The document discusses accelerating machine learning algorithms by integrating GPUs into MapReduce clusters. It proposes modifying the MapReduce runtime to satisfy the requirements of machine learning algorithms and integrate massively parallel processors like GPUs. Many machine learning algorithms can be represented as MapReduce primitives. The implementation would allow multithreaded MapReduce tasks, interleaving of parallel BLAS operations using static and variable data, and support for iterative algorithms through stateful nodes. This could accelerate machine learning on big data by taking advantage of the parallelism of GPUs within the MapReduce framework.
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 a new block cipher that blends concepts from the modified Feistel cipher and advanced Hill cipher. The cipher uses an involutory key matrix K to encrypt plaintext matrices P and Q through iterative applications of mixing, permutation, and XOR operations per equations 1.1 and 1.2. Cryptanalysis shows the cipher is strong as the encryption equations are nonlinear and functions like Shift() and Mix() cause diffusion in each round. The encryption and decryption processes are illustrated through flowcharts and algorithms.
This document proposes a low complexity algorithm for jointly estimating the reflection coefficient, spatial location, and Doppler shift of a target for MIMO radar systems. It splits the estimation problem into two parts. The first part estimates the reflection coefficient in closed form. The second part jointly estimates the spatial location and Doppler shift using a 2D FFT approach. This allows significantly lower computational complexity compared to maximum likelihood estimation. Simulation results show the proposed estimator achieves the Cramér-Rao lower bound, providing optimal performance with low complexity.
SchNet: A continuous-filter convolutional neural network for modeling quantum...Kazuki Fujikawa
The document summarizes a paper about modeling quantum interactions using a continuous-filter convolutional neural network called SchNet. Some key points:
1) SchNet performs convolution using distances between nodes in 3D space rather than graph connectivity, allowing it to model interactions between arbitrarily positioned nodes.
2) This is useful for cases where graphs have different configurations that impact properties, or where graph and physical distances differ.
3) The paper proposes a continuous-filter convolutional layer and interaction block to incorporate distance information into graph convolutions performed by the SchNet model.
A Unified PDE model for image multi-phase segmentation and grey-scale inpaint...vijayakrishna rowthu
A Unified PDE model for image multi-phase segmentation and grey-scale inpainting phd-kanpur.
Cahn-Hilliard equation and Histogram are the key elements in this research work. Convexity-Splitting scheme with Fourier-spectral method solves this numerically.
DLT stands for Direct Linear Transformation. It is an algorithm that estimates the camera matrix P by minimizing the algebraic error between measured image points xi and projected 3D points PXi. Specifically, DLT finds P by solving the equation Ap=0, where A is constructed from point correspondences and p contains the entries of P. This minimizes the sum of squared algebraic distances between the points. For affine cameras, the algebraic and geometric distances are equivalent. DLT provides an initial estimate of P that can be refined using nonlinear optimization techniques.
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
Computing Inner Eigenvalues of Matrices in Tensor Train Matrix FormatThomas Mach
Talk given at ENUMATH 2011 in Leicester and GAMM ANLA Workshop 2011 in Bremen. There is a preprint available under http://www.mpi-magdeburg.mpg.de/preprints/index.php
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 a new block cipher that blends concepts from the modified Feistel cipher and advanced Hill cipher. The cipher uses an involutory key matrix K to encrypt plaintext matrices P and Q through iterative applications of mixing, permutation, and XOR operations per equations 1.1 and 1.2. Cryptanalysis shows the cipher is strong as the encryption equations are nonlinear and functions like Shift() and Mix() cause diffusion in each round. The encryption and decryption processes are illustrated through flowcharts and algorithms.
This document proposes a low complexity algorithm for jointly estimating the reflection coefficient, spatial location, and Doppler shift of a target for MIMO radar systems. It splits the estimation problem into two parts. The first part estimates the reflection coefficient in closed form. The second part jointly estimates the spatial location and Doppler shift using a 2D FFT approach. This allows significantly lower computational complexity compared to maximum likelihood estimation. Simulation results show the proposed estimator achieves the Cramér-Rao lower bound, providing optimal performance with low complexity.
SchNet: A continuous-filter convolutional neural network for modeling quantum...Kazuki Fujikawa
The document summarizes a paper about modeling quantum interactions using a continuous-filter convolutional neural network called SchNet. Some key points:
1) SchNet performs convolution using distances between nodes in 3D space rather than graph connectivity, allowing it to model interactions between arbitrarily positioned nodes.
2) This is useful for cases where graphs have different configurations that impact properties, or where graph and physical distances differ.
3) The paper proposes a continuous-filter convolutional layer and interaction block to incorporate distance information into graph convolutions performed by the SchNet model.
A Unified PDE model for image multi-phase segmentation and grey-scale inpaint...vijayakrishna rowthu
A Unified PDE model for image multi-phase segmentation and grey-scale inpainting phd-kanpur.
Cahn-Hilliard equation and Histogram are the key elements in this research work. Convexity-Splitting scheme with Fourier-spectral method solves this numerically.
DLT stands for Direct Linear Transformation. It is an algorithm that estimates the camera matrix P by minimizing the algebraic error between measured image points xi and projected 3D points PXi. Specifically, DLT finds P by solving the equation Ap=0, where A is constructed from point correspondences and p contains the entries of P. This minimizes the sum of squared algebraic distances between the points. For affine cameras, the algebraic and geometric distances are equivalent. DLT provides an initial estimate of P that can be refined using nonlinear optimization techniques.
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
Computing Inner Eigenvalues of Matrices in Tensor Train Matrix FormatThomas Mach
Talk given at ENUMATH 2011 in Leicester and GAMM ANLA Workshop 2011 in Bremen. There is a preprint available under http://www.mpi-magdeburg.mpg.de/preprints/index.php
PERFORMANCE EVALUATIONS OF GRIORYAN FFT AND COOLEY-TUKEY FFT ONTO XILINX VIRT...cscpconf
A large family of signal processing techniques consist of Fourier-transforming a signal,manipulating the Fourier-transformed data in a simple way, and reversing the transformation.We widely use Fourier frequency analysis in equalization of audio recordings, X-ray crystallography, artefact removal in Neurological signal and image processing, Voice Activity Detection in Brain stem speech evoked potentials, speech processing spectrograms are used to identify phonetic sounds and so on. Discrete Fourier Transform (DFT) is a principal mathematical method for the frequency analysis. The way of splitting the DFT gives out various fast algorithms. In this paper, we present the implementation of two fast algorithms for the DFT for evaluating their performance. One of them is the popular radix-2 Cooley-Tukey fast Fourier transform algorithm (FFT) [1] and the other one is the Grigoryan FFT based on the splitting by the paired transform [2]. We evaluate the performance of these algorithms by implementing
them on the Xilinx Virtex-II pro [3] and Virtex-5 [4] FPGAs, by developing our own FFT processor architectures. Finally we show that the Grigoryan FFT is working fatser than
Cooley-Tukey FFT, consequently it is useful for higher sampling rates. Operating at higher
sampling rates is a challenge in DSP applications
Performance evaluations of grioryan fft and cooley tukey fft onto xilinx virt...csandit
A large family of signal processing techniques consist of Fourier-transforming a signal,
manipulating the Fourier-transformed data in a simple way, and reversing the transformation.
