APPROACHES IN USING EXPECTATIONMAXIMIZATION ALGORITHM FOR MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF A CONSTRAINED STATE SPACE MODEL WITH AN EXTERNAL INPUT SERIES
EM algorithm is popular in maximum likelihood estimation of parameters for state-space models. However, extant approaches for the realization of EM algorithm are still not able to fulfill the task of identification systems, which have external inputs and constrained parameters. In this paper, we propose new approaches for both initial guessing and MLE of the parameters of a constrained state-space model with an external input. Using weighted least square for the initial guess and the partial differentiation of the joint log-likelihood function for the EM algorithm, we estimate the parameters and compare the estimated values with the “actual” values, which are set to generate simulation data. Moreover, asymptotic variances of the estimated parameters are calculated when the sample size is large, while statistics of the estimated parameters are obtained through bootstrapping when the sample size issmall. The results demonstrate that the estimated values are close to the “actual” values.Consequently, our approaches are promising and can applied in future research.
LOGNORMAL ORDINARY KRIGING METAMODEL IN SIMULATION OPTIMIZATIONorajjournal
This paper presents a lognormal ordinary kriging (LOK) metamodel algorithm and its application to
optimize a stochastic simulation problem. Kriging models have been developed as an interpolation method
in geology. They have been successfully used for the deterministic simulation optimization (SO) problem. In
recent years, kriging metamodeling has attracted a growing interest with stochastic problems. SO
researchers have begun using ordinary kriging through global optimization in stochastic systems. The
goals of this study are to present LOK metamodel algorithm and to analyze the result of the application
step-by-step. The results show that LOK is a powerful alternative metamodel in simulation optimization
when the data are too skewed.
A MODIFIED VORTEX SEARCH ALGORITHM FOR NUMERICAL FUNCTION OPTIMIZATIONijaia
This document presents a modified version of the Vortex Search (VS) algorithm called the Modified Vortex Search (MVS) algorithm for numerical function optimization. The VS algorithm has the drawback that it can get trapped in local minima for functions with multiple local minima. The MVS algorithm addresses this by generating candidate solutions around multiple points at each iteration rather than a single point, allowing it to escape local minima more easily. Computational results on benchmark functions showed the MVS algorithm outperformed the original VS algorithm, as well as PSO2011 and ABC algorithms.
GENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATIONijaia
Function Approximation is a popular engineering problems used in system identification or Equation
optimization. Due to the complex search space it requires, AI techniques has been used extensively to spot
the best curves that match the real behavior of the system. Genetic algorithm is known for their fast
convergence and their ability to find an optimal structure of the solution. We propose using a genetic
algorithm as a function approximator. Our attempt will focus on using the polynomial form of the
approximation. After implementing the algorithm, we are going to report our results and compare it with
the real function output.
Sca a sine cosine algorithm for solving optimization problemslaxmanLaxman03209
The document proposes a new population-based optimization algorithm called the Sine Cosine Algorithm (SCA) for solving optimization problems. SCA creates multiple random initial solutions and uses sine and cosine functions to fluctuate the solutions outward or toward the best solution, emphasizing exploration and exploitation. The performance of SCA is evaluated on test functions, qualitative metrics, and by optimizing the cross-section of an aircraft wing, showing it can effectively explore, avoid local optima, converge to the global optimum, and solve real problems with constraints.
This document discusses various applications of interpolation in computer science and engineering. It describes interpolation as a method of constructing new data points within the range of a known discrete data set. Some examples of interpolation applications mentioned include estimating population values, image processing through transformations like resizing and rotation, zooming digital images using different interpolation functions, and ray tracing in computer graphics. Numerical integration techniques like the trapezoidal rule, Simpson's rule, and Romberg's method are also briefly covered.
Inference & Learning in Linear Chain Conditional Random Fields (CRFs)Anmol Dwivedi
This mini-project will consider performing inference and learning in Linear Chain CRFs. In particular, it will consider an application to hand-written word recognition. Handwritten word recognition is a task many have explored with different methods of machine learning. Some written characters can be evaluated individually or as a whole word to account for the context in characters. In this mini-project, we use linear chain CRF models to account for context between the characters of a word to improve word recognition accuracy.
Tutorial on Markov Random Fields (MRFs) for Computer Vision ApplicationsAnmol Dwivedi
The goal of this mini-project is to implement a pairwise binary label-observation Markov Random Field
model for bi-level image segmentation. Specifically, two inference algorithms, i.e., the Iterative
Conditional Mode (ICM) and Gibbs sampling methods will be implemented to perform image segmentation.
LOGNORMAL ORDINARY KRIGING METAMODEL IN SIMULATION OPTIMIZATIONorajjournal
This paper presents a lognormal ordinary kriging (LOK) metamodel algorithm and its application to
optimize a stochastic simulation problem. Kriging models have been developed as an interpolation method
in geology. They have been successfully used for the deterministic simulation optimization (SO) problem. In
recent years, kriging metamodeling has attracted a growing interest with stochastic problems. SO
researchers have begun using ordinary kriging through global optimization in stochastic systems. The
goals of this study are to present LOK metamodel algorithm and to analyze the result of the application
step-by-step. The results show that LOK is a powerful alternative metamodel in simulation optimization
when the data are too skewed.
A MODIFIED VORTEX SEARCH ALGORITHM FOR NUMERICAL FUNCTION OPTIMIZATIONijaia
This document presents a modified version of the Vortex Search (VS) algorithm called the Modified Vortex Search (MVS) algorithm for numerical function optimization. The VS algorithm has the drawback that it can get trapped in local minima for functions with multiple local minima. The MVS algorithm addresses this by generating candidate solutions around multiple points at each iteration rather than a single point, allowing it to escape local minima more easily. Computational results on benchmark functions showed the MVS algorithm outperformed the original VS algorithm, as well as PSO2011 and ABC algorithms.
GENETIC ALGORITHM FOR FUNCTION APPROXIMATION: AN EXPERIMENTAL INVESTIGATIONijaia
Function Approximation is a popular engineering problems used in system identification or Equation
optimization. Due to the complex search space it requires, AI techniques has been used extensively to spot
the best curves that match the real behavior of the system. Genetic algorithm is known for their fast
convergence and their ability to find an optimal structure of the solution. We propose using a genetic
algorithm as a function approximator. Our attempt will focus on using the polynomial form of the
approximation. After implementing the algorithm, we are going to report our results and compare it with
the real function output.
Sca a sine cosine algorithm for solving optimization problemslaxmanLaxman03209
The document proposes a new population-based optimization algorithm called the Sine Cosine Algorithm (SCA) for solving optimization problems. SCA creates multiple random initial solutions and uses sine and cosine functions to fluctuate the solutions outward or toward the best solution, emphasizing exploration and exploitation. The performance of SCA is evaluated on test functions, qualitative metrics, and by optimizing the cross-section of an aircraft wing, showing it can effectively explore, avoid local optima, converge to the global optimum, and solve real problems with constraints.
This document discusses various applications of interpolation in computer science and engineering. It describes interpolation as a method of constructing new data points within the range of a known discrete data set. Some examples of interpolation applications mentioned include estimating population values, image processing through transformations like resizing and rotation, zooming digital images using different interpolation functions, and ray tracing in computer graphics. Numerical integration techniques like the trapezoidal rule, Simpson's rule, and Romberg's method are also briefly covered.
Inference & Learning in Linear Chain Conditional Random Fields (CRFs)Anmol Dwivedi
This mini-project will consider performing inference and learning in Linear Chain CRFs. In particular, it will consider an application to hand-written word recognition. Handwritten word recognition is a task many have explored with different methods of machine learning. Some written characters can be evaluated individually or as a whole word to account for the context in characters. In this mini-project, we use linear chain CRF models to account for context between the characters of a word to improve word recognition accuracy.
Tutorial on Markov Random Fields (MRFs) for Computer Vision ApplicationsAnmol Dwivedi
The goal of this mini-project is to implement a pairwise binary label-observation Markov Random Field
model for bi-level image segmentation. Specifically, two inference algorithms, i.e., the Iterative
Conditional Mode (ICM) and Gibbs sampling methods will be implemented to perform image segmentation.
KNN and ARL Based Imputation to Estimate Missing Valuesijeei-iaes
Missing data are the absence of data items for a subject; they hide some information that may be important. In practice, missing data have been one major factor affecting data quality. Thus, Missing value imputation is needed. Methods such as hierarchical clustering and K-means clustering are not robust to missing data and may lose effectiveness even with a few missing values. Therefore, to improve the quality of data method for missing value imputation is needed. In this paper KNN and ARL based Imputation are introduced to impute missing values and accuracy of both the algorithms are measured by using normalized root mean sqare error. The result shows that ARL is more accurate and robust method for missing value estimation.
This paper introduces a new comparison base stable sorting algorithm, named RA sort. The RA sort
involves only the comparison of pair of elements in an array which ultimately sorts the array and does not
involve the comparison of each element with every other element. It tries to build upon the relationship
established between the elements in each pass. Instead of going for a blind comparison we prefer a
selective comparison to get an efficient method. Sorting is a fundamental operation in computer science.
This algorithm is analysed both theoretically and empirically to get a robust average case result. We have
performed its Empirical analysis and compared its performance with the well-known quick sort for various
input types. Although the theoretical worst case complexity of RA sort is Yworst(n) = O(n√), the
experimental results suggest an empirical Oemp(nlgn)1.333 time complexity for typical input instances, where
the parameter n characterizes the input size. The theoretical complexity is given for comparison operation.
We emphasize that the theoretical complexity is operation specific whereas the empirical one represents the
overall algorithmic complexity.
And Then There Are Algorithms - Danilo Poccia - Codemotion Rome 2018Codemotion
In machine learning, training large models on a massive amount of data usually improves results. Our customers report, however, that training such models and deploying them is either operationally prohibitive or outright impossible for them. We created a collection of machine learning algorithms that scale to any amount of data, including k-means clustering for data segmentation, factorization machines for recommendations, time-series forecasting, linear regression, topic modeling, and image classification. This talk will discuss those algorithms, understand where and how they can be used.
BINARY SINE COSINE ALGORITHMS FOR FEATURE SELECTION FROM MEDICAL DATAacijjournal
A well-constructed classification model highly depends on input feature subsets from a dataset, which may contain redundant, irrelevant, or noisy features. This challenge can be worse while dealing with medical datasets. The main aim of feature selection as a pre-processing task is to eliminate these features and select the most effective ones. In the literature, metaheuristic algorithms show a successful performance to find optimal feature subsets. In this paper, two binary metaheuristic algorithms named S-shaped binary Sine Cosine Algorithm (SBSCA) and V-shaped binary Sine Cosine Algorithm (VBSCA) are proposed for feature selection from the medical data. In these algorithms, the search space remains continuous, while a binary position vector is generated by two transfer functions S-shaped and V-shaped for each solution. The proposed algorithms are compared with four latest binary optimization algorithms over five medical datasets from the UCI repository. The experimental results confirm that using both bSCA variants enhance the accuracy of classification on these medical datasets compared to four other algorithms.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
The document presents an overview of mathematical models. It defines mathematical models as mathematical descriptions of real situations that make assumptions and simplifications about reality. There are three main types of models: linear, quadratic, and exponential models. The document discusses how to develop a mathematical model by comparing model predictions to real data. It provides an example of a differential equation model of the spread of a contagious flu.
