Principal Component Analysis Networks And Algorithms
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Principal Component Analysis Networks And Algorithms
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Author : Xiangyu Kong
language : en
Publisher: Springer
Release Date : 2017-01-09
Principal Component Analysis Networks And Algorithms written by Xiangyu Kong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-09 with Technology & Engineering categories.
This book not only provides a comprehensive introduction to neural-based PCA methods in control science, but also presents many novel PCA algorithms and their extensions and generalizations, e.g., dual purpose, coupled PCA, GED, neural based SVD algorithms, etc. It also discusses in detail various analysis methods for the convergence, stabilizing, self-stabilizing property of algorithms, and introduces the deterministic discrete-time systems method to analyze the convergence of PCA/MCA algorithms. Readers should be familiar with numerical analysis and the fundamentals of statistics, such as the basics of least squares and stochastic algorithms. Although it focuses on neural networks, the book only presents their learning law, which is simply an iterative algorithm. Therefore, no a priori knowledge of neural networks is required. This book will be of interest and serve as a reference source to researchers and students in applied mathematics, statistics, engineering, and other related fields.
Principal Component Neural Networks
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Author : K. I. Diamantaras
language : en
Publisher: Wiley-Interscience
Release Date : 1996-03-08
Principal Component Neural Networks written by K. I. Diamantaras and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-03-08 with Computers categories.
Systematically explores the relationship between principal component analysis (PCA) and neural networks. Provides a synergistic examination of the mathematical, algorithmic, application and architectural aspects of principal component neural networks. Using a unified formulation, the authors present neural models performing PCA from the Hebbian learning rule and those which use least squares learning rules such as back-propagation. Examines the principles of biological perceptual systems to explain how the brain works. Every chapter contains a selected list of applications examples from diverse areas.
Independent Component Analysis
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Author : Aapo Hyvärinen
language : en
Publisher: John Wiley & Sons
Release Date : 2004-03-22
Independent Component Analysis written by Aapo Hyvärinen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-22 with Science categories.
A comprehensive introduction to ICA for students and practitioners Independent Component Analysis (ICA) is one of the most exciting new topics in fields such as neural networks, advanced statistics, and signal processing. This is the first book to provide a comprehensive introduction to this new technique complete with the fundamental mathematical background needed to understand and utilize it. It offers a general overview of the basics of ICA, important solutions and algorithms, and in-depth coverage of new applications in image processing, telecommunications, audio signal processing, and more. Independent Component Analysis is divided into four sections that cover: * General mathematical concepts utilized in the book * The basic ICA model and its solution * Various extensions of the basic ICA model * Real-world applications for ICA models Authors Hyvarinen, Karhunen, and Oja are well known for their contributions to the development of ICA and here cover all the relevant theory, new algorithms, and applications in various fields. Researchers, students, and practitioners from a variety of disciplines will find this accessible volume both helpful and informative.
Generalized Principal Component Analysis
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Author : René Vidal
language : en
Publisher: Springer
Release Date : 2016-04-11
Generalized Principal Component Analysis written by René Vidal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-11 with Science categories.
This book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.
Efficient Online Learning Algorithms For Total Least Square Problems
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Author : Xiangyu Kong
language : en
Publisher: Springer Nature
Release Date : 2024-07-17
Efficient Online Learning Algorithms For Total Least Square Problems written by Xiangyu Kong and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-17 with Mathematics categories.
This book reports the developments of the Total Least Square (TLS) algorithms for parameter estimation and adaptive filtering. Specifically, it introduces the authors’ latest achievements in the past 20 years, including the recursive TLS algorithms, the approximate inverse power iteration TLS algorithm, the neural based MCA algorithm, the neural based SVD algorithm, the neural based TLS algorithm, the TLS algorithms under non-Gaussian noises, performance analysis methods of TLS algorithms, etc. In order to faster the understanding and mastering of the new methods provided in this book for readers, before presenting each new method in each chapter, a specialized section is provided to review the closely related several basis models. Throughout the book, large of procedure of new methods are provided, and all new algorithms or methods proposed by us are tested and verified by numerical simulations or actual engineering applications. Readers will find illustrative demonstration examples on a range of industrial processes to study. Readers will find out the present deficiency and recent developments of the TLS parameter estimation fields, and learn from the the authors’ latest achievements or new methods around the practical industrial needs. In my opinion, this book can be assimilated by advanced undergraduates and graduate students, as well as statisticians, because of the new tools in data analysis, applied mathematics experts, because of the novel theories and techniques that we propose, engineers, above all for the applications in control, system identification, computer vision, and signal processing.