We widely use Fourier frequency analysis in equalization of audio recordings, X-ray
crystallography, artefact removal in Neurological signal and image processing, Voice Activity
Detection in Brain stem speech evoked potentials, speech processing spectrograms are used to
identify phonetic sounds and so on. Discrete Fourier Transform (DFT) is a principal
mathematical method for the frequency analysis. The way of splitting the DFT gives out various
fast algorithms. In this paper, we present the implementation of two fast algorithms for the DFT
for evaluating their performance. One of them is the popular radix-2 Cooley-Tukey fast Fourier
transform algorithm (FFT) [1] and the other one is the Grigoryan FFT based on the splitting by
the paired transform [2]. We evaluate the performance of these algorithms by implementing
them on the Xilinx Virtex-II pro [3] and Virtex-5 [4] FPGAs, by developing our own FFT
processor architectures. Finally we show that the Grigoryan FFT is working fatser than
Cooley-Tukey FFT, consequently it is useful for higher sampling rates. Operating at higher
sampling rates is a challenge in DSP applications.
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
Optimization of distributed generation of renewable energy sources by intelli...Beniamino Murgante
Optimization of distributed generation of renewable energy sources by intelligent techniques
Marcello Pucci – Institute for Studies on Intelligent Systems for Automation (I.S.S.I.A), National Research Council, Palermo (Italy)
Intelligent Analysis of Environmental Data (S4 ENVISA Workshop 2009)
The document provides an overview and review of topics related to tracking and filtering fundamentals, including:
- Linear algebra and linear systems, probability, hypothesis testing, and state estimation.
- Linear and non-linear filtering, multiple model filtering, track maintenance, data association techniques, and activity control.
- Mathematics topics like linear algebra, probability, estimation, vector/matrix properties, and state-space representations are reviewed for continuous and discrete time systems. Concepts include the Jacobian, gradient, Dirac delta function, and observability criteria.
This document describes the POTFIT algorithm for approximating multi-dimensional arrays as products of lower-dimensional matrices. It uses POTFIT to approximate a photo (represented as a 3D tensor of pixel color values) using single particle potentials. Approximating a dark photo requires fewer SPPs than a colorful photo, as errors are more obvious in colorful areas. The document shows approximations using different numbers of SPPs and the resulting file sizes.
PAC-Bayesian Bound for Gaussian Process Regression and Multiple Kernel Additi...Taiji Suzuki
The document discusses the aggregated estimator technique for sparse estimation. The aggregated estimator averages over multiple models, each weighted by their risk. This allows fast learning rates without strong assumptions on the design matrix. The technique is applied to sparse regression problems using an exponential screening estimator. The risk bound of this estimator is compared to other estimators like BIC and Lasso, showing it provides a tighter bound.
Solving Unit Commitment Problem Using Chemo-tactic PSO–DE Optimization Algori...IDES Editor
This paper presents Chemo-tactic PSO-DE
(CPSO-DE) optimization algorithm combined with
Lagrange Relaxation method (LR) for solving Unit
Commitment (UC) problem. The proposed approach
employs Chemo-tactic PSO-DE algorithm for optimal
settings of Lagrange multipliers. It provides high-quality
performance and reaches global solution and is a hybrid
heuristic algorithm based on Bacterial Foraging
Optimization (BFO), Particle Swarm Optimization (PSO)
and Differential Evolution (DE). The feasibility of the
proposed method is demonstrated for 10-unit, 20-unit,
and 40-unit systems respectively. The test results are
compared with those obtained by Lagrangian relaxation
(LR), genetic algorithm (GA), evolutionary programming
(EP), and genetic algorithm based on unit characteristic
classification (GAUC), enhanced adaptive Lagrangian
relaxation (ELR), integer-coded genetic algorithm
(ICGA) and hybrid particle swarm optimization (HPSO)
in terms of solution quality. Simulation results show that
the proposed method can provide a better solution.
This presentation begins with explaining the basic algorithms of machine learning and using the same concepts, discusses in detail 2 supervised learning/deep learning algorithms - Artificial neural nets and Convolutional Neural Nets. The relationship between Artificial neural nets and basic machine learning algorithms such as logistic regression and soft max is also explored. For hands on the implementation of ANN's and CNN's on MNIST dataset is also explained.
Skiena algorithm 2007 lecture18 application of dynamic programmingzukun
The document summarizes a lecture on applications of dynamic programming. It provides examples of how to use dynamic programming to solve problems involving string breaking, high density bar code encoding, dividing work evenly among workers, and the traveling salesman problem. Dynamic programming can be applied when problems exhibit the principle of optimality and the problem space can be broken down into overlapping subproblems that are stored in a table to avoid recomputing solutions.
1. The document discusses various image transforms including discrete cosine transform (DCT), discrete wavelet transform (DWT), and contourlet transform.
2. DCT transforms an image into frequency domain and organizes values based on human visual system importance. DWT analyzes images using wavelets of different scales and positions.
3. Contourlet transform is derived directly from discrete domain to capture smooth contours and edges at any orientation, decoupling multiscale and directional decompositions. It provides better efficiency than DWT for representing images.
This document provides an outline and summaries for a two-day MATLAB workshop presented by Bhavesh Shah from 27-28 September 2012. The workshop will cover introductory topics such as what MATLAB is, the MATLAB screen interface, variables, arrays, matrices, built-in math functions, control structures, and toolboxes. It will also discuss more advanced topics like writing user-defined functions, neural networks, GUIs, and image processing. The goal is to introduce participants to the basics of using MATLAB for technical computing, modeling, simulation, and data analysis.
This summary provides the key details from the document in 3 sentences:
The document proposes a new method for encrypting two images into a single encrypted image using generalized weighted fractional Fourier transform (GWFRFT) with double random phase encoding. The encryption process involves applying pixel scrambling, phase encoding, and two rounds of GWFRFT with random phase masks on the combined image signal. This technique is shown to provide comparable security to the Advanced Encryption Standard (AES) with a 232-bit key size through a high number of possible permutations in the GWFRFT parameters and orders.
The document discusses various image transforms. It begins by explaining why transforms are used, such as for fast computation and obtaining conceptual insights. It then introduces image transforms as unitary matrices that represent images using a discrete set of basis images. It proceeds to describe one-dimensional orthogonal and unitary transforms using matrices. It also discusses separable two-dimensional transforms and provides properties of unitary transforms such as energy conservation. Specific transforms discussed in more detail include the discrete Fourier transform, discrete cosine transform, discrete sine transform, and Hadamard transform.
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Iaetsd implementation of power efficient iterative logarithmic multiplier usi...Iaetsd Iaetsd
This document describes the design and implementation of a power efficient iterative logarithmic multiplier using Mitchell's algorithm and reversible logic. It involves converting multiplication to addition using logarithmic numbers. The proposed design implements a basic block consisting of leading one detectors, encoders, barrel shifters and a decoder to calculate an approximate product. Error correction circuits are then cascaded with the basic blocks to improve accuracy. The 4x4 reversible logarithmic multiplier is designed and simulated using Xilinx tools, demonstrating lower power consumption through the use of reversible logic.