This document presents a new method for creating proxy models called Simulated Annealing Programming (SAP). SAP uses simulated annealing optimization on a tree structure to find the equation that best predicts outputs with minimum error. The authors apply SAP to create a model for predicting gas compressor torque based on fuel rate and speed. They find the SAP model is highly accurate, roughly independent of internal parameters, and has smaller overestimation/underestimation compared to other methods like polynomials and neural networks.
A review of automatic differentiationand its efficient implementationssuserfa7e73
Automatic differentiation is a powerful tool for automatically calculating derivatives of mathematical functions and algorithms. It works by expressing the target function as a sequence of elementary operations and then applying the chain rule to differentiate each operation. This can be done using either forward or reverse mode. Forward mode calculates how changes in inputs propagate through the function to influence the outputs, while reverse mode calculates how changes in outputs backpropagate to influence the inputs. Both modes require performing the computation twice - once for the forward pass and once for the derivative pass. Careful implementation is required to make automatic differentiation efficient in terms of speed and memory usage.
This document presents new certified optimal solutions found by the Charibde algorithm for six difficult benchmark optimization problems. Charibde combines an evolutionary algorithm and interval-based methods in a cooperative framework. It has achieved optimality proofs for five bound-constrained problems and one nonlinearly constrained problem. These problems are highly multimodal and some had not been solved before even with approximate methods. The document also compares Charibde's performance to other state-of-the-art solvers, showing it is highly competitive while providing reliable optimality proofs.
This document discusses numerical integration and solving ordinary differential equations (ODEs) numerically in MATLAB. It describes built-in integration functions such as quad, quadl, and trapz that can integrate functions and data points. It also outlines the basic steps for solving first-order ODEs numerically, including writing the ODE as an initial value problem, defining the derivative function, selecting an ODE solver, and using the solver to generate the solution over a time span. An example demonstrates solving an ODE numerically using ode45 and plotting the results.
Optimization is considered to be one of the pillars of statistical learning and also plays a major role in the design and development of intelligent systems such as search engines, recommender systems, and speech and image recognition software. Machine Learning is the study that gives the computers the ability to learn and also the ability to think without being explicitly programmed. A computer is said to learn from an experience with respect to a specified task and its performance related to that task. The machine learning algorithms are applied to the problems to reduce efforts. Machine learning algorithms are used for manipulating the data and predict the output for the new data with high precision and low uncertainty. The optimization algorithms are used to make rational decisions in an environment of uncertainty and imprecision. In this paper a methodology is presented to use the efficient optimization algorithm as an alternative for the gradient descent machine learning algorithm as an optimization algorithm.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Machine learning and linear regression programmingSoumya Mukherjee
Overview of AI and ML
Terminology awareness
Applications in real world
Use cases within Nokia
Types of Learning
Regression
Classification
Clustering
Linear Regression Single Variable with python
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Medical Conferences, Pharma Conferences, Engineering Conferences, Science Conferences, Manufacturing Conferences, Social Science Conferences, Business Conferences, Scientific Conferences Malaysia, Thailand, Singapore, Hong Kong, Dubai, Turkey 2014 2015 2016
Global Research & Development Services (GRDS) is a leading academic event organizer, publishing Open Access Journals and conducting several professionally organized international conferences all over the globe annually. GRDS aims to disseminate knowledge and innovation with the help of its International Conferences and open access publications. GRDS International conferences are world-class events which provide a meaningful platform for researchers, students, academicians, institutions, entrepreneurs, industries and practitioners to create, share and disseminate knowledge and innovation and to develop long-lasting network and collaboration.
GRDS is a blend of Open Access Publications and world-wide International Conferences and Academic events. The prime mission of GRDS is to make continuous efforts in transforming the lives of people around the world through education, application of research and innovative ideas.
Global Research & Development Services (GRDS) is also active in the field of Research Funding, Research Consultancy, Training and Workshops along with International Conferences and Open Access Publications.
International Conferences 2014 – 2015
Malaysia Conferences, Thailand Conferences, Singapore Conferences, Hong Kong Conferences, Dubai Conferences, Turkey Conferences, Conference Listing, Conference Alerts
Design of optimized Interval Arithmetic MultiplierVLSICS Design
Many DSP and Control applications that require the user to know how various numerical errors(uncertainty) affect the result. This uncertainty is eliminated by replacing non-interval values with intervals. Since most DSPs operate in real time environments, fast processors are required to implement interval arithmetic. The goal is to develop a platform in which Interval Arithmetic operations are performed at the same computational speed as present day signal processors. So we have proposed the design and implementation of Interval Arithmetic multiplier, which operates with IEEE 754 numbers. The proposed unit consists of a floating point CSD multiplier, Interval operation selector. This architecture implements an algorithm which is faster than conventional algorithm of Interval multiplier . The cost overhead of the proposed unit is 30% with respect to a conventional floating point multiplier. The
performance of proposed architecture is better than that of a conventional CSD floating-point multiplier, as it can perform both interval multiplication and floating-point multiplication as well as Interval comparisons
IRJET - Movie Genre Prediction from Plot Summaries by Comparing Various C...IRJET Journal
This document discusses predicting movie genres from plot summaries using various classification algorithms. It analyzes Multinomial Naive Bayes, Logistic Regression, Random Forest, and Stochastic Gradient Descent algorithms on a dataset of over 40,000 movie plots labeled with 12 genres. It finds that Multinomial Naive Bayes performs best, achieving the highest AUC scores for predicting each genre individually. It then builds separate classifiers for each genre using the best performing algorithm to predict the genre of new movie plots.
On the Performance of the Pareto Set Pursuing (PSP) Method for Mixed-Variable...Amir Ziai
This document describes a study on modifying the Pareto Set Pursuing (PSP) method to solve multi-objective optimization problems with mixed continuous and discrete variables. The PSP method was originally developed for problems with only continuous variables. The modifications allow it to handle mixed variable problems. The performance of the modified PSP method is compared to other multi-objective algorithms based on metrics like efficiency, robustness, and closeness to the true Pareto front with a limited number of function evaluations. Preliminary results on benchmark problems and two engineering design examples show that the modified PSP is competitive when the number of function evaluations is limited, but its performance decreases as the number of design variables increases.
COMPARING THE CUCKOO ALGORITHM WITH OTHER ALGORITHMS FOR ESTIMATING TWO GLSD ...csandit
This study introduces and compares different methods for estimating the two parameters of
generalized logarithmic series distribution. These methods are the cuckoo search optimization,
maximum likelihood estimation, and method of moments algorithms. All the required
derivations and basic steps of each algorithm are explained. The applications for these
algorithms are implemented through simulations using different sample sizes (n = 15, 25, 50,
100). Results are compared using the statistical measure mean square error.
The document discusses using clustering models like subtractive fuzzy clustering (SFC) and fuzzy c-means clustering (FCM) to generate an adaptive neuro-fuzzy inference system (ANFIS) for medical diagnoses. Experimental results on medical diagnosis datasets show that ANFIS models using SFC and FCM clustering (ANFIS-SFC and ANFIS-FCM) had better average training and checking errors compared to ANFIS without clustering. Specifically, ANFIS-SFC performed best using backpropagation learning, while ANFIS-FCM performed best using a hybrid learning model. Clustering the datasets without ANFIS was also able to identify different disease clusters.
This document summarizes the derivation of the EM algorithm for parameter estimation in a mixed normal model. It begins by presenting the log-likelihood function and derives update equations for the mean (μk) and covariance (Σk) parameters of each normal component. An experimental design is then described to statistically analyze the performance of the EM algorithm under different conditions. The results show that the EM estimates are most accurate when the normal components have distinct means and covariances, and when more training data is available. Interactions between factors are also examined.
KNN and ARL Based Imputation to Estimate Missing Valuesijeei-iaes
Missing data are the absence of data items for a subject; they hide some information that may be important. In practice, missing data have been one major factor affecting data quality. Thus, Missing value imputation is needed. Methods such as hierarchical clustering and K-means clustering are not robust to missing data and may lose effectiveness even with a few missing values. Therefore, to improve the quality of data method for missing value imputation is needed. In this paper KNN and ARL based Imputation are introduced to impute missing values and accuracy of both the algorithms are measured by using normalized root mean sqare error. The result shows that ARL is more accurate and robust method for missing value estimation.
This paper introduces a new comparison base stable sorting algorithm, named RA sort. The RA sort
involves only the comparison of pair of elements in an array which ultimately sorts the array and does not
involve the comparison of each element with every other element. It tries to build upon the relationship
established between the elements in each pass. Instead of going for a blind comparison we prefer a
selective comparison to get an efficient method. Sorting is a fundamental operation in computer science.
This algorithm is analysed both theoretically and empirically to get a robust average case result. We have
performed its Empirical analysis and compared its performance with the well-known quick sort for various
input types. Although the theoretical worst case complexity of RA sort is Yworst(n) = O(n√), the
experimental results suggest an empirical Oemp(nlgn)1.333 time complexity for typical input instances, where
the parameter n characterizes the input size. The theoretical complexity is given for comparison operation.
We emphasize that the theoretical complexity is operation specific whereas the empirical one represents the
overall algorithmic complexity.
And Then There Are Algorithms - Danilo Poccia - Codemotion Rome 2018Codemotion
In machine learning, training large models on a massive amount of data usually improves results. Our customers report, however, that training such models and deploying them is either operationally prohibitive or outright impossible for them. We created a collection of machine learning algorithms that scale to any amount of data, including k-means clustering for data segmentation, factorization machines for recommendations, time-series forecasting, linear regression, topic modeling, and image classification. This talk will discuss those algorithms, understand where and how they can be used.
BINARY SINE COSINE ALGORITHMS FOR FEATURE SELECTION FROM MEDICAL DATAacijjournal
A well-constructed classification model highly depends on input feature subsets from a dataset, which may contain redundant, irrelevant, or noisy features. This challenge can be worse while dealing with medical datasets. The main aim of feature selection as a pre-processing task is to eliminate these features and select the most effective ones. In the literature, metaheuristic algorithms show a successful performance to find optimal feature subsets. In this paper, two binary metaheuristic algorithms named S-shaped binary Sine Cosine Algorithm (SBSCA) and V-shaped binary Sine Cosine Algorithm (VBSCA) are proposed for feature selection from the medical data. In these algorithms, the search space remains continuous, while a binary position vector is generated by two transfer functions S-shaped and V-shaped for each solution. The proposed algorithms are compared with four latest binary optimization algorithms over five medical datasets from the UCI repository. The experimental results confirm that using both bSCA variants enhance the accuracy of classification on these medical datasets compared to four other algorithms.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
The document presents an overview of mathematical models. It defines mathematical models as mathematical descriptions of real situations that make assumptions and simplifications about reality. There are three main types of models: linear, quadratic, and exponential models. The document discusses how to develop a mathematical model by comparing model predictions to real data. It provides an example of a differential equation model of the spread of a contagious flu.
