! � � � � �
8
.
In the above derivation (24) we assumed that the mapped
input data was centered in the feature space. The kernel
matrices and the empirical kernel maps have to be properly
centered as was shown in subsection 3.2
5 Linear SMF and Kernel Spectral
Matched Filter
5.1 Linear Spectral Matched Filter
In this section, we introduce the concept of linear SMF.
The constrained least squares approach is used to derive
the linear SMF. Let the input spectral signal ( be ( �' 9 � : � �
9 � ; � � � � � � 9 � < � +
consisting of < spectral bands. We
can model each spectral observation as a linear combination
of the target spectral signature and noise( � = > �
� (25)
where = is an attenuation constant (target abundance mea-
sure). When = � ? no target is present and when = @ ? tar-
60. sion
Consider the linear model of the input data in a kernel fea-
ture space which is equivalent to a non-linear model in the
input space � � � � � � � � � � � �
� (28)
where � is the non-linear mapping that maps the input data
into a kernel feature space, �
is an attenuation constant
(abundance measure), the high dimensional vector � � � �
contains the spectral signature of the target in the feature
space, and vector
contains the added noise in the feature
space.
Using the constrained least squares approach it can eas-
ily be shown that the output of the desired matched filter for
the input � � � � is given by
� � � � � � � � � � �� � �
� � � �� � � � � �� � �
� � � � (29)
where ��
is the estimated covariance of pixels in the fea-
ture space.
We now show how to kernelize the matched filter ex-
pression (29) where the resulting non-linear matched filter
is called the kernel matched filter. The pseudoinverse (in-
verse) of the estimated background covariance matrix can
be written in terms of its eigenvector decomposition as [10]��
�
� �
� � � � � � � �
(30)
where �
= � � � � � � � � � � � � � � � � � � � � is a matrix
61. whose
columns are the mapped background reference data in the
feature space and � � � � � � � � � ! � are the nonzero
eigenvectors of the centered kernel matrix (Gram matrix)" � �
� � � normalized by the square root of their corre-
sponding eigenvalues.
Inserting Equation (30) into (29) it can be rewritten as
� � � � � � � � � � �
� � � � � � � �
� � � �� � � � � �
� � � � � � � �
� � � � � (31)
Also using the properties of the Kernel PCA [7], we have
the relationship " � � � � � � � � . We denote " �" � � �
� � � � " � # $ an % & % Gram kernel matrix whose
entries are the dot products ' � � � # � � � � � $ � ( .
Finally, the
kernelized version of SMF is now given by
) � � " � � � � � � " � � " � � � � �" � � � � � � " �
� " � � � � � � " �* " � � " +" �* " � � " * (32)
where the empirical kernel maps " * � " � � � � � and " + �"
� � � � � . As in the previous section the kernel matrix "
as well as the empirical kernel maps need to be properly
centered.
6 Adaptive Subspace Detector and
Kernel Adaptive Subspace Detec-
tor
6.1 Linear ASD
In this section, the GLRT under the two competing hypothe-
ses ( , - and , � ) for a certain mixture model is described.
The subpixel detection model for a measurement � (a pixel
vector) is expressed as, - . � � � Target absent (33), � . �
� / 0 � 1 � Target present
62. where / represents an orthogonal matrix whose column
vectors are the eigenvectors that span the target subspace' / ( ; 0
is an unknown vector whose entries are coeffi-
cients that account for the abundances of the corresponding
column vectors of / ; represents Gaussian random noise
distributed as 2 � 3 � � � .
In the model, � is assumed to be a background noise un-
der , - and a linear combination of a target subspace signal
and a scaled background noise, distributed as 2 � / 0 � 1 � �
� ,
under , � . The background noise under the two hypothe-
ses is represented by the same covariance but different vari-
ances because of the existence of subpixel targets under , � .
The GLRT for the subpixel problem as described in [5] (so
called ASD) is given by4 5 6 7 � � � � � � �� � � / � / �
�� � � / � � � / � �� � � �� � �� � � � 8 9:8 ; <
5 6 7 �
(34)
where �� is the MLE (maximum likelihood estimate) of the
covariance � and <
5 6 7 represents a threshold. Expression
(34) has a constant false alarm rate (CFAR) property and
is also referred to as the adaptive cosine estimator because
(34) measures the angle between =� and ' =/ ( where =� ���
� � > � � and =/ � �� � � > � / .