This document discusses the design of a parallel BCH encoder for satellite transmitters. Key points:
1) It proposes a new parallel algorithm for BCH encoding to increase throughput while meeting ASIC requirements for space systems.
2) The algorithm models BCH encoding as a linear system and exploits regularities in the state transition matrix to parallelize encoding.
3) A prototype parallel BCH encoder was designed and integrated with an LDPC encoder. Lab tests showed the modulator achieved low error vector magnitude at transmission rates up to 30 MBaud.
An approach to incentive based reputation for communities of web servicesBabak Khosravifar
This document presents an approach for incentive-based reputation modeling for communities of web services. It proposes a reputation model that uses metrics like responsiveness, demand, and satisfaction, and combines them. It also describes a logging mechanism to address fake positive and negative ratings through adjustments. Experimental results show the community's quality of service improves over runs as the model provides incentives to accurately report reputation. The contributions include a reputation assessment protocol for web service communities and an analysis of incentives. Future work involves further comparing communities to single services and additional incentive investigations.
All Pair Shortest Path Algorithm – Parallel Implementation and AnalysisInderjeet Singh
This project report discusses the parallel implementation of the all pair shortest path algorithm using MPI and OpenMP. The algorithm was implemented by decomposing the adjacency matrix row-wise across processes. Results show that the parallel algorithm achieves speedup over the sequential version, especially for large graph sizes. The MPI implementation performed better than the OpenMP version. Graphs in the report compare execution time, speedup, and efficiency for different problem sizes and numbers of processes/threads.
Alpine Data Labs presents a deep dive into our implementation of Multinomial Logistic Regression with Apache Spark. Machine Learning Engineer DB Tsai takes us through the technical implementation details step by step. First, he explains how the state of the art Machine Learning on Hadoop is not doing fulfilling the promise of Big Data. Next, he explains how Spark is a perfect match for machine learning through their in-memory cache-ing capability demonstrating 100x performance improvement. Third, he takes us through each aspect of a multinomial logistic regression and how this is developed with Spark APIs. Fourth, he demonstrates an extension of MLOR and training parameters. Finally, he benchmarks MLOR with 11M rows, 123 features, 11% non-zero elements with a 5 node Hadoop cluster. Finally, he shows Alpine's unique visual environment with Spark and verifies the performance with the job tracker. In conclusion, Alpine supports the state of the art Cloudera and Pivotal Hadoop clusters and performances at a level that far exceeds its next nearest competitor.
Multinomial Logistic Regression with Apache SparkDB Tsai
Logistic Regression can not only be used for modeling binary outcomes but also multinomial outcome with some extension. In this talk, DB will talk about basic idea of binary logistic regression step by step, and then extend to multinomial one. He will show how easy it's with Spark to parallelize this iterative algorithm by utilizing the in-memory RDD cache to scale horizontally (the numbers of training data.) However, there is mathematical limitation on scaling vertically (the numbers of training features) while many recent applications from document classification and computational linguistics are of this type. He will talk about how to address this problem by L-BFGS optimizer instead of Newton optimizer.
Bio:
DB Tsai is a machine learning engineer working at Alpine Data Labs. He is recently working with Spark MLlib team to add support of L-BFGS optimizer and multinomial logistic regression in the upstream. He also led the Apache Spark development at Alpine Data Labs. Before joining Alpine Data labs, he was working on large-scale optimization of optical quantum circuits at Stanford as a PhD student.
PERFORMANCE EVALUATIONS OF GRIORYAN FFT AND COOLEY-TUKEY FFT ONTO XILINX VIRT...cscpconf
A large family of signal processing techniques consist of Fourier-transforming a signal,manipulating the Fourier-transformed data in a simple way, and reversing the transformation.We widely use Fourier frequency analysis in equalization of audio recordings, X-ray crystallography, artefact removal in Neurological signal and image processing, Voice Activity Detection in Brain stem speech evoked potentials, speech processing spectrograms are used to identify phonetic sounds and so on. Discrete Fourier Transform (DFT) is a principal mathematical method for the frequency analysis. The way of splitting the DFT gives out various fast algorithms. In this paper, we present the implementation of two fast algorithms for the DFT for evaluating their performance. One of them is the popular radix-2 Cooley-Tukey fast Fourier transform algorithm (FFT) [1] and the other one is the Grigoryan FFT based on the splitting by the paired transform [2]. We evaluate the performance of these algorithms by implementing
them on the Xilinx Virtex-II pro [3] and Virtex-5 [4] FPGAs, by developing our own FFT processor architectures. Finally we show that the Grigoryan FFT is working fatser than
Cooley-Tukey FFT, consequently it is useful for higher sampling rates. Operating at higher
sampling rates is a challenge in DSP applications
Performance evaluations of grioryan fft and cooley tukey fft onto xilinx virt...csandit
A large family of signal processing techniques consist of Fourier-transforming a signal,
manipulating the Fourier-transformed data in a simple way, and reversing the transformation.
We widely use Fourier frequency analysis in equalization of audio recordings, X-ray
crystallography, artefact removal in Neurological signal and image processing, Voice Activity
Detection in Brain stem speech evoked potentials, speech processing spectrograms are used to
identify phonetic sounds and so on. Discrete Fourier Transform (DFT) is a principal
mathematical method for the frequency analysis. The way of splitting the DFT gives out various
fast algorithms. In this paper, we present the implementation of two fast algorithms for the DFT
for evaluating their performance. One of them is the popular radix-2 Cooley-Tukey fast Fourier
transform algorithm (FFT) [1] and the other one is the Grigoryan FFT based on the splitting by
the paired transform [2]. We evaluate the performance of these algorithms by implementing
them on the Xilinx Virtex-II pro [3] and Virtex-5 [4] FPGAs, by developing our own FFT
processor architectures. Finally we show that the Grigoryan FFT is working fatser than
Cooley-Tukey FFT, consequently it is useful for higher sampling rates. Operating at higher
sampling rates is a challenge in DSP applications.
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
Optimization of distributed generation of renewable energy sources by intelli...Beniamino Murgante
Optimization of distributed generation of renewable energy sources by intelligent techniques
Marcello Pucci – Institute for Studies on Intelligent Systems for Automation (I.S.S.I.A), National Research Council, Palermo (Italy)
Intelligent Analysis of Environmental Data (S4 ENVISA Workshop 2009)
The document provides an overview and review of topics related to tracking and filtering fundamentals, including:
- Linear algebra and linear systems, probability, hypothesis testing, and state estimation.
- Linear and non-linear filtering, multiple model filtering, track maintenance, data association techniques, and activity control.
- Mathematics topics like linear algebra, probability, estimation, vector/matrix properties, and state-space representations are reviewed for continuous and discrete time systems. Concepts include the Jacobian, gradient, Dirac delta function, and observability criteria.