This document presents a new method for creating proxy models called Simulated Annealing Programming (SAP). SAP uses simulated annealing optimization on a tree structure to find the equation that best predicts outputs with minimum error. The authors apply SAP to create a model for predicting gas compressor torque based on fuel rate and speed. They find the SAP model is highly accurate, roughly independent of internal parameters, and has smaller overestimation/underestimation compared to other methods like polynomials and neural networks.
A review of automatic differentiationand its efficient implementationssuserfa7e73
Automatic differentiation is a powerful tool for automatically calculating derivatives of mathematical functions and algorithms. It works by expressing the target function as a sequence of elementary operations and then applying the chain rule to differentiate each operation. This can be done using either forward or reverse mode. Forward mode calculates how changes in inputs propagate through the function to influence the outputs, while reverse mode calculates how changes in outputs backpropagate to influence the inputs. Both modes require performing the computation twice - once for the forward pass and once for the derivative pass. Careful implementation is required to make automatic differentiation efficient in terms of speed and memory usage.
This document presents new certified optimal solutions found by the Charibde algorithm for six difficult benchmark optimization problems. Charibde combines an evolutionary algorithm and interval-based methods in a cooperative framework. It has achieved optimality proofs for five bound-constrained problems and one nonlinearly constrained problem. These problems are highly multimodal and some had not been solved before even with approximate methods. The document also compares Charibde's performance to other state-of-the-art solvers, showing it is highly competitive while providing reliable optimality proofs.
This document discusses numerical integration and solving ordinary differential equations (ODEs) numerically in MATLAB. It describes built-in integration functions such as quad, quadl, and trapz that can integrate functions and data points. It also outlines the basic steps for solving first-order ODEs numerically, including writing the ODE as an initial value problem, defining the derivative function, selecting an ODE solver, and using the solver to generate the solution over a time span. An example demonstrates solving an ODE numerically using ode45 and plotting the results.
Optimization is considered to be one of the pillars of statistical learning and also plays a major role in the design and development of intelligent systems such as search engines, recommender systems, and speech and image recognition software. Machine Learning is the study that gives the computers the ability to learn and also the ability to think without being explicitly programmed. A computer is said to learn from an experience with respect to a specified task and its performance related to that task. The machine learning algorithms are applied to the problems to reduce efforts. Machine learning algorithms are used for manipulating the data and predict the output for the new data with high precision and low uncertainty. The optimization algorithms are used to make rational decisions in an environment of uncertainty and imprecision. In this paper a methodology is presented to use the efficient optimization algorithm as an alternative for the gradient descent machine learning algorithm as an optimization algorithm.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Machine learning and linear regression programmingSoumya Mukherjee
Overview of AI and ML
Terminology awareness
Applications in real world
Use cases within Nokia
Types of Learning
Regression
Classification
Clustering
Linear Regression Single Variable with python
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Medical Conferences, Pharma Conferences, Engineering Conferences, Science Conferences, Manufacturing Conferences, Social Science Conferences, Business Conferences, Scientific Conferences Malaysia, Thailand, Singapore, Hong Kong, Dubai, Turkey 2014 2015 2016
Global Research & Development Services (GRDS) is a leading academic event organizer, publishing Open Access Journals and conducting several professionally organized international conferences all over the globe annually. GRDS aims to disseminate knowledge and innovation with the help of its International Conferences and open access publications. GRDS International conferences are world-class events which provide a meaningful platform for researchers, students, academicians, institutions, entrepreneurs, industries and practitioners to create, share and disseminate knowledge and innovation and to develop long-lasting network and collaboration.
GRDS is a blend of Open Access Publications and world-wide International Conferences and Academic events. The prime mission of GRDS is to make continuous efforts in transforming the lives of people around the world through education, application of research and innovative ideas.
Global Research & Development Services (GRDS) is also active in the field of Research Funding, Research Consultancy, Training and Workshops along with International Conferences and Open Access Publications.
International Conferences 2014 – 2015
Malaysia Conferences, Thailand Conferences, Singapore Conferences, Hong Kong Conferences, Dubai Conferences, Turkey Conferences, Conference Listing, Conference Alerts
Design of optimized Interval Arithmetic MultiplierVLSICS Design
Many DSP and Control applications that require the user to know how various numerical errors(uncertainty) affect the result. This uncertainty is eliminated by replacing non-interval values with intervals. Since most DSPs operate in real time environments, fast processors are required to implement interval arithmetic. The goal is to develop a platform in which Interval Arithmetic operations are performed at the same computational speed as present day signal processors. So we have proposed the design and implementation of Interval Arithmetic multiplier, which operates with IEEE 754 numbers. The proposed unit consists of a floating point CSD multiplier, Interval operation selector. This architecture implements an algorithm which is faster than conventional algorithm of Interval multiplier . The cost overhead of the proposed unit is 30% with respect to a conventional floating point multiplier. The
performance of proposed architecture is better than that of a conventional CSD floating-point multiplier, as it can perform both interval multiplication and floating-point multiplication as well as Interval comparisons
IRJET - Movie Genre Prediction from Plot Summaries by Comparing Various C...IRJET Journal
This document discusses predicting movie genres from plot summaries using various classification algorithms. It analyzes Multinomial Naive Bayes, Logistic Regression, Random Forest, and Stochastic Gradient Descent algorithms on a dataset of over 40,000 movie plots labeled with 12 genres. It finds that Multinomial Naive Bayes performs best, achieving the highest AUC scores for predicting each genre individually. It then builds separate classifiers for each genre using the best performing algorithm to predict the genre of new movie plots.
On the Performance of the Pareto Set Pursuing (PSP) Method for Mixed-Variable...Amir Ziai
This document describes a study on modifying the Pareto Set Pursuing (PSP) method to solve multi-objective optimization problems with mixed continuous and discrete variables. The PSP method was originally developed for problems with only continuous variables. The modifications allow it to handle mixed variable problems. The performance of the modified PSP method is compared to other multi-objective algorithms based on metrics like efficiency, robustness, and closeness to the true Pareto front with a limited number of function evaluations. Preliminary results on benchmark problems and two engineering design examples show that the modified PSP is competitive when the number of function evaluations is limited, but its performance decreases as the number of design variables increases.
On the Performance of the Pareto Set Pursuing (PSP) Method for Mixed-Variable...
Similar to APPROACHES IN USING EXPECTATIONMAXIMIZATION ALGORITHM FOR MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF A CONSTRAINED STATE SPACE MODEL WITH AN EXTERNAL INPUT SERIES
COMPARING THE CUCKOO ALGORITHM WITH OTHER ALGORITHMS FOR ESTIMATING TWO GLSD ...csandit
This study introduces and compares different methods for estimating the two parameters of
generalized logarithmic series distribution. These methods are the cuckoo search optimization,
maximum likelihood estimation, and method of moments algorithms. All the required
derivations and basic steps of each algorithm are explained. The applications for these
algorithms are implemented through simulations using different sample sizes (n = 15, 25, 50,
100). Results are compared using the statistical measure mean square error.
The document discusses using clustering models like subtractive fuzzy clustering (SFC) and fuzzy c-means clustering (FCM) to generate an adaptive neuro-fuzzy inference system (ANFIS) for medical diagnoses. Experimental results on medical diagnosis datasets show that ANFIS models using SFC and FCM clustering (ANFIS-SFC and ANFIS-FCM) had better average training and checking errors compared to ANFIS without clustering. Specifically, ANFIS-SFC performed best using backpropagation learning, while ANFIS-FCM performed best using a hybrid learning model. Clustering the datasets without ANFIS was also able to identify different disease clusters.
This document summarizes the derivation of the EM algorithm for parameter estimation in a mixed normal model. It begins by presenting the log-likelihood function and derives update equations for the mean (μk) and covariance (Σk) parameters of each normal component. An experimental design is then described to statistically analyze the performance of the EM algorithm under different conditions. The results show that the EM estimates are most accurate when the normal components have distinct means and covariances, and when more training data is available. Interactions between factors are also examined.
MIXTURES OF TRAINED REGRESSION CURVESMODELS FOR HANDRITTEN ARABIC CHARACTER R...ijaia
In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2nd order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We proceed then, by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.
- The document details a state space solver approach for analog mixed-signal simulations using SystemC. It models analog circuits as sets of linear differential equations and solves them using the Runge-Kutta method of numerical integration.
- Two examples are provided: a digital voltage regulator simulation and a digital phase locked loop simulation. Both analog circuits are modeled in state space and simulated alongside a digital design to verify mixed-signal behavior.
- The state space approach allows modeling analog circuits without transistor-level details, improving simulation speed over traditional mixed-mode simulations while still capturing system-level behavior.
Fuzzy clustering algorithm can not obtain good clustering effect when the sample characteristic is not obvious and need to determine the number of clusters firstly. For thi0s reason, this paper proposes an adaptive fuzzy kernel clustering algorithm. The algorithm firstly use the adaptive function of clustering number to calculate the optimal clustering number, then the samples of input space is mapped to highdimensional feature space using gaussian kernel and clustering in the feature space. The Matlab simulation results confirmed that the algorithm's performance has greatly improvement than classical clustering algorithm and has faster convergence speed and more accurate clustering results.
Fuzzy clustering algorithm can not obtain good clustering effect when the sample characteristic is not
obvious and need to determine the number of clusters firstly. For thi0s reason, this paper proposes an
adaptive fuzzy kernel clustering algorithm. The algorithm firstly use the adaptive function of clustering
number to calculate the optimal clustering number, then the samples of input space is mapped to highdimensional
feature space using gaussian kernel and clustering in the feature space. The Matlab simulation
results confirmed that the algorithm's performance has greatly improvement than classical clustering algorithm and has faster convergence speed and more accurate clustering results
On Selection of Periodic Kernels Parameters in Time Series Prediction cscpconf
In the paper the analysis of the periodic kernels parameters is described. Periodic kernels can
be used for the prediction task, performed as the typical regression problem. On the basis of the
Periodic Kernel Estimator (PerKE) the prediction of real time series is performed. As periodic
kernels require the setting of their parameters it is necessary to analyse their influence on the
prediction quality. This paper describes an easy methodology of finding values of parameters of
periodic kernels. It is based on grid search. Two different error measures are taken into
consideration as the prediction qualities but lead to comparable results. The methodology was
tested on benchmark and real datasets and proved to give satisfactory results.