6.2 ASD in the Feature Space and its Kernel
Version
We define a new subpixel model by assuming that the input
data has been implicitly mapped by a nonlinear function �
into a high dimensional feature space ? . The model in ? is
then given by, - � . � � � � �
64. � � � � �
! � � " � � � ��# � �
� � � �
� � � # � �
�
where � � � # � �
� � � �
� � � � �
! � �
background spectral signatures is denoted by � � � � � $ % %
% � & " , target spectral signa-
tures are denoted by ! � � ' � ' $ % % % ' ( " and� � � ) � ) $
% % % ) ( * "
+ � � +
is a matrix consistingof the + � eigenvectors of the kernel
matrix � � !
! � . As
in the previous section, all the kernel matrices as well as
the empirical kernel maps need to be properly centered [7].
7 Experimental Results
In this section, the kernel-based matched signal detectors,
such as the kernel MSD (KMSD), kernel ASD (KASD),
kernel OSP (KOSP) and kernel SMF (KSMF) as well as
the corresponding conventional detectors are implemented
based on two different types of data sets – illustrative
toy data sets and a real hyperspectral image that contains
military targets. The Gaussian RBF kernel,
, � �
' � �
exp � � - � � . - /0 �
was used to implement the kernel-based de-
tectors. � represents the width of the Gaussian distribution
and the value of c was chosen such that the overall data vari-
65. ations can be fully exploited by the Gaussian RBF function.
In this paper, the values of � were determined experimen-
tally.
A. Illustrative Toy Examples
Figs 1 and 2 show contour and surface plots of the con-
ventional detectors and the kernel-based detectors, on two
different types of two-dimensional toy data sets: a Gaus-
sian mixture in Fig. 1 and nonlinearly mapped data in Fig.
2. In the contour and surface plots, data points for the
desired target were represented by the star-shaped symbol
and the background points were represented by the circles.
In Fig. 2 the two-dimensional data points � � � 1
2 � for
each class were obtained by nonlinearly mapping the orig-
inal Gaussian mixture data points � 3 � � 1 4
2 4 � in Fig. 1.
All the data points in Fig. 2 were nonlinearly mapped by� � �
1
2 � � � 1 4
1 $4 5 2 4 � . In the new data set the second
component of each data point is nonlinearly related to its
first component.
For both data sets, the contours generated by the kernel-
based detectors are highly nonlinear and naturally following
the dispersion of the data and thus successfully separating
the two classes, as opposed to the linear contours obtained
by the conventional detectors. Therefore, the kernel-based
detectors clearly provided significantly improved discrimi-
nation over the conventional detectors for both the Gaussian
mixture and nonlinearly mapped data. Among the kernel-
based detectors, KMSD and KASD outperform KOSP and
KSMF mainly because targets in KMSD and KASD are bet-
ter represented by the associated target subspace than by a
66. single spectral signature used in KOSP and KSMF. Note
that the contour plots for MSD (Fig. 1(a) and Fig. 2 (a))
represent only the numerator of Eq. 4 because the denomi-
nator becomes unstable for the two-dimensional cases: i.e.,
for the two-dimensional data � 6 7 8 9 : � becomes zero.
B. Hyperspectral Images
In this section, a HYDICE (HYperspectral Digital Imagery
Collection Experiment) image from the Desert Radiance II
data collection (DR-II) was used to compare detection per-
formance between the kernel-based and conventional meth-
ods. The HYDICE imaging sensor generates 210 bands
across the whole spectral range (0.4 – 2.5 � � ) which in-
cludes the visible and short-wave infrared (SWIR) bands.
But we only use 150 bands by discarding water absorp-
tion and low signal to noise ratio (SNR) bands; the spectral
bands used are the 23rd–101st, 109th–136th, and 152nd–
194th for the HYDICE images. The DR-II image includes 6
military targets along the road, as shown in the sample band
images in Fig. 3. The detection performance of the DR-
II image was provided in both the qualitative and quantita-
tive – the receiver operating characteristics (ROC) curves –
forms. The spectral signatures of the desired target and un-
desired background signatures were directly collected from
the given hyperspectral data to implement both the kernel-
based and conventional detectors.
Figs. 4-5 show the detection results including the ROC
curves generated by applying the kernel-based and conven-
tional detectors to the DR-II image. In general, the detected
targets by the kernel-based detectors are much more evi-
dent than the ones detected by the conventional detectors,
as shown in Fig. 4. Fig. 5 shows the ROC curve plots
for the kernel-based and conventional detectors; the kernel-
based detectors clearly outperformed the conventional de-
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