This document describes the POTFIT algorithm for approximating multi-dimensional arrays as products of lower-dimensional matrices. It uses POTFIT to approximate a photo (represented as a 3D tensor of pixel color values) using single particle potentials. Approximating a dark photo requires fewer SPPs than a colorful photo, as errors are more obvious in colorful areas. The document shows approximations using different numbers of SPPs and the resulting file sizes.
PAC-Bayesian Bound for Gaussian Process Regression and Multiple Kernel Additi...Taiji Suzuki
The document discusses the aggregated estimator technique for sparse estimation. The aggregated estimator averages over multiple models, each weighted by their risk. This allows fast learning rates without strong assumptions on the design matrix. The technique is applied to sparse regression problems using an exponential screening estimator. The risk bound of this estimator is compared to other estimators like BIC and Lasso, showing it provides a tighter bound.
Solving Unit Commitment Problem Using Chemo-tactic PSO–DE Optimization Algori...IDES Editor
This paper presents Chemo-tactic PSO-DE
(CPSO-DE) optimization algorithm combined with
Lagrange Relaxation method (LR) for solving Unit
Commitment (UC) problem. The proposed approach
employs Chemo-tactic PSO-DE algorithm for optimal
settings of Lagrange multipliers. It provides high-quality
performance and reaches global solution and is a hybrid
heuristic algorithm based on Bacterial Foraging
Optimization (BFO), Particle Swarm Optimization (PSO)
and Differential Evolution (DE). The feasibility of the
proposed method is demonstrated for 10-unit, 20-unit,
and 40-unit systems respectively. The test results are
compared with those obtained by Lagrangian relaxation
(LR), genetic algorithm (GA), evolutionary programming
(EP), and genetic algorithm based on unit characteristic
classification (GAUC), enhanced adaptive Lagrangian
relaxation (ELR), integer-coded genetic algorithm
(ICGA) and hybrid particle swarm optimization (HPSO)
in terms of solution quality. Simulation results show that
the proposed method can provide a better solution.
This presentation begins with explaining the basic algorithms of machine learning and using the same concepts, discusses in detail 2 supervised learning/deep learning algorithms - Artificial neural nets and Convolutional Neural Nets. The relationship between Artificial neural nets and basic machine learning algorithms such as logistic regression and soft max is also explored. For hands on the implementation of ANN's and CNN's on MNIST dataset is also explained.
Skiena algorithm 2007 lecture18 application of dynamic programmingzukun
The document summarizes a lecture on applications of dynamic programming. It provides examples of how to use dynamic programming to solve problems involving string breaking, high density bar code encoding, dividing work evenly among workers, and the traveling salesman problem. Dynamic programming can be applied when problems exhibit the principle of optimality and the problem space can be broken down into overlapping subproblems that are stored in a table to avoid recomputing solutions.
1. The document discusses various image transforms including discrete cosine transform (DCT), discrete wavelet transform (DWT), and contourlet transform.
2. DCT transforms an image into frequency domain and organizes values based on human visual system importance. DWT analyzes images using wavelets of different scales and positions.
3. Contourlet transform is derived directly from discrete domain to capture smooth contours and edges at any orientation, decoupling multiscale and directional decompositions. It provides better efficiency than DWT for representing images.
This document provides an outline and summaries for a two-day MATLAB workshop presented by Bhavesh Shah from 27-28 September 2012. The workshop will cover introductory topics such as what MATLAB is, the MATLAB screen interface, variables, arrays, matrices, built-in math functions, control structures, and toolboxes. It will also discuss more advanced topics like writing user-defined functions, neural networks, GUIs, and image processing. The goal is to introduce participants to the basics of using MATLAB for technical computing, modeling, simulation, and data analysis.
This summary provides the key details from the document in 3 sentences:
The document proposes a new method for encrypting two images into a single encrypted image using generalized weighted fractional Fourier transform (GWFRFT) with double random phase encoding. The encryption process involves applying pixel scrambling, phase encoding, and two rounds of GWFRFT with random phase masks on the combined image signal. This technique is shown to provide comparable security to the Advanced Encryption Standard (AES) with a 232-bit key size through a high number of possible permutations in the GWFRFT parameters and orders.
The document discusses various image transforms. It begins by explaining why transforms are used, such as for fast computation and obtaining conceptual insights. It then introduces image transforms as unitary matrices that represent images using a discrete set of basis images. It proceeds to describe one-dimensional orthogonal and unitary transforms using matrices. It also discusses separable two-dimensional transforms and provides properties of unitary transforms such as energy conservation. Specific transforms discussed in more detail include the discrete Fourier transform, discrete cosine transform, discrete sine transform, and Hadamard transform.
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Iaetsd implementation of power efficient iterative logarithmic multiplier usi...Iaetsd Iaetsd
This document describes the design and implementation of a power efficient iterative logarithmic multiplier using Mitchell's algorithm and reversible logic. It involves converting multiplication to addition using logarithmic numbers. The proposed design implements a basic block consisting of leading one detectors, encoders, barrel shifters and a decoder to calculate an approximate product. Error correction circuits are then cascaded with the basic blocks to improve accuracy. The 4x4 reversible logarithmic multiplier is designed and simulated using Xilinx tools, demonstrating lower power consumption through the use of reversible logic.
This document discusses the design of a parallel BCH encoder for satellite transmitters. Key points:
1) It proposes a new parallel algorithm for BCH encoding to increase throughput while meeting ASIC requirements for space systems.
2) The algorithm models BCH encoding as a linear system and exploits regularities in the state transition matrix to parallelize encoding.
3) A prototype parallel BCH encoder was designed and integrated with an LDPC encoder. Lab tests showed the modulator achieved low error vector magnitude at transmission rates up to 30 MBaud.
An approach to incentive based reputation for communities of web servicesBabak Khosravifar
This document presents an approach for incentive-based reputation modeling for communities of web services. It proposes a reputation model that uses metrics like responsiveness, demand, and satisfaction, and combines them. It also describes a logging mechanism to address fake positive and negative ratings through adjustments. Experimental results show the community's quality of service improves over runs as the model provides incentives to accurately report reputation. The contributions include a reputation assessment protocol for web service communities and an analysis of incentives. Future work involves further comparing communities to single services and additional incentive investigations.
All Pair Shortest Path Algorithm – Parallel Implementation and AnalysisInderjeet Singh
This project report discusses the parallel implementation of the all pair shortest path algorithm using MPI and OpenMP. The algorithm was implemented by decomposing the adjacency matrix row-wise across processes. Results show that the parallel algorithm achieves speedup over the sequential version, especially for large graph sizes. The MPI implementation performed better than the OpenMP version. Graphs in the report compare execution time, speedup, and efficiency for different problem sizes and numbers of processes/threads.