ON SELECTION OF PERIODIC KERNELS PARAMETERS IN TIME SERIES PREDICTIONcscpconf
In the paper the analysis of the periodic kernels parameters is described. Periodic kernels can
be used for the prediction task, performed as the typical regression problem. On the basis of the
Periodic Kernel Estimator (PerKE) the prediction of real time series is performed. As periodic
kernels require the setting of their parameters it is necessary to analyse their influence on the
prediction quality. This paper describes an easy methodology of finding values of parameters of
periodic kernels. It is based on grid search. Two different error measures are taken into
consideration as the prediction qualities but lead to comparable results. The methodology was
tested on benchmark and real datasets and proved to give satisfactory results.
A GENERALIZED SAMPLING THEOREM OVER GALOIS FIELD DOMAINS FOR EXPERIMENTAL DESIGNcscpconf
In this paper, the sampling theorem for bandlimited functions over
domains is
generalized to one over ∏
domains. The generalized theorem is applicable to the
experimental design model in which each factor has a different number of levels and enables us
to estimate the parameters in the model by using Fourier transforms. Moreover, the relationship
between the proposed sampling theorem and orthogonal arrays is also provided.
A Generalized Sampling Theorem Over Galois Field Domains for Experimental Des...csandit
In this paper, the sampling theorem for bandlimited functions over
domains is
generalized to one over ∏
domains. The generalized theorem is applicable to the
experimental design model in which each factor has a different number of levels and enables us
to estimate the parameters in the model by using Fourier transforms. Moreover, the relationship
between the proposed sampling theorem and orthogonal arrays is also provided.
KEY
PREDICTION MODELS BASED ON MAX-STEMS Episode Two: Combinatorial Approachahmet furkan emrehan
This document describes prediction models that use combinations of stems from documents to make predictions, as an extension of models from the previous chapter that used individual stems. It defines the parameters and components adapted for the combinatorial approach, including combinations of stems (comboijs) from documents and the counts and probabilities associated with them. It then presents the general scheme for prediction models using the combinatorial approach and describes 5 specific models, noting that for s=1 the models are equivalent to those from the previous chapter. It introduces an application of these models to news data from a Turkish website.
We consider the problem of finding anomalies in high-dimensional data using popular PCA based anomaly scores. The naive algorithms for computing these scores explicitly compute the PCA of the covariance matrix which uses space quadratic in the dimensionality of the data. We give the first streaming algorithms
that use space that is linear or sublinear in the dimension. We prove general results showing that any sketch of a matrix that satisfies a certain operator norm guarantee can be used to approximate these scores. We instantiate these results with powerful matrix sketching techniques such as Frequent Directions and random projections to derive efficient and practical algorithms for these problems, which we validate over real-world data sets. Our main technical contribution is to prove matrix perturbation
inequalities for operators arising in the computation of these measures.
-Proceedings: https://arxiv.org/abs/1804.03065
-Origin: https://arxiv.org/abs/1804.03065
This document analyzes and models a rotational mechanical system to determine its time domain characteristics. The system is modeled using a second-order differential equation and Laplace transform. MATLAB is used to verify results and simulate the system. Key findings include:
1) The system has poles at -8 ± j20, a damping ratio of 0.3714, and 28.46% overshoot.
2) The impulse and step responses are determined and match simulations in MATLAB.
3) A state space model is developed using A, B, C, and D matrices to reduce the system to first-order equations.
1) The paper introduces the influence function for interpreting black-box machine learning models. The influence function traces a model's predictions back to the training data by examining how the model's parameters would change if a particular training point was removed or perturbed.
2) The influence function approximates this change in parameters by assuming a quadratic approximation to the empirical risk function around the learned parameters and taking a single Newton step. It shows the parameter change due to removing a point is approximated by the influence function.
3) The paper demonstrates how the influence function can be used to understand model behavior, find adversarial examples, debug issues, and correct errors, among other applications. It also proposes practical methods to compute the influence function for
Hierarchical algorithms of quasi linear ARX Neural Networks for Identificatio...Yuyun Wabula
This document summarizes a research paper on hierarchical algorithms for training a quasi-linear ARX neural network model for identification of nonlinear systems. The key points are:
1) A hierarchical algorithm is proposed that first estimates the system using a linear sub-model and least squares estimation to obtain linear parameters. It then trains a neural network nonlinear sub-model to refine the errors of the linear sub-model.
2) The linear parameter estimates are fixed and used as biases for the neural network, which is trained to minimize the residual errors of the linear sub-model.
3) This hierarchical approach separates the identification into linear and nonlinear parts, allowing analysis of the system linearly while also capturing nonlinearities. The neural
On selection of periodic kernels parameters in time series predictioncsandit
This document discusses parameter selection for periodic kernels used in time series prediction. Periodic kernels are a type of kernel function used in kernel regression to perform nonparametric time series prediction. The document examines how the parameters of two periodic kernels - the first periodic kernel (FPK) and second periodic kernel (SPK) - influence prediction error. It presents an easy methodology for finding parameter values based on grid search. This methodology was tested on benchmark and real datasets and showed satisfactory results.
Cone Crusher Model Identification Using Block-Oriented Systems with Orthonorm...ijctcm
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models are tested and the MATLAB simulation results are compared. The mean square error is used for models validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the quality of approximation plant dynamics. The mean square error for this model is 11% on average throughout the considered range of the external disturbances amplitude. The analysis also showed that Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener model will be used to the design nonlinear model predictive control application
In this paper, block-oriented systems with linear parts based on Laguerre functions is used to
approximation of a cone crusher dynamics. Adaptive recursive least squares algorithm is used to
identification of Laguerre model. Various structures of Hammerstein, Wiener, Hammerstein-Wiener models
are tested and the MATLAB simulation results are compared. The mean square error is used for models
validation.It has been found that Hammerstein-Wiener with orthonormal basis functions improves the
quality of approximation plant dynamics. The mean square error for this model is 11% on average
throughout the considered range of the external disturbances amplitude. The analysis also showed that
Wiener model cannot provide sufficient approximation accuracy of the cone crusher dynamics. During the
process it is unstable due to the high sensitivity to disturbances on the output.The Hammerstein-Wiener
model will be used to the design nonlinear model predictive control application.
Scikit-learn is a popular machine learning library for Python that provides simple and efficient tools for data mining and data analysis. It includes algorithms for classification, regression, clustering and dimensionality reduction. The scikit-learn API is designed for consistency, with common estimator, predictor and transformer interfaces that allow algorithms to be used interchangeably. This standardized interface helps users easily try different algorithms and preprocessing techniques for their machine learning tasks.
Similar to APPROACHES IN USING EXPECTATIONMAXIMIZATION ALGORITHM FOR MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF A CONSTRAINED STATE SPACE MODEL WITH AN EXTERNAL INPUT SERIES (20)
ANALYSIS OF LAND SURFACE DEFORMATION GRADIENT BY DINSAR cscpconf
The progressive development of Synthetic Aperture Radar (SAR) systems diversify the exploitation of the generated images by these systems in different applications of geoscience. Detection and monitoring surface deformations, procreated by various phenomena had benefited from this evolution and had been realized by interferometry (InSAR) and differential interferometry (DInSAR) techniques. Nevertheless, spatial and temporal decorrelations of the interferometric couples used, limit strongly the precision of analysis results by these techniques. In this context, we propose, in this work, a methodological approach of surface deformation detection and analysis by differential interferograms to show the limits of this technique according to noise quality and level. The detectability model is generated from the deformation signatures, by simulating a linear fault merged to the images couples of ERS1 / ERS2 sensors acquired in a region of the Algerian south.
4D AUTOMATIC LIP-READING FOR SPEAKER'S FACE IDENTIFCATIONcscpconf
A novel based a trajectory-guided, concatenating approach for synthesizing high-quality image real sample renders video is proposed . The lips reading automated is seeking for modeled the closest real image sample sequence preserve in the library under the data video to the HMM predicted trajectory. The object trajectory is modeled obtained by projecting the face patterns into an KDA feature space is estimated. The approach for speaker's face identification by using synthesise the identity surface of a subject face from a small sample of patterns which sparsely each the view sphere. An KDA algorithm use to the Lip-reading image is discrimination, after that work consisted of in the low dimensional for the fundamental lip features vector is reduced by using the 2D-DCT.The mouth of the set area dimensionality is ordered by a normally reduction base on the PCA to obtain the Eigen lips approach, their proposed approach by[33]. The subjective performance results of the cost function under the automatic lips reading modeled , which wasn’t illustrate the superior performance of the
method.
MOVING FROM WATERFALL TO AGILE PROCESS IN SOFTWARE ENGINEERING CAPSTONE PROJE...cscpconf
Universities offer software engineering capstone course to simulate a real world-working environment in which students can work in a team for a fixed period to deliver a quality product. The objective of the paper is to report on our experience in moving from Waterfall process to Agile process in conducting the software engineering capstone project. We present the capstone course designs for both Waterfall driven and Agile driven methodologies that highlight the structure, deliverables and assessment plans.To evaluate the improvement, we conducted a survey for two different sections taught by two different instructors to evaluate students’ experience in moving from traditional Waterfall model to Agile like process. Twentyeight students filled the survey. The survey consisted of eight multiple-choice questions and an open-ended question to collect feedback from students. The survey results show that students were able to attain hands one experience, which simulate a real world-working environment. The results also show that the Agile approach helped students to have overall better design and avoid mistakes they have made in the initial design completed in of the first phase of the capstone project. In addition, they were able to decide on their team capabilities, training needs and thus learn the required technologies earlier which is reflected on the final product quality
PROMOTING STUDENT ENGAGEMENT USING SOCIAL MEDIA TECHNOLOGIEScscpconf
This document discusses using social media technologies to promote student engagement in a software project management course. It describes the course and objectives of enhancing communication. It discusses using Facebook for 4 years, then switching to WhatsApp based on student feedback, and finally introducing Slack to enable personalized team communication. Surveys found students engaged and satisfied with all three tools, though less familiar with Slack. The conclusion is that social media promotes engagement but familiarity with the tool also impacts satisfaction.
A SURVEY ON QUESTION ANSWERING SYSTEMS: THE ADVANCES OF FUZZY LOGICcscpconf
In real world computing environment with using a computer to answer questions has been a human dream since the beginning of the digital era, Question-answering systems are referred to as intelligent systems, that can be used to provide responses for the questions being asked by the user based on certain facts or rules stored in the knowledge base it can generate answers of questions asked in natural , and the first main idea of fuzzy logic was to working on the problem of computer understanding of natural language, so this survey paper provides an overview on what Question-Answering is and its system architecture and the possible relationship and
different with fuzzy logic, as well as the previous related research with respect to approaches that were followed. At the end, the survey provides an analytical discussion of the proposed QA models, along or combined with fuzzy logic and their main contributions and limitations.
