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Generalized Principal Component Analysis
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Book Synopsis Generalized Principal Component Analysis by : René Vidal
Download or read book Generalized Principal Component Analysis written by René Vidal and published by Springer. This book was released on 2016-04-11 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Principal Component Analysis (GPCA) by : René Esteban Vidal
Download or read book Generalized Principal Component Analysis (GPCA) written by René Esteban Vidal and published by . This book was released on 2003 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in Principal Component Analysis by : Ganesh R. Naik
Download or read book Advances in Principal Component Analysis written by Ganesh R. Naik and published by Springer. This book was released on 2017-12-11 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports on the latest advances in concepts and further developments of principal component analysis (PCA), addressing a number of open problems related to dimensional reduction techniques and their extensions in detail. Bringing together research results previously scattered throughout many scientific journals papers worldwide, the book presents them in a methodologically unified form. Offering vital insights into the subject matter in self-contained chapters that balance the theory and concrete applications, and especially focusing on open problems, it is essential reading for all researchers and practitioners with an interest in PCA.
Book Synopsis Principal Component Analysis by : I.T. Jolliffe
Download or read book Principal Component Analysis written by I.T. Jolliffe and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Low Rank Models by : Madeleine Udell
Download or read book Generalized Low Rank Models written by Madeleine Udell and published by . This book was released on 2016-05-03 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well-known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, k-means, k-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.
Book Synopsis Nonlinear Principal Component Analysis and Its Applications by : Yuichi Mori
Download or read book Nonlinear Principal Component Analysis and Its Applications written by Yuichi Mori and published by Springer. This book was released on 2016-12-09 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book expounds the principle and related applications of nonlinear principal component analysis (PCA), which is useful method to analyze mixed measurement levels data. In the part dealing with the principle, after a brief introduction of ordinary PCA, a PCA for categorical data (nominal and ordinal) is introduced as nonlinear PCA, in which an optimal scaling technique is used to quantify the categorical variables. The alternating least squares (ALS) is the main algorithm in the method. Multiple correspondence analysis (MCA), a special case of nonlinear PCA, is also introduced. All formulations in these methods are integrated in the same manner as matrix operations. Because any measurement levels data can be treated consistently as numerical data and ALS is a very powerful tool for estimations, the methods can be utilized in a variety of fields such as biometrics, econometrics, psychometrics, and sociology. In the applications part of the book, four applications are introduced: variable selection for mixed measurement levels data, sparse MCA, joint dimension reduction and clustering methods for categorical data, and acceleration of ALS computation. The variable selection methods in PCA that originally were developed for numerical data can be applied to any types of measurement levels