Alpine Data Labs presents a deep dive into our implementation of Multinomial Logistic Regression with Apache Spark. Machine Learning Engineer DB Tsai takes us through the technical implementation details step by step. First, he explains how the state of the art Machine Learning on Hadoop is not doing fulfilling the promise of Big Data. Next, he explains how Spark is a perfect match for machine learning through their in-memory cache-ing capability demonstrating 100x performance improvement. Third, he takes us through each aspect of a multinomial logistic regression and how this is developed with Spark APIs. Fourth, he demonstrates an extension of MLOR and training parameters. Finally, he benchmarks MLOR with 11M rows, 123 features, 11% non-zero elements with a 5 node Hadoop cluster. Finally, he shows Alpine's unique visual environment with Spark and verifies the performance with the job tracker. In conclusion, Alpine supports the state of the art Cloudera and Pivotal Hadoop clusters and performances at a level that far exceeds its next nearest competitor.
Multinomial Logistic Regression with Apache SparkDB Tsai
Logistic Regression can not only be used for modeling binary outcomes but also multinomial outcome with some extension. In this talk, DB will talk about basic idea of binary logistic regression step by step, and then extend to multinomial one. He will show how easy it's with Spark to parallelize this iterative algorithm by utilizing the in-memory RDD cache to scale horizontally (the numbers of training data.) However, there is mathematical limitation on scaling vertically (the numbers of training features) while many recent applications from document classification and computational linguistics are of this type. He will talk about how to address this problem by L-BFGS optimizer instead of Newton optimizer.
Bio:
DB Tsai is a machine learning engineer working at Alpine Data Labs. He is recently working with Spark MLlib team to add support of L-BFGS optimizer and multinomial logistic regression in the upstream. He also led the Apache Spark development at Alpine Data Labs. Before joining Alpine Data labs, he was working on large-scale optimization of optical quantum circuits at Stanford as a PhD student.
Predicting organic reaction outcomes with weisfeiler lehman networkKazuki Fujikawa
This document discusses neural message passing networks for modeling quantum chemistry. It defines message passing networks as having message functions that update node states based on neighboring node states, vertex update functions that update node states based to accumulated messages, and a readout function that produces an output for the full graph. It provides examples of specific message, update, and readout functions used in existing message passing models like interaction networks and molecular graph convolutions.
Processor Allocation and Task Scheduling of Matrix Chain Products
on Parallel Systems(Parallelizing matrix chain products)
Heejo Lee, Jong Kim, Sungje Hong, Sunggu Lee
Dept of Computer Science and Engineering Pohang University of
Science and Technology, Korea
This document discusses 2-D plotting in MATLAB. It introduces 2-D plotting and its uses, including for data analysis and visualization. It provides an example coding for plotting two functions simultaneously. The output shows the variation of quantities over time. Applications of 2-D plotting include building custom interfaces, improving code quality, and integrating algorithms with other languages and applications like Excel.
This document provides an introduction and overview of MATLAB (Matrix Laboratory). It outlines key topics that will be covered, including what MATLAB is, the MATLAB screen and workspace, variables and arrays, built-in math functions, flow control, and toolboxes. The document also lists some common commands and functions in MATLAB. It is intended to familiarize readers with the basics of MATLAB through examples and explanations of its main capabilities and features.
The document proposes the Layered Spiral Algorithm (LSA) for memory-aware application mapping and scheduling onto Network-on-Chip (NoC) architectures. LSA extends the existing spiral mapping algorithm to consider memory constraints and task scheduling. It models applications as Memory-Aware Communication Task Graphs (MACTG) and platforms as Platform Architecture Graphs (PAG). LSA aims to minimize energy consumption during mapping and scheduling while maintaining high parallelism. It compares results to optimal solutions from an Mixed Integer Linear Programming (MILP) formulation to evaluate performance.
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Accelerating Machine Learning Algorithms by integrating GPUs into MapReduce Clusters
1. ACCELERATING MACHINE LEARNING ALGORITHMS BY INTEGRATING
GPUS INTO MAPREDUCE CLUSTERS
Sergio Herrero-Lopez
Intelligent Engineering Systems Laboratory (IESL)
November 30, 2011
1 Accelerating ML algorithms by integrating GPUs in MR Clusters
2. INTRODUCTION
ABOUT ME:
Ph.D (December 2011) at Massachusetts Institute of Technology (USA)
M.Sc (2007) and B.Sc (2005) in Electrical Engineering at University of Navarra (Spain)
Microsoft Research (Redmond WA, 2008), Tampere University of Technology (Finland,
2005) and IKUSI (Spain, 2003)
ABOUT PROF. WILLIAMS RESEARCH GROUP (ENGINEERING SYSTEMS DIVISION):
High Performance Price Analytics for the Smart Grid (2008-2009)
Large-Scale Simulator for Global Data Infrastructure Optimization (2009-2011)
Music Event Detection from Tweets in New York (2010-2011)
Accelerating Machine Learning Algorithms by integrating GPUs into
MapReduce Clusters
2 Accelerating ML algorithms by integrating GPUs in MR Clusters
3. AGENDA
o PROBLEM STATEMENT: Big Data & Need for scale and/or speed
o PROPOSITION: Modify MapReduce runtime to
o Satisfy the particular requirements of ML algorithms
o Integrate Massively Parallel Processors in the system
o PREVIOUS WORK MapReduce for ML in Multicore/Single-GPU/Multi-
GPU/GPU-Cluster/FPGA
o IMPLEMENTATION of new MR runtime using Port abstractions