DYNAMIC PHONE WARPING – A METHOD TO MEASURE THE DISTANCE BETWEEN PRONUNCIATIONS cscpconf
Human beings generate different speech waveforms while speaking the same word at different times. Also, different human beings have different accents and generate significantly varying speech waveforms for the same word. There is a need to measure the distances between various words which facilitate preparation of pronunciation dictionaries. A new algorithm called Dynamic Phone Warping (DPW) is presented in this paper. It uses dynamic programming technique for global alignment and shortest distance measurements. The DPW algorithm can be used to enhance the pronunciation dictionaries of the well-known languages like English or to build pronunciation dictionaries to the less known sparse languages. The precision measurement experiments show 88.9% accuracy.
INTELLIGENT ELECTRONIC ASSESSMENT FOR SUBJECTIVE EXAMS cscpconf
In education, the use of electronic (E) examination systems is not a novel idea, as Eexamination systems have been used to conduct objective assessments for the last few years. This research deals with randomly designed E-examinations and proposes an E-assessment system that can be used for subjective questions. This system assesses answers to subjective questions by finding a matching ratio for the keywords in instructor and student answers. The matching ratio is achieved based on semantic and document similarity. The assessment system is composed of four modules: preprocessing, keyword expansion, matching, and grading. A survey and case study were used in the research design to validate the proposed system. The examination assessment system will help instructors to save time, costs, and resources, while increasing efficiency and improving the productivity of exam setting and assessments.
TWO DISCRETE BINARY VERSIONS OF AFRICAN BUFFALO OPTIMIZATION METAHEURISTICcscpconf
African Buffalo Optimization (ABO) is one of the most recent swarms intelligence based metaheuristics. ABO algorithm is inspired by the buffalo’s behavior and lifestyle. Unfortunately, the standard ABO algorithm is proposed only for continuous optimization problems. In this paper, the authors propose two discrete binary ABO algorithms to deal with binary optimization problems. In the first version (called SBABO) they use the sigmoid function and probability model to generate binary solutions. In the second version (called LBABO) they use some logical operator to operate the binary solutions. Computational results on two knapsack problems (KP and MKP) instances show the effectiveness of the proposed algorithm and their ability to achieve good and promising solutions.
DETECTION OF ALGORITHMICALLY GENERATED MALICIOUS DOMAINcscpconf
In recent years, many malware writers have relied on Dynamic Domain Name Services (DDNS) to maintain their Command and Control (C&C) network infrastructure to ensure a persistence presence on a compromised host. Amongst the various DDNS techniques, Domain Generation Algorithm (DGA) is often perceived as the most difficult to detect using traditional methods. This paper presents an approach for detecting DGA using frequency analysis of the character distribution and the weighted scores of the domain names. The approach’s feasibility is demonstrated using a range of legitimate domains and a number of malicious algorithmicallygenerated domain names. Findings from this study show that domain names made up of English characters “a-z” achieving a weighted score of < 45 are often associated with DGA. When a weighted score of < 45 is applied to the Alexa one million list of domain names, only 15% of the domain names were treated as non-human generated.
GLOBAL MUSIC ASSET ASSURANCE DIGITAL CURRENCY: A DRM SOLUTION FOR STREAMING C...cscpconf
The document proposes a blockchain-based digital currency and streaming platform called GoMAA to address issues of piracy in the online music streaming industry. Key points:
- GoMAA would use a digital token on the iMediaStreams blockchain to enable secure dissemination and tracking of streamed content. Content owners could control access and track consumption of released content.
- Original media files would be converted to a Secure Portable Streaming (SPS) format, embedding watermarks and smart contract data to indicate ownership and enable validation on the blockchain.
- A browser plugin would provide wallets for fans to collect GoMAA tokens as rewards for consuming content, incentivizing participation and addressing royalty discrepancies by recording
IMPORTANCE OF VERB SUFFIX MAPPING IN DISCOURSE TRANSLATION SYSTEMcscpconf
This document discusses the importance of verb suffix mapping in discourse translation from English to Telugu. It explains that after anaphora resolution, the verbs must be changed to agree with the gender, number, and person features of the subject or anaphoric pronoun. Verbs in Telugu inflect based on these features, while verbs in English only inflect based on number and person. Several examples are provided that demonstrate how the Telugu verb changes based on whether the subject or pronoun is masculine, feminine, neuter, singular or plural. Proper verb suffix mapping is essential for generating natural and coherent translations while preserving the context and meaning of the original discourse.
EXACT SOLUTIONS OF A FAMILY OF HIGHER-DIMENSIONAL SPACE-TIME FRACTIONAL KDV-T...cscpconf
In this paper, based on the definition of conformable fractional derivative, the functional
variable method (FVM) is proposed to seek the exact traveling wave solutions of two higherdimensional
space-time fractional KdV-type equations in mathematical physics, namely the
(3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-
dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony
(GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which
contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave
solutions, have many potential applications in mathematical physics and engineering. The
simplicity and reliability of the proposed method is verified.
AUTOMATED PENETRATION TESTING: AN OVERVIEWcscpconf
The document discusses automated penetration testing and provides an overview. It compares manual and automated penetration testing, noting that automated testing allows for faster, more standardized and repeatable tests but has limitations in developing new exploits. It also reviews some current automated penetration testing methodologies and tools, including those using HTTP/TCP/IP attacks, linking common scanning tools, a Python-based tool targeting databases, and one using POMDPs for multi-step penetration test planning under uncertainty. The document concludes that automated testing is more efficient than manual for known vulnerabilities but cannot replace manual testing for discovering new exploits.
CLASSIFICATION OF ALZHEIMER USING fMRI DATA AND BRAIN NETWORKcscpconf
Since the mid of 1990s, functional connectivity study using fMRI (fcMRI) has drawn increasing
attention of neuroscientists and computer scientists, since it opens a new window to explore
functional network of human brain with relatively high resolution. BOLD technique provides
almost accurate state of brain. Past researches prove that neuro diseases damage the brain
network interaction, protein- protein interaction and gene-gene interaction. A number of
neurological research paper also analyse the relationship among damaged part. By
computational method especially machine learning technique we can show such classifications.
In this paper we used OASIS fMRI dataset affected with Alzheimer’s disease and normal
patient’s dataset. After proper processing the fMRI data we use the processed data to form
classifier models using SVM (Support Vector Machine), KNN (K- nearest neighbour) & Naïve
Bayes. We also compare the accuracy of our proposed method with existing methods. In future,
we will other combinations of methods for better accuracy.
VALIDATION METHOD OF FUZZY ASSOCIATION RULES BASED ON FUZZY FORMAL CONCEPT AN...cscpconf
The document proposes a new validation method for fuzzy association rules based on three steps: (1) applying the EFAR-PN algorithm to extract a generic base of non-redundant fuzzy association rules using fuzzy formal concept analysis, (2) categorizing the extracted rules into groups, and (3) evaluating the relevance of the rules using structural equation modeling, specifically partial least squares. The method aims to address issues with existing fuzzy association rule extraction algorithms such as large numbers of extracted rules, redundancy, and difficulties with manual validation.
PROBABILITY BASED CLUSTER EXPANSION OVERSAMPLING TECHNIQUE FOR IMBALANCED DATAcscpconf
In many applications of data mining, class imbalance is noticed when examples in one class are
overrepresented. Traditional classifiers result in poor accuracy of the minority class due to the
class imbalance. Further, the presence of within class imbalance where classes are composed of
multiple sub-concepts with different number of examples also affect the performance of
classifier. In this paper, we propose an oversampling technique that handles between class and
within class imbalance simultaneously and also takes into consideration the generalization
ability in data space. The proposed method is based on two steps- performing Model Based
Clustering with respect to classes to identify the sub-concepts; and then computing the
separating hyperplane based on equal posterior probability between the classes. The proposed
method is tested on 10 publicly available data sets and the result shows that the proposed
method is statistically superior to other existing oversampling methods.
CHARACTER AND IMAGE RECOGNITION FOR DATA CATALOGING IN ECOLOGICAL RESEARCHcscpconf
Data collection is an essential, but manpower intensive procedure in ecological research. An
algorithm was developed by the author which incorporated two important computer vision
techniques to automate data cataloging for butterfly measurements. Optical Character
Recognition is used for character recognition and Contour Detection is used for imageprocessing.
Proper pre-processing is first done on the images to improve accuracy. Although
there are limitations to Tesseract’s detection of certain fonts, overall, it can successfully identify
words of basic fonts. Contour detection is an advanced technique that can be utilized to
measure an image. Shapes and mathematical calculations are crucial in determining the precise
location of the points on which to draw the body and forewing lines of the butterfly. Overall,
92% accuracy were achieved by the program for the set of butterflies measured.
SOCIAL MEDIA ANALYTICS FOR SENTIMENT ANALYSIS AND EVENT DETECTION IN SMART CI...cscpconf
Smart cities utilize Internet of Things (IoT) devices and sensors to enhance the quality of the city
services including energy, transportation, health, and much more. They generate massive
volumes of structured and unstructured data on a daily basis. Also, social networks, such as
Twitter, Facebook, and Google+, are becoming a new source of real-time information in smart
cities. Social network users are acting as social sensors. These datasets so large and complex
are difficult to manage with conventional data management tools and methods. To become
valuable, this massive amount of data, known as 'big data,' needs to be processed and
comprehended to hold the promise of supporting a broad range of urban and smart cities
functions, including among others transportation, water, and energy consumption, pollution
surveillance, and smart city governance. In this work, we investigate how social media analytics
help to analyze smart city data collected from various social media sources, such as Twitter and
Facebook, to detect various events taking place in a smart city and identify the importance of
events and concerns of citizens regarding some events. A case scenario analyses the opinions of
users concerning the traffic in three largest cities in the UAE
SOCIAL NETWORK HATE SPEECH DETECTION FOR AMHARIC LANGUAGEcscpconf
The anonymity of social networks makes it attractive for hate speech to mask their criminal
activities online posing a challenge to the world and in particular Ethiopia. With this everincreasing
volume of social media data, hate speech identification becomes a challenge in
aggravating conflict between citizens of nations. The high rate of production, has become
difficult to collect, store and analyze such big data using traditional detection methods. This
paper proposed the application of apache spark in hate speech detection to reduce the
challenges. Authors developed an apache spark based model to classify Amharic Facebook
posts and comments into hate and not hate. Authors employed Random forest and Naïve Bayes
for learning and Word2Vec and TF-IDF for feature selection. Tested by 10-fold crossvalidation,
the model based on word2vec embedding performed best with 79.83%accuracy. The
proposed method achieve a promising result with unique feature of spark for big data.