Neural Networks In A Softcomputing Framework
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Author : Ke-Lin Du
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-02
Neural Networks In A Softcomputing Framework written by Ke-Lin Du and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-02 with Computers categories.
Conventional model-based data processing methods are computationally expensive and require experts’ knowledge for the modelling of a system. Neural networks are a model-free, adaptive, parallel-processing solution. This textbook provides a powerful and universal paradigm for information processing; it reviews the most popular neural-network methods and their associated techniques. Each chapter has a systematic survey of each neural-network model. Computational intelligence topics like fuzzy logic and genetic algorithms (tools for neural-network learning) are introduced. Array signal processing problems are used to show the applications of each model. This is an ideal textbook for graduate students and researchers; as well as introducing the basics, the exhaustive list of references included will aid their future research. It is also a valuable reference for scientists and practitioners working in pattern recognition, signal processing, speech and image processing, data analysis and A.I.
Principal Component Analysis
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Author : I.T. Jolliffe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Principal Component Analysis written by I.T. Jolliffe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Principal component analysis is probably the oldest and best known of the It was first introduced by Pearson (1901), techniques ofmultivariate analysis. and developed independently by Hotelling (1933). Like many multivariate methods, it was not widely used until the advent of electronic computers, but it is now weIl entrenched in virtually every statistical computer package. The central idea of principal component analysis is to reduce the dimen sionality of a data set in which there are a large number of interrelated variables, while retaining as much as possible of the variation present in the data set. This reduction is achieved by transforming to a new set of variables, the principal components, which are uncorrelated, and which are ordered so that the first few retain most of the variation present in all of the original variables. Computation of the principal components reduces to the solution of an eigenvalue-eigenvector problem for a positive-semidefinite symmetrie matrix. Thus, the definition and computation of principal components are straightforward but, as will be seen, this apparently simple technique has a wide variety of different applications, as weIl as a number of different deri vations. Any feelings that principal component analysis is a narrow subject should soon be dispelled by the present book; indeed some quite broad topics which are related to principal component analysis receive no more than a brief mention in the final two chapters.
Principal Manifolds For Data Visualization And Dimension Reduction
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Author : Alexander N. Gorban
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10
Principal Manifolds For Data Visualization And Dimension Reduction written by Alexander N. Gorban and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10 with Computers categories.
The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described. Presentation of algorithms is supplemented by case studies. The volume ends with a tutorial PCA deciphers genome.
Neural Networks And Statistical Learning
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Author : Ke-Lin Du
language : en
Publisher: Springer Nature
Release Date : 2019-09-12
Neural Networks And Statistical Learning written by Ke-Lin Du and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-12 with Mathematics categories.
This book provides a broad yet detailed introduction to neural networks and machine learning in a statistical framework. A single, comprehensive resource for study and further research, it explores the major popular neural network models and statistical learning approaches with examples and exercises and allows readers to gain a practical working understanding of the content. This updated new edition presents recently published results and includes six new chapters that correspond to the recent advances in computational learning theory, sparse coding, deep learning, big data and cloud computing. Each chapter features state-of-the-art descriptions and significant research findings. The topics covered include: • multilayer perceptron; • the Hopfield network; • associative memory models;• clustering models and algorithms; • t he radial basis function network; • recurrent neural networks; • nonnegative matrix factorization; • independent component analysis; •probabilistic and Bayesian networks; and • fuzzy sets and logic. Focusing on the prominent accomplishments and their practical aspects, this book provides academic and technical staff, as well as graduate students and researchers with a solid foundation and comprehensive reference on the fields of neural networks, pattern recognition, signal processing, and machine learning.