o PERFORMANCE results running SVMs on the proposed system
o CONCLUSIONS: Contributions and Limitations. Lessons learned
o FUTURE WORK
3 Accelerating ML algorithms by integrating GPUs in MR Clusters
4. MACHINE LEARNING PARALLELIZATION
{ xi, yi },i =1… n, "i, n -Representative sample 1. Does not fit in resources
d -Feature selection 2. Takes too long
xi Î R d , yi Î Y = {1… k} k -Consolidate classes 3. Accuracy was sacrificed
Algorithm 1 Algorithm 1 Independent Runs
L1 Worker X Worker Y
(Cluster)
Algorithm 1 Summation Form
L2 (MapReduce)
Worker X Worker Y
Algorithm 1
L3 Structural Parallelism
(MPPs)
Machine Learning Algorithms decomposable into MR primitives
Naïve Bayes
K-means Expectation Maximization
Neural Network Support Vector Machine Classification
Principal Component Analysis Hidden Markov Models
4 Accelerating ML algorithms by integrating GPUs in MR Clusters
5. MAPREDUCE PRIMITIVES & RUNTIME
Input
M [ k1, v1 ] ® [ k2, v2 ]
Split
R ék2 , {v2,i }k
ë
ù® v WORKER 1 WORKER 2 WORKER M-1 WORKER M
2,i =k2 û
3
Map
Sort
WORKER 1 WORKER 2 WORKER N-1 WORKER N
Reduce
Merge
Output
5 Accelerating ML algorithms by integrating GPUs in MR Clusters
6. MAPREDUCE REPRESENTATION OF K-MEANS
M ékit , xi ù ® éki¢t , xi ù
ë û ë û
kit
{
ki¢t = x j : x j - mit £ x j - mit¢ "i¢ =1… k } ki¢t
Rék¢t , { xi }k¢t =k¢t ù ® mk¢t
ë û
t+1
{ xi }k¢ =k¢
i
t t
i
å
1
mk¢t =
t+1
x
xi ki¢t =k ¢t x Î{ xi }k¢t =k¢t
t+1
mk¢t
i
6 Accelerating ML algorithms by integrating GPUs in MR Clusters
7. MAPREDUCE REPRESENTATION OF EM FOR MIXTURE OF GAUSSIANS
M [(i, k), xi ] ® é(i, k), pi,k ù
ë û xi
a f ( xi | m , S
t
k
t
k
t
k )
pi,k = K
åa f ( x | m , S )
t
k i
t
k
t
k pi,k
k=1
Rék, { pi,k¢ }k¢=k ù ® ak
t+1 { pi,k¢ }k¢=k
ë û
n
åp i,k t+1
a t+1
k = i=1 ak
n
Rék, { xi , pi,k¢ }k¢=k ù ® mk
ë û
t+1
{ xi, pi,k¢ }k¢=k
n
åx p i i,k
m t+1
k = i=1
t+1 mk
t+1
nak
Rék, { xi , pi,k¢ }k¢=k ù ® St+1
ë û k
{ xi, pi,k¢ }k¢=k
n
å p (x i - m k ) ( xi - m k )
t+1 t+1 T
i,k
S t+1
k = i=1
na t+1 St+1
k
k
7 Accelerating ML algorithms by integrating GPUs in MR Clusters
8. MAPREDUCE REPRESENTATION OF SVM (SMO)
M [i, fi ] ® [i, fi¢] fi
fi¢= fi + Da Iup yIup k(x Iup , x i )+ Da Ilow yIlow k(x Ilow , x i ) fi¢
M [i, ai ] ® [i, ki ]
I 0 = {i : yi = {1, -1}, 0 < a i < C}
ai
I1 = {i : yi = 1, a i = 0} È {i : yi = -1, a i = C }
I 2 = {i : yi = 1, ai = C} È {i : yi = -1, a i = 0} ki
kup = {i Î I 0 È I1 }, klow = {i Î I 0 È I 2 }
ki Î kup , klow
R ék, { fi }k =k ù ® (b, I )
ë i û
{ fi }k =k
i
bup = min{ fi : ki = kup }, Iup = argmin ki =kup fi
blow = max{ fi : ki = klow }, I low = argmax ki =klow fi (b, I)
M [i, ai ] ® [i, ai¢]
yIup ( fIlow - fIup ) ai
a¢ = aI -
Iup up
2k(xIlow , xIup ) - k(xIlow , xIlow ) - k(xIup , xIup )
a ¢ = a I + yI yI (a I - a ¢ )
I
low low low Iup up up
a i¢
8 Accelerating ML algorithms by integrating GPUs in MR Clusters
9. MAPREDUCE FOR ML WISHLIST
Static Variable
mk
Static vs Variable data
xi x
Static: Largest, fixed, used in every iteration
i (a , mk , St+1 )
t+1 t+1
( xi, yi )
k k
Variable: Results of each iteration, consumed in the next
iteration ( fi, ai )
DFS
Iterate until convergence
Avoid reloading static data between iterations MEM
Utilize memory hierarchy as opposed to DFS or LFS
DFS
Massively Threaded MapReduce Tasks
Map is embarrassingly parallel
CPU MPP
Reduce is highly parallelizable
Dimensionality & Algebra - b xi -x j
2
Map Tasks may encapsulate high dimensional matrix-vector k(xi , x j ) = e
or matrix-matrix operations
Interleave multithreaded BLAS operations using static data i = 1...n, j Î { I up, I low }
Sparse data structures
9 Accelerating ML algorithms by integrating GPUs in MR Clusters
10. COMPUTING ECOSYSTEM
COMMODITY HIGH PERFORMANCE/SUPER
COMPUTING COMPUTING
RELATIONAL DB
HADOOP INFINIBAND
BIGTABLE
DRYAD
CASSANDRA OPENMPI
GPU
DYNAMO GPU
1/10 GB ETHERNET
FPGA
COLUMN DB
HADOOP
20 GB INFINIBAND
SSD
DATA APPLIANCE/ WAREHOUSE
COMPUTING
10 Accelerating ML algorithms by integrating GPUs in MR Clusters
11. MAPREDUCE CLUSTER: ARCHITECTURE
Client 1) Distributed File System.
- Unstructured data
File Job - Scales to thousands of nodes
- High reliability through
NameNode
replication
DFS MRF
2) Map Reduce Framework Runtime
JobTracker - Batch processing system
- Load balancing
Task Task
Task
DataNode 1 Block DataNode 2 DataNode 3
Block
Block
MRF MRF MRF
TaskTracker TaskTracker TaskTracker
DFS DFS DFS
11 Accelerating ML algorithms by integrating GPUs in MR Clusters
12. MAPREDUCE CLUSTER: LIMITATIONS
DataNode 1 DataNode 2
Task Task
MRF Tracker
MRF Tracker
One (or two) tasks per node
DFS Block DFS Block
One Task One Data Block
CPU CPU
One Core One Thread
Map Map
Task Task
HD Block HD Block
Synchronization by materialization of
intermediate results
CPU CPU
Reduce Reduce
Task Task
DFS Block DFS Block
No support for iterative jobs
12 Accelerating ML algorithms by integrating GPUs in MR Clusters
13. MASSIVELY PARALLEL PROCESSORS: NVIDIA TESLA ARCHITECTURE
Host Device
Stream Multiprocessor N
Stream Multiprocessor 2 Memory
Shared
1 Cycle coalesced
Stream Multiprocessor 1 Memory
Shared ~10 Cycles uncoalesced
Registers Registers Registers
Shared Memory
Registers Registers Registers Instruction
Registers Unit
ProcessorRegisters
1 Processor 2 Registers
…. Processor M Instruction
Unit
0 Cycles Processor 1 Processor 2 …. Processor M Instruction
Constant Cache Unit
SP 1 SP 2 …. SP M
Constant Cache
Texture Cache
~10 Cycles Cache Hit
Constant Memory
Texture Cache
Texture Memory
~400 Cycles ~400 Cycles
102 GB/s 102 GB/s
Host
Memory Device Memory
PCI-E 16x
(8GB/s)
13 Accelerating ML algorithms by integrating GPUs in MR Clusters
14. NVIDIA TESLA: REPRESENTATIONS
Logical Representation Physical Representation
Thread Processor
Block MultiProcessor
Maximum
(512,512,64)
But max 512
threads per
block
Grid Device
Shared
Shared
Register Memor
Register Register
Maximum
Register Memor s
s Register yRegister
s
Processs y …. s
s Process Process
(65535, Process or ConstantM
Process…. or
65535) or 1 2 Process
or 1 or ConstantM
2 Texture
or
Cache
Cache
Cache
14 Accelerating ML algorithms by integrating GPUs in MR Clusters