GENERAL REGRESSION NEURAL NETWORK BASED POS TAGGING FOR NEPALI TEXTcscpconf
This article presents Part of Speech tagging for Nepali text using General Regression Neural
Network (GRNN). The corpus is divided into two parts viz. training and testing. The network is
trained and validated on both training and testing data. It is observed that 96.13% words are
correctly being tagged on training set whereas 74.38% words are tagged correctly on testing
data set using GRNN. The result is compared with the traditional Viterbi algorithm based on
Hidden Markov Model. Viterbi algorithm yields 97.2% and 40% classification accuracies on
training and testing data sets respectively. GRNN based POS Tagger is more consistent than the
traditional Viterbi decoding technique.
Pushing the limits of ePRTC: 100ns holdover for 100 daysAdtran
At WSTS 2024, Alon Stern explored the topic of parametric holdover and explained how recent research findings can be implemented in real-world PNT networks to achieve 100 nanoseconds of accuracy for up to 100 days.
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?Speck&Tech
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
Programming Foundation Models with DSPy - Meetup SlidesZilliz
Prompting language models is hard, while programming language models is easy. In this talk, I will discuss the state-of-the-art framework DSPy for programming foundation models with its powerful optimizers and runtime constraint system.
UiPath Test Automation using UiPath Test Suite series, part 5DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 5. In this session, we will cover CI/CD with devops.
Topics covered:
CI/CD with in UiPath
End-to-end overview of CI/CD pipeline with Azure devops
Speaker:
Lyndsey Byblow, Test Suite Sales Engineer @ UiPath, Inc.
“An Outlook of the Ongoing and Future Relationship between Blockchain Technologies and Process-aware Information Systems.” Invited talk at the joint workshop on Blockchain for Information Systems (BC4IS) and Blockchain for Trusted Data Sharing (B4TDS), co-located with with the 36th International Conference on Advanced Information Systems Engineering (CAiSE), 3 June 2024, Limassol, Cyprus.
HCL Notes and Domino License Cost Reduction in the World of DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
Join HCL Ambassador Marc Thomas in this webinar with a special guest appearance from Franz Walder. It will give you the tools and know-how to stay on top of what is going on with Domino licensing. You will be able lower your cost through an optimized configuration and keep it low going forward.
These topics will be covered
- Reducing license cost by finding and fixing misconfigurations and superfluous accounts
- How do CCB and CCX licenses really work?
- Understanding the DLAU tool and how to best utilize it
- Tips for common problem areas, like team mailboxes, functional/test users, etc
- Practical examples and best practices to implement right away
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/building-and-scaling-ai-applications-with-the-nx-ai-manager-a-presentation-from-network-optix/
Robin van Emden, Senior Director of Data Science at Network Optix, presents the “Building and Scaling AI Applications with the Nx AI Manager,” tutorial at the May 2024 Embedded Vision Summit.
In this presentation, van Emden covers the basics of scaling edge AI solutions using the Nx tool kit. He emphasizes the process of developing AI models and deploying them globally. He also showcases the conversion of AI models and the creation of effective edge AI pipelines, with a focus on pre-processing, model conversion, selecting the appropriate inference engine for the target hardware and post-processing.
van Emden shows how Nx can simplify the developer’s life and facilitate a rapid transition from concept to production-ready applications.He provides valuable insights into developing scalable and efficient edge AI solutions, with a strong focus on practical implementation.
GraphRAG for Life Science to increase LLM accuracyTomaz Bratanic
GraphRAG for life science domain, where you retriever information from biomedical knowledge graphs using LLMs to increase the accuracy and performance of generated answers
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APPROACHES IN USING EXPECTATIONMAXIMIZATION ALGORITHM FOR MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF A CONSTRAINED STATE SPACE MODEL WITH AN EXTERNAL INPUT SERIES
2. 58 Computer Science & Information Technology (CS & IT)
൜
ݔ௧ = αݔ௧ିଵ + ߛݑ୲ + ݁୲
ݕ௧ = ℎݔ௧ + ݓ௧
, (1)
where ݔ௧ is the invisible brand equity, ݑ୲ is the investment, the external input, ݕ௧ is the brand
performance, the output, at a certain step .ݐ The transition coefficient, α(|ߙ| < 1), and the input
coefficient, ߛ, are parameters of interest. The observation coefficient, ℎ, is constrained to be a
constant, i.e., ℎ=1. The observation noise, ݓ௧, the process noise,݁௧, and the initial state,ݔ, at each
step, {x0, ݁ଵ, ..., ݁୲, ݓଵ ... ݓ௧}, are all assumed to be mutually independent, where
ݓ௧~ܰ(0, ߪ௪
ଶ
),݁௧~ܰ(0, ߪ
ଶ
), and ݔ~ܰ(ߤ, ߪ
ଶ
).
As exemplified in Equation (1) where ℎ=1, a constrained state-space modemeans that some
parameters, some elements in the parameter matrix of a Kalman filter, are fixed or shared thus not
all of them have to be estimated. Conversely, if the model is unconstrained, any parameters or any
elements of each parameter matrix will be estimated. Moreover, the model has an time-variant
external input series, ݑ୲. By the way, parameter estimation of state space models with external
inputs can be seen as supervised problems while that of state space models without external
inputs can be treated as unsupervised problems.
Maximum likelihood estimation (MLE) [2] is used to obtain the time-invariant parameters of the
Kalman filter from input, ݑ୲, and the output, ݕ௧. Because of the existence of hidden variables, ݔ௧,
in the formulated likelihood function, expectation-maximization (EM) algorithm [3], an iterative
method, is used to complete MLE of parameters in state-space models.
The approaches for the implementation of EM algorithm in the MLE of unconstrained state-space
model are delivered in [4]-[7]. The approaches for certain constrained state-space models are
covered in [7]-[10]. Since those constraints are quite specific, the approaches proposed are lack of
generalicity. On the other hand, approaches for state-space models with external inputs are
usually not provided except in [7]-[9]. However, the state space mode in [7]-[9] is not typical
because the inputs are constants or do not affect the hidden variable. Especially in [5], the
external input is actually a constant, which is a parameter to be estimated. Therefore, as we know
from extant literature, no innovative methods are explored to estimate the unknown parameters of
such constrained state-space modelsin the recent years.
Our research is to find appropriate methods for the supervised problem: using EM algorithm for
the MLE of those constrained state-space models who have external inputs. In this paper, we use
the model represented by Equation (1) as an example. Our target is to estimate the parameters,α,
ߛ, ߪ, ߪ௪, ߤ and ߪ. Our work is carried out mainly in two phases: (i) initial guessing using our
innovative approach, and (ii) implementation of MLE using EM algorithm with approaches
different from those in extant literature. In addition, if the sample size is large, we use the
asymptotic variances of the estimated parameters to check the accuracy of the estimation. If the
sample size is small, we introduced bootstrapping to examine the distribution of the estimated
parameters.
2. INITIAL GUESSING
The initial guess is performed through two steps. Firstly, the system parameter ߙ and the
variances ߪ, ߪ௪ and ߪ are guessed using autocovariance of the observations. Then the initial
state mean ߤ and input parameter γ are guessed using weighted linear square.
2.1.GuessingSystem Parameter and the Variances
Denote ߟ௧ = ∑ ߙ
݁௧ି
ஶ
ୀ , from (1) it can be proved that
3. Computer Science & Information Technology (CS & IT) 59
ݔ௧ =
ఊ௨౪
ଵିఈ
+ ߟ௧ . (2)
For ℎ = 0,1,2 … …, we can obtain the covariance and autocovariance of ߟ௧ as
ߛఎ(ℎ) =
మఈ
ଵିఈమ, (3)
while it is obvious that
σ
ଶ
=
మ
ଵିమ. (4)
which means that we don’t have to estimate ߪ and ߪ separately, as was performed in extant
literature.
Moreover, we have the variance of ݕ୲
ߛ௬(0) = ݒ + ݒ୵, (5)
and the covariance of ݕ୲ when ℎ = 1, 2, 3 ⋯,
ߛ௬(ℎ) = ߛఎ(ℎ). (6)
Hence we can obtain the guessed initial values for system parameter,ߙ, and standard deviations,
ߪ and ߪ௪, from
ە
ۖ
۔
ۖ
ۓ ߙ =
ఊ(ଶ)
ఊ(ଵ)
ߪ
ଶ
=
൫ଵିమ൯ఊ(ଵ)
ߪ௪
ଶ
= ߛ௬(0) −
ఙ
మ
ଵିమ
. (7)
2.2. Guessing Initial State Mean and Input Parameter
Denoting
ݖ௧ = ∑ α୲ି୧
ݑ୧
௧
ୀଵ , (8)
and
ߞ௧ = ∑ α୲ି୧
݁୧
௧
ୀଵ + ݓ௧, (9)
we have,
ݕ௧ = α୲
ߤ + ߛݖ௧ + ߞ௧, (10)
where ߞ௧~ܰ൫0, ߪ
ଶ
൯ and
ߪ
ଶ
=
ଵିమ౪
ଵିమ ߪ
ଶ
+ ߪ௪
ଶ
(11)
In order to estimate ߤ and ߛ, we perform linear regression between ݕ௧, as dependent variable,
and α୲
and ݖ௧, as independent variables, using T samples of ݑ௧ and ݕ௧. Since ߞ௧ is
heteroscadestical, we apply weighted least square (WLS). WLS finds its optimum when the
weighted sum, S, of squared residuals is minimized where
ܵ = ∑
൫௬ି౪ఓబିఊ௭൯
మ
భషಉమ౪
భషಉమ ఙ
మାఙೢ
మ
்
௧ୀଵ . (12)
Denote that ݒ௧ = (1 − αଶ୲)ߪ
ଶ + (1 − αଶ)ߪ௪
ଶ , we solve the gradient equation (regarding ߤ and ߛ
respectively) for the sum of squares
4. 60 Computer Science & Information Technology (CS & IT)
൞
∑
౪൫௬ି౪ఓబିఊ௭൯൫ଵିమ൯
௩
்
௧ୀଵ = 0
∑
௭൫௬ି౪ఓబିఊ௭൯൫ଵିమ൯
௩
்
௧ୀଵ = 0
. (13)
Therefore, we will have initial guess about as below:
ە
ۖ
۔
ۖ
ۓߛ =
∑
ಉమ౪
ೡ
సభ ∑
ೡ
సభ ି∑
ಉ౪
ೡ
సభ ∑
ಉ౪
ೡ
సభ
∑
ಉమ౪
ೡ
సభ ∑
మ
ೡ
సభ ି∑
ಉ౪
ೡ
సభ ∑
ಉ౪
ೡ
సభ
ߤ =
∑
ಉ౪
ೡ
సభ ∑
మ
ೡ
సభ ି∑
ಉ౪
ೡ
సభ ∑
ೡ
సభ
∑
ಉమ౪
ೡ
సభ ∑
మ
ೡ
సభ ି∑
ಉ౪
ೡ
సభ ∑
ಉ౪
ೡ
సభ
. (14)
3. ESTIMATION USING EM ALGORITHM
The conditional density for the states and outputs are,
ܲ(ݔ௧|ݔ௧ିଵ) =
ଵ
ఙ√ଶగ
݁ݔ ቂ−
(௫ି௫షభିఊ௨)మ
ଶఙ
మ ቃ, (15)
ܲ(ݕ௧|ݔ௧) =
ଵ
ఙೢ√ଶగ
݁ݔ ቂ−
(௬ି௫)మ
ଶఙೢ
మ ቃ. (16)
Assuming a Gaussian initial state density
ܲ(ݔ) =
ଵ
ఙబ√ଶగ
݁ݔ ቂ−
(௫బିఓబ)మ
ଶఙబ
మ ቃ, (17)
By the Markov property implicit in this model, we calculate the joint probability, not the partial
probability used by Shumway (2011), regarding all T samples of ݔ௧ and ݕ௧, denoted as ሼݔሽ and
ሼݕሽ respectively:
ܲ(ሼݔሽ, ሼݕሽ) = ܲ(ݔ) ∏ ܲ(ݔ௧|ݔ௧ିଵ)்
௧ୀଵ ∏ ܲ(ݕ௧|ݕ௧ିଵ)்
௧ୀଵ (18)
We denote the joint log probability as
ߗ = logܲ(ሼݔሽ, ሼݕሽ). (19)
According to Equation (4), we only need to estimate the parameter set, ߖ = ሼα, ߛ, ߪ, ߪ௪, ߤሽ,
through maximizing the objective function:
ߗ(α, ߛ, ߪ, ߪ௪, ߤ) = −
൫ଵିమ൯(௫బିఓబ)మ
ଶఙ
మ −
ଵ
ଶ
log
ఙ
మ
ଵିమ − ∑
(௫ି௫షభିఊ௨)మ
ଶఙ
మ
்
௧ୀଵ −
ଵ
ଶ
ܶlogߪ
ଶ
−
∑
(௬ି௫)మ
ଶఙೢ
మ
்
௧ୀଵ −
ଵ
ଶ
ܶlogߪ௪
ଶ
−
ଶ்ାଵ
ଶ
log(2ߨ). (20)
3.1. EM Algorithm
Since the objective function expressed by Equation(20) depends on the unobserved data
series,ݔ௧(ݐ = 1, 2, … T), we consider applying the EM algorithm conditionally with respect to the
observed output series ݕଵ, ݕଶ, …, ݕ. The objective function above has an input series.
Accordingly, the input coefficient has to be estimated. Consequently, our approaches are unlike
the approaches[6] used inthe implementation ofEM algorithm for linear dynamic systems.
5. Computer Science & Information Technology (CS & IT) 61
The EM algorithm mainly has two steps: the E-STEP and the M-Step. During the E-Step, the
parameters are assumed known, the hidden states and their variance are estimated over all the
samples, and then the likelihood function constructed from joint probability are calculated.
During the M step, we have to find the parameter set ߖ(݇) = ሼα(݇), ߛ(݇), ߪ(݇), ߪ௪(݇), ߤ(݇)ሽ
for the kth counts of the recursions by maximizing the conditional expectation, or the above
objective function.
The overall procedure for the implementation of EM algorithm is as below:
(i) Initialize the procedure by selecting the guessed values as starting values for the
parameters.
On iteration k, (k=1,2,……)
(ii) Compute the log-likelihood (optional),
(iii) Use the parameters to obtain the smoothed values of the hidden states and their
correlations, for t= 1,2, …...,T.
(iv) Use the smoothed values to calculate the updated parameters.
(v) Repeat Steps (ii) – (iv) to convergence.
We mainly perform two sub-steps in the E-step of EM algorithm: Kalman filtering and Kalman
smoothing.
3.2. Kalman Filtering and Smoothing
Assuming thatwe already know the parameter set { α, ߛ, ߪ,ߪ௪,ߤ,ߪ}(ݔ~ܰ(ߤ, ߪ
ଶ
)), and the
observations ݕ௧ and ݑ௧, we have the estimation of the hidden state, as well as the variances
estimated based on the observations for the period 1 to t.
ݔ௧|௧ିଵ = αݔ௧ିଵ|௧ିଵ + ߛݑ௧, (21a)
ݒ௧|௧ିଵ = αଶ
ݒ௧ିଵ|௧ିଵ + ߪ
ଶ
, (21b)
ݕ௧ = ݕ௧ − ݔ௧|௧ିଵ, (21c)
ݏ௧ = ݒ௧|௧ିଵ + ݒ௪, (21d)
݇௧ = ݒ௧|௧ିଵݏ௧
ିଵ
, (21e)
ݔ௧
௧
= ݔ௧|௧ିଵ + ݇௧ݕ௧ , (21f)
ݒ௧
௧
= (1 − ݇௧)ݒ௧|௧ିଵ, (21g)
where ݔ| = ߤ and ݒ| = ߪ
ଶ
.
According to [6],to computeܧሾݔ௧|ሼ,ݕ ݑሽሿ ≡ ݔ௧
்
and the correlation matrices ௧ ≡ ݒ௧
்
+ ݔ௧
்(ݔ௧
்)ᇱ
one performs a set of backward recursion using
݆௧ିଵ = α
௩షభ|షభ
௩|షభ
, (22)
6. 62 Computer Science & Information Technology (CS & IT)
ݔ௧ିଵ
்
= ݔ௧ିଵ|௧ିଵ + ݆௧ିଵ൫ݔ௧
்
− αݔ௧ିଵ|௧ିଵ − ߛݑ௧൯, (23)
ݒ௧ିଵ
்
= ݒ௧ିଵ|௧ିଵ + ݆௧ିଵ൫ݒ௧
்
− ݒ௧|௧ିଵ൯݆௧ିଵ
ᇱ
, (24)
where ݔ்
்
= ݔ்|் and ݒ்
்
= ݒ்|். We also have ௧,௧ିଵ ≡ ܸ௧,௧ିଵ
்
+ ݔ௧
்(ݔ௧ିଵ
் )ᇱ, where ݒ௧,௧ିଵ
்
can be
obtained through the backward recursions
ݒ௧ିଵ,௧ିଶ
்
= ݒ௧ିଵ|௧ିଵ݆௧ିଶ
ᇱ
+ ݆௧ିଵ൫ݒ௧,௧ିଵ
்
− αݒ௧ିଵ|௧ିଵ൯݆௧ିଶ
ᇱ
, (25)
which is initialized using ݒ்,்ିଵ
்
= α(1 − ்݇)ݒ்ିଵ
்ିଵ
.
Note that the state estimate, ݔ௧
்
, differs from the one computed in a Kalman filter in that it is the
smoothed estimator of ݔ௧ based on all of the observed data (and input data), i.e. it depends on past
and future observations; the Kalman filter estimatesܧሾݔ௧|ሼݕሽଵ
௧ ሿ is the usual Kalman filter
estimator based on the obsearved data up to the current time instant ࢚.
3.3. Expected Log-Likelihood Formulation
After we have got the expected values for ݔandݔ௧ as ݔ
்
≡ ܧሾݔ|ሼ,ݕ ݑሽሿ and ݔ௧
்
≡ ܧሾݔ௧|ሼ,ݕ ݑሽሿ
respectively, we can calculate the expectation of the log-likelihood
)ߗ(ܧ = ܧሾlogܲ(ሼݔሽ, ሼݕሽ)ሿ. (26)
Denote
ቐ
ܲ௧ିଵ
்
= ∑ ܧሾݔ௧ିଵݔ௧ିଵ
ᇱ
|ሼݕሽሿ்
௧ୀଵ
ܲ௧
்
= ∑ ܧሾݔ௧ݔ௧
ᇱ
|ሼݕሽሿ்
௧ୀଵ
ܲ௧,௧ିଵ
்
= ∑ ܧሾݔ௧ݔ௧ିଵ
ᇱ
|ሼݕሽሿ்
௧ୀଵ
, ቐ
ܯ௧ିଵ
்
= ∑ ݔ(ܧ௧ିଵݑ௧)்
௧ୀଵ
ܯ௧
் = ∑ ݔ(ܧ௧ݑ௧)்
௧ୀଵ
ܷ௧
்
= ∑ ݑ௧
ଶ்
௧ୀଵ
, and ቐ
ܹ௧ିଵ
்
= ∑ ݔ(ܧ௧ିଵݕ௧)்
௧ୀଵ
ܹ௧
் = ∑ ݔ(ܧ௧ݕ௧)்
௧ୀଵ
ܻ௧
்
= ∑ ݕ௧
ଶ்
௧ୀଵ
,
we have
)ߗ(ܧ = −
ଵ
ଶ
ߗ(ܧ) −
ଵ
ଶ
ߗ(ܧଵ) −
ଵ
ଶ
ߗ(ܧଶ) −
ଶ்ାଵ
ଶ
log(2ߨ) (27)
where
ߗ(ܧ) =
ଵିమ
ఙ
మ ሾݒ
்
+ (ݔ
்
− ߤ)ଶሿ + log
ఙ
మ
ଵିమ (27a)
ߗ(ܧଵ) = ߪ
ିଶ
൫ܲ௧
்
+ αଶ
ܲ௧ିଵ
்
+ ߛଶ
ܷ௧
்
− 2αܲ௧,௧ିଵ
்
− 2ߛܯ௧
்
+ 2αߛܯ௧ିଵ
்
൯ + ܶlogߪ
ଶ
(27b)
ߗ(ܧଶ) = ߪ௪
ିଶ(ܻ௧
்
+ ܲ௧
்
− 2ܹ௧
்) + ܶlogߪ௪
ଶ
(27c)
3.4. Estimation of the Parameters
We use the first order condition on partial derivatives of )ߗ(ܧ to individual parameters to obtain
the gradient and then the values of individual parameters. This method is not the multivariate
regression approach [6]. The parameters are chosen when the objective function is maximized,
i.e., the gradients are all zero. The estimates of α, ߛ, ߪ
ଶ
, ߪ௪
ଶ
and ߤare from below five equations:
α(1 − αଶ)ݒ
்
− αߪ
ଶ
− α(1 − αଶ)ܲ௧ିଵ
்
+ (1 − αଶ)ܲ௧,௧ିଵ
்
− ߛ(1 − αଶ)ܯ௧ିଵ
்
= 0 (28a)
ߛܷ௧
்
− ܯ௧
்
+ αܯ௧ିଵ
்
= 0 (28b)
(1 − αଶ)ݒ
்
− (1 + ܶ)ߪ
ଶ
+ ܲ௧
்
+ αଶ
ܲ௧ିଵ
்
+ ߛଶ
ܷ௧
்
− 2αܲ௧,௧ିଵ
்
− 2ߛܯ௧
்
+ 2αߛܯ௧ିଵ
்
= 0 (28c)
7. Computer Science & Information Technology (CS & IT) 63
ߪ௪
ଶ
=
ଵ
்
(ܻ௧
்
+ ܲ௧
்
− 2ܹ௧
்) (28d)
ߤ = ݔ
்
(28e)
Moreover, we use the second orders of the derivatives of )ߗ(ܧ to calculate the second derivatives
and then the information matrix. Most of the second order derivatives of )ߗ(ܧ are zero except
those listed below:
డమா(ఆ)
డఈమ =
௩బ
ା൫௫బ
ିఓబ൯
మ
ିషభ
ఙ
మ −
ଵାమ
(ଵିమ)మ, (29)
డమா(ఆ)
డఊడఈ
=
డమா(ఆ)
డఈడఊ
= −
ெషభ
ఙ
మ , (30)
డమா(ఆ)
డఙడఈ
=
డమா(ఆ)
డఈడఙ
=
ଶ൫షభ
ି,షభ
ାఊெషభ
൯ିଶቂ௩బ
ା൫௫బ
ିఓబ൯
మ
ቃ
ఙ
య , (31)
డమா(ఆ)
డఊమ = −
ఙ
మ (32)
డమா(ఆ)
డఙడఊ
=
డమா(ఆ)
డఊడఙ
=
ଶ൫ఊ
ିெ
ାெషభ
൯
ఙ
య (33)
డమா(ఆ)
డఙ
మ =
்ାଵ
ఙ
మ −
ଷ൫ଵିమ൯ቂ௩బ
ା൫௫బ
ିఓబ൯
మ
ቃ
ఙ
ర −
ଷ൫
ାమషభ
ାఊమ
ିଶ,షభ
ିଶఊெ
ାଶఊெషభ
൯
ఙ
ర (34)
డమா(ఆ)
డఙೢ
మ =
்
ఙೢ
మ −
ଷ൫
ା
ିଶௐ
൯
ఙೢ
ర (35)
డమா(ఆ)
డఓబ
మ = −
ଵିమ
ఙ
మ (36)
According to Cramer-Rao Theorem, the MLE is an efficient estimate. When the sample size is
large enough, the asymptotic variances of the estimates can be considered as the metric of the
accuracy of the estimation. The asymptotic variances are calculated using the inverse of the
information matrix, which is the inverse of the negative of the expected value of the Hessian
matrix. The vector of the asymptotic variances of the estimates is
ۏ
ێ
ێ
ێ
ێ
ێ
ێ
ێ
ێ
ێ
ۍ
(ܶ + 1)(αଶ
− 1)ଶ
ܷߪ
ଶ
(ܶ + 1)(1 − αଶ)ଶ(Pܷ − ܷߪ
ଶ − M
ଶ) + ( 1 + ܶ − αଶ + ܶαଶ)ܷߪ
ଶ
ሾ(1 + ܶ)(1 − αଶ)ଶ(P − ߪ
ଶ) + (1 + ܶ − αଶ
+ ܶαଶ)ߪ
ଶሿߪ
ଶ
(ܶ + 1)(1 − αଶ)ଶ(Pܷ − ܷߪ
ଶ
− M
ଶ) + ( 1 + ܶ − αଶ + ܶαଶ)ܷߪ
ଶ
ሾ(1 − αଶ)ଶ(Pܷ − M
ଶ
− ܷߪ
ଶ) + ( 1 + αଶ)ܷߪ
ଶሿߪ
ଶ
(ܶ + 1)(1 − αଶ)ଶ(Pܷ − ܷߪ
ଶ
− M
ଶ) + ( 1 + ܶ − αଶ + ܶαଶ)ܷߪ
ଶ
ߪ௪
ଶ
2ܶ
ߪ
ଶ
ے
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ۑ
ې
If the sample size is small, we introduce boot-strapping procedure where the estimates are
obtained from likelihood constructed from re-sampled standardized innovation, ݕ௧ , in Equation
(21c). Moreover, the mean squared errors (MSE) of the state variables which is estimated from
Equations (21a-g) using estimated parameters are also estimated.
8. 64 Computer Science & Information Technology (CS & IT)
4. SIMULATION AND RESULTS
The output data is generated through presetting the input series and the values of the parameters.
We implement the initial guessing, EM iteration, and finally obtain the parameter estimates. This
makes it easier to evaluate our work by comparing the actual values with the estimated values, or
by checking the standard deviation of the estimates.
4.1. Data Generation
We generate data from the state-space model described as Equation (1). We assume α = 0.8,
γ = 1.5, and ߤ = 0. Moreover, the process noises, ݁୲, and observation noise, ݓ௧, are generated
independently where ݁୲~ܰ(0, 1.1ଶ) and ݓ୲~ܰ(0, 0.9ଶ). We assume that the input,ݑ௧, is a slow