15. PROPOSED RUNTIME: MR + GPU
Block Block
DFS MRF Task Tracker
HState
HMem
Split
H->D Transfers
DMem DState Pre-Map BLAS
GPU Map
DMem DState Post-Map D->H Transfers
HState Cross-Node
HMem Sort
DMem DState H->D Transfers
Pre-Reduce BLAS
Local
GPU Reduce
DMem DState D->H Transfers
Post-Reduce
HState
Cross-Node Global
HMem
Reduce
Block Block
State Snapshot every
DFS x iterations
15 Accelerating ML algorithms by integrating GPUs in MR Clusters
17. PREVIOUS WORK
MAPREDUCE ON SINGLE GPU/ SINGLE FPGA Interleave Multithreaded BLAS
•Mars (He et al. PACT 2008)
•NVIDIA (Catanzaro et al. STMCS 2008)
•Cell (de Kruijf and Sankaralingam IBM Journal R&D 2009)
Massively Multithreaded MR Tasks
MAPREDUCE ON MULTICORE Shared-Memory
•Phoenix (Ranger et al. HPCA 2007)
•Phoenix 2 (Yoo et al. IISWC 2009)
•Phoenix ++ (Talbot et al. MAPREDUCE 2011)
Fault-Tolerance Relaxation
MAPREDUCE ON MULTI-GPU/GPU CLUSTERS Intermediate data in-memory
•CellMR (Rafique et al. IPDPS 2009)
•GPMR (Stuart and Owens IPDPS 2011)
Local/Global Reduction
MAPREDUCE FOR MACHINE LEARNING
•Mahout (Apache) Long running (iterative) Tasks
•Multicore (Chu et al. NIPS 2006)
•FGPA (Xu NIPS 2009)
•Twister (Ekanayake et al. MAPREDUCE 2010)
•SystemML (Ghoting et al. ICDE 2011) Static vs Variable Data
17 Accelerating ML algorithms by integrating GPUs in MR Clusters
18. PORT-BASED PROGRAMMING: ABSTRACTION
Message
Port
Single Item Receiver
Arbiter Multiple Item Receiver
Dispatcher
Handler
Handler Task
Handler
Join Receiver
Dispatcher
Queue Choice Receiver
Teardown
State Handler Concurrent
Exclusive
Scatter
Gather
18 Accelerating ML algorithms by integrating GPUs in MR Clusters
21. BINARY SVM
Binary Classification:
Given l samples x1, y1 ,, xl , yl with xi Rn , yi Y , i and Y 1,1 ,
a binary classifier predicts the label y Y of an unseen sample x Rn
1
f*
f*
2
xi x j
k ( xi , x j ) e
21 Accelerating ML algorithms by integrating GPUs in MR Clusters
22. PRIMAL & DUAL FORM OF THE SVM
Find the function f that solves the following regularization problem:
l k maxk,0
1 2
min f HC 1 yi f xi f where
i 1 2 C 0
Then slack variables i are introduced to classify non-separable data:
Primal form: Dual form:
l l
1 2 1 T
min f H C i f max K
i 1 2 Rl i 1
i
2
subject to: subject to:
l
yi f xi 1 yi i 0
i
i 1, , l i 1 i 1, , l
i 0 0 i C
where Kij yi y j k xi , x j
is the kernel function
l
Solving the dual: f ( x ) yi i k x , xi b where b is an unreagularized bias term
i 1
22 Accelerating ML algorithms by integrating GPUs in MR Clusters
23. MULTICLASS CLASSIFICATION
Multiclass Classification:
Given l samples x1, y1 ,, xl , yl with xi Rn , yi Y , i and Y 1, M ,
,
a multiclass classifier predicts the label y Y of an unseen sample x Rn
Multiclass SVM: Combination of N independent binary classification tasks. Binary tasks
are defined by an output code matrix R of size MxN and R ij 1,0,1
1 1 0 1 1 1
M
All vs All (AVA): R 1 0 1 N
2 One vs All (OVA): R 1 1 1 N M
0 1 1 1 1 1
23 Accelerating ML algorithms by integrating GPUs in MR Clusters
24. BINARY SVM AS MAP REDUCE PRIMITIVES IN A SINGLE-GPU
GPU
Processor 1 Processor p Processor P
fi
MAP
f i'
MAP
(ai , ki )
LOCAL
REDUCE (ki , fi ' ) (ki , fi ' )
GLOBAL
REDUCE (bup , I up ) Pre-MAP (blow, Ilow)
MAP ' '
up low
2
- b xi -x j
k(xi , x j ) = e
i = 1...n, j Î { I up, I low }
Device State: (xi , yi ) ( fi , ai , ki , b, I, K) LRU Cache
Static Variable
24 Accelerating ML algorithms by integrating GPUs in MR Clusters
26. EXPERIMENTS AND HARDWARE
Host Device
Ubuntu 8.10 64bit 4x Tesla C1060
Dual Socket Intel Xeon
# Stream Processors: 240
E5520
Frequency of Frequency of Processors:
Cores: 2.26 GHz 1.3GHz
145 GFlops 933 GFlops
Memory: Memory:
32GB DDR3 4GB DDR3
Memory Bandwidth: Memory Bandwidth:
25.6GB/s 102GB/s
Host <-> Device
PCIe x16 (8GB/s)
LIBSVM Hadoop Multicore Single GPU Multi GPU
• Single threaded • 4 VMs with one • 8 Worker Threads • 1 Worker Thread • 4 Worker Threads
• Double precision datanode each in H-Dispatch • 1 GPU • 4 GPUs
• Sparse • Pegasos SVM • 1 Block – 1 Thread • Single Precision • Single Precision
• Double Precision • Double Precision • Dense-Sparse • Dense-Sparse
• Sparse • Dense
26 Accelerating ML algorithms by integrating GPUs in MR Clusters
27. PERFORMANCE RESULTS: DATASETS
SVM Experiment Setup # Training # Testing # (Features,
Dataset (C,β)
Points Points Classes)
Same kernel types (RBF) WEB 49749 14951 (300,2) (64,7.8125)
Same regularization parameter C
Same stopping criteria: 0.001 MNIST 60000 10000 (780,10) (10,0.125)
SMO based (Except Hadoop version)
RCV1 518571 15564 (47236,53) (1,0.1)
One vs All in multiclass problems
1GB kernel cache PROTEIN 17766 6621 (357,3) (10,0.05)
SENSIT 78823 19705 (100,3) (1,0.7)
27 Accelerating ML algorithms by integrating GPUs in MR Clusters
28. PERFORMANCE RESULT COMPARISON
Single Multi
Dataset (Non-Zero %) LIBSVM Hadoop Multicore
GPU(Dense) GPU(Dense)
Time(s) 2364.2 1698.7 912.81 154.3 73.6
WEB (3%) Gain (x) 1.00 1.39 2.59 15.32 32.12
Accuracy (%) 82.69 82.69 82.69 82.69 82.69
Time(s) 118943.5 66753.5 22873.75 2010.3 726.9
MNIST (19%) Gain (x) 1.00 1.78 5.20 59.17 163.63
Accuracy (%) 95.76 95.76 95.76 95.76 95.76
Time(s) 710664 231486 N/A N/A N/A
RCV1 (0.1%) Gain (x) 1.00 3.07 N/A N/A N/A
Accuracy (%) 94.67 94.67 94.67 94.67 94.67
Time(s) 861 717.5 260.12 32.93 16.06
PROTEIN (29%) Gain (x) 1.00 1.20 3.31 26.15 53.61
Accuracy (%) 70.03 70.03 70.03 70.03 70.03
Time(s) 8162 4295.78 2005.4 134.67 58.29
SENSIT (100%) Gain (x) 1.00 1.90 4.07 60.61 140.02
Accuracy (%) 83.46 83.46 83.46 83.46 83.46
28 Accelerating ML algorithms by integrating MapReduce Clusters
SVMs by integrating GPUs in GPUs in MR
29. ELLPACK-R (Vazquez et al. IEEE CIT 2010)
Dataset Single Multi
(Non-Zero %) GPU(Sparse) GPU(Sparse)
Time(s) 107.35 57.3
WEB (3%) Gain (x) 22.02 (1.43) 41.26 (1.26)
Accuracy (%) 82.69 82.69
Time(s) N/A 3686
RCV1 (0.1%) Gain (x) N/A 192.80
Accuracy (%) 94.67 94.67
~8.2 days -> ~1hour
29 Accelerating ML algorithms by integrating GPUs in MR Clusters
30. CONCLUSIONS
CONCLUSIONS:
Constructed a MR runtime that satisfies the requirements of many ML algorithms and integrates GPUs.