changing periodical square wave signal whose period is 10 time unit. The standard deviation of
initial state, ߪ, is not needed during the data generation but can be calculated according to
Equation (2). The expected log-likelihood can be calculated using Equation (27). Both are treated
as “actual” values to be compared with guessed values and estimated values.
We performed our simulation using two different sample sizes: the large size of 1000 and the
small size of 50. When the sample size is small, we applied bootstrapping method to estimate the
accuracy of the estimate.
4.2. Results
We provide the results of the simulation with small sample size of 50 in Table 1, and the results
of the simulation with large sample size of 1000 in Table 2.
Table 1. The parameters estimate with small sample size
Parameters Actual Guessed Estimated Std. Dev.
α 0.8 0.879 0.801 0.023
γ 1.5 1.075 1.438 0.104
σe 1.1 1.400 0.708 0.158
σw 0.9 0.922 0.862 0.193
µ0 0 0.992 2.143 1.231
σ0 1.83 3.811 1.183 0.252
In Table 1and Table 2, we displayed the actual values, the guessed values, the estimated values
and the standard deviations of the estimated values for transition coefficient, α, input coefficient,
γ, standard deviation of process errors, σe, standard deviation of observation errors, σw, mean of
initial state, µ0, and standard deviation of initial state, σ0. In general, the guessed value is near the
actual value while the estimated value is much more close to the actual value than the guessed
ones for the parameters of the most interest: α and γ. The standard deviations in Table 1 are from
bootstrapped distribution while the standard deviations in Table 2 are from the asymptotic
variances.
Table 2: The parameters estimated with large sample size
Parameters Actual Guessed Estimated Std. Dev.
α 0.8 0.879 0.800 0.0001
γ 1.5 1.276 1.424 0.0012
σe 1.1 2.024 1.033 0.0011
σw 0.9 0.533 0.971 0.0005
µ0 0 2.459 1.667 2.9614
σ0 1.83 4.250 1.721 NA
9. Computer Science & Information Technology (CS & IT) 65
In general, the guessed value is near the ‘actual” value while the estimated value is much closer to
the “actual” value than the guessed ones, especially for the parameters of interest: ߙ and ߛ. It is
worth noting that the deviations of the estimated values are larger than the asymptotic ones due to
the imperfectly generated data.
5. CONCLUSIONS
The research is to validate our innovative approaches in the application of EM algorithm in the
MLE of a constrained dynamic linear system with external input. There are two main
contributions in this research. Firstly, we realized that σ0 and σe has the relationship expressed by
Equation (4) thus we don’t have to estimate both of them during the implementation of EM
algorithm. Accordingly, the likelihood function in Equation (27) is not similar with those
researchers who ignored the relationship. Secondly, in initial guessing of the value of input
coefficient and the mean of initial state, we introduce weighted least square for the guessing of
input coefficient, γ, and the mean of the initial state, µ0.
It is obvious that more techniques have to be discovered for the initial guessing, and the
estimating based on the guessed initial guessing of, the parameter values, especially for the
implementation of the M-step of the EM algorithm. The approaches we proposed can be a new
start point for the future research on the estimation of dynamic systems with higher dimensions of
external inputs, hidden states and observations.
REFERENCES
[1] Kalman,R. E.,(1960) "A new approach to linear filtering and prediction problems",Journal of Basic
Engineering, 82 (1), pp. 35–45.
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[3] Dempster,A.P., Laird, N.M. and Rubin, D.B. (1977) "Maximum likelihood from incomplete data via
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reportCRC-TR-96-2, Department of Computer Science, University of Toronto.
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10. 66 Computer Science & Information Technology (CS & IT)
AUTHORS
Chengliang Huang is currently a Ph. D. candidate at Ryerson University. He had been a
senior engineer and project manager at Huawei and Intel for four years respectively. He
graduated as MASc in Electrical and Computer Engineering, Ryerson University in
2009, MBA in Economic Management, Beijing Jiaotong University and B. Sci. in
Electronic Engineering, Fudan University in 1990.He has published papers on peer-
reviewed academic journals, including IEEE Sensor Journal and Wireless Personal
Communications. His research interest includes wireless communications, random signal
processing, and system identification, time series analysis, marketing data mining/analysis, and marketing
productivity.
Xiao-Ping Zhang (M'97, SM'02) received the B.S. and Ph.D. degrees from Tsinghua
University, in 1992 and 1996, respectively, all in electronic engineering. He holds an
MBA in Finance, Economics and Entrepreneurship with Honors from Booth School of
Business, the University of Chicago. Since Fall 2000, he has been with the Department
of Electrical and Computer Engineering, Ryerson University, where he is now Professor,
Director of Communication and Signal Processing Applications Laboratory (CASPAL)
and Program Director of Graduate Studies. His research interests include multimedia
communications and signal processing, multimedia retrieval and video content analysis,
sensor networks and electronic systems, computational intelligence, and applications in bioinformatics,
finance, and marketing. He is a frequent consultant for biotech companies and investment firms. He is
cofounder and CEO for EidoSearch, Inc., which offers a content-based search and analysis engine for
financial data. Dr. Zhang is a registered Professional Engineer in Ontario, Canada, a Senior Member of
IEEE and a member of Beta Gamma Sigma Honor Society. He is the publicity co-chair for ICME'06 and
program co-chair for ICIC'05. He is currently an Associate Editor for IEEE Transactions on Signal
Processing, IEEE Signal Processing Letters and Journal of Multimedia.
Dr. Wang’s research focuses on brand equity assessment, marketing data
mining/analysis, long-term marketing productivity, and marketing strategy. She also
works on e-commerce and information systems related topics. Her research on brand
equity assessment is funded by the Social Sciences and Humanities Research Council
of Canada (SSHRC). She is a key team member for a NSERC (Natural Sciences and
Engineering Research Council of Canada) supported project on financial market
information analysis. Her work has appeared in many academic journals, including
Journal of Marketing, Journal of the Academy of Marketing Science, Information & Management, Journal
of Consumer Marketing, among others.