Iterative stateful jobs
Multithreaded BLAS to prepare Map or Reduce Tasks
Static/Variable data
Tested the runtime solving popular classification problems.
Delivered up to two orders of magnitude of acceleration using 4 GPUs
Compared different runtimes
LIMITATIONS:
H-Dispatch (Pull) dependent on H->D state transfers
Relaxation of Fault-tolerance must be acceptable
d>>n -> MapReduce will have little benefit
30 Accelerating ML algorithms by integrating GPUs in MR Clusters
31. FUTURE WORK
FUTURE:
GPU Technology:
Concurrent Kernel Execution-> Maximize utilization
GPUDirect-> Facilitate Sort operation
Distributed Memory -> Intermediate Results
Shared memory space CPU-GPU
Communication
Cross-Node performance
GPU-Port-Abstraction
In-node: Cross-Thread pointer exchange
Out-node: MVAPICH2 and MVAPICH2-GPU
Algorithms
Requirements for incremental classification and clustering
31 Accelerating ML algorithms by integrating GPUs in MR Clusters
32. CONCURRENT KERNEL EXECUTION
Port
CPU
Task
Thread 1
Queue
CPU
Thread 2
• CUDA Compute Capability 2.0
allows up to sixteen concurrent
kernels.
• Concurrent kernels need to run
on the same context.
32 Accelerating ML algorithms by integrating GPUs in MR Clusters
33. INTEGRATING THE MPP IN THE MR CLUSTER ARCHITECTURE
Block Block
DFS MRF Task Tracker
HState
HMem
DMem DState
GPUDirect:
GPU • GPU to GPU memory copy
DState • Communication with network
DMem devices
HState Cross-Node
HMem
DMem DState
Minimal Communication to HState
GPU
DState
DMem
HState
Cross-Node
HMem
Block Block
State Snapshot every
DFS x iterations
33 Accelerating ML algorithms by integrating GPUs in MR Clusters
34. PIPELINING/MEMCACHED
DataNode 1 DataNode 2
Task Task
MRF Tracker
MRF Tracker
DFS Block DFS Block
Memcached
node
CPU CPU
Map Map
Task Task
node
MEM MEM
node
CPU CPU
Reduce Reduce
Task Task
DFS Block DFS Block
34 Accelerating ML algorithms by integrating GPUs in MR Clusters
35. QUESTIONS
35 Accelerating ML algorithms by integrating MapReduce Clusters
SVMs by integrating GPUs in GPUs in MR
36. APPLICATION I: EVENT DETECTION USING TWEETS
Sakaki et al: Detect Tweet
outbreaks about large-scale and
infrequent events: Natural
Disasters: Earthquakes, floods.
Accidents: Fire, road accidents
INFREQUENT EVENTS
36 Accelerating ML algorithms by integrating GPUs in MR Clusters
37. APPLICATION I: EVENT DETECTION USING TWEETS
Listening to the New
York Philarmonic,
amazing performance
Lots of people trying
to enter the MSG for
the Alice in Chains
concert. I wish I had
tickets.
Goal: Detect popular Nassau County Museum of Art is
events on locations with looking for volunteers to greet,
high volume of tweets. work in gift shop or perform
clerical support.
37 Accelerating ML algorithms by integrating GPUs in MR Clusters
38. APPLICATION I: FEATURE VECTOR
It/PRP is/VBZ a/DT good/JJ day/NN when/WRB the/DT CEO/NN
of/IN a/DT multinational/JJ ,/, multi-million/JJ
dollar/NN company/NN tells/VBZ you/PRP you/PRP 're/VBP
a/DT genius/NN ./.:/: D/NNP
Lots/NNS of/IN people/NNS trying/VBG to/TO enter/VB
the/DT MSG/NNP for/IN the/DT Alice/NNP in/IN
Chains/NNP concert/NN ./.I/PRP wish/VBP I/PRP
had/VBD tickets/NNS ./.
Feature Vectors:
- Has unigram with POS
ì 1 If (x,y) contains___
- Has bigram with POSs
hi (x, y) = í - Has trigram with POSs
î 0 otherwise - X1 is subject of X2
- ….
38 Accelerating ML algorithms by integrating GPUs in MR Clusters
39. APPLICATION I: EXPERIMENT
Used NYC.com event calendar (Oct 9-11,2009). Extracted ~400 features
Title Location Description
Alice in Chains has sold more than twenty million albums in the
Madison Square Garden, 2 United States (and an estimated 40 million worldwide), released
Alice in
Penn Plaza, New York, NY, two number-one albums and 19 top 40 singles, and has received
Chains
10001 six Grammy nominations…
EXPERIMENT 1:
• 2000 Tweets from the same weekend (160 (%8) “Concert”, 1840 (%92) “Background”)
• RBF Kernel (C=10, gamma=1.0). Testing 20% -> Accuracy of %97
• “False positives”
EXPERIMENT 2:
• 2000 Tweets from the next weekend (160 (%8) “Concert”, 1840 (%92) “Background”)
• RBF Kernel (C=10, gamma=1.0). Testing 100% -> Accuracy of %93
• “False positives” + “False negative”
• After using NYC.com again -> Accuracy of %96
39 Accelerating ML algorithms by integrating GPUs in MR Clusters
40. APPLICATION II: PRICE CALCULATIONS FOR EACH HOUSEHOLD
30 x 96 = 2880 Values
8
40 Accelerating ML algorithms by integrating GPUs in MR Clusters
41. APPLICATION II: PRICE CALCULATIONS FOR EACH HOUSEHOLD
41 Accelerating ML algorithms by integrating GPUs in MR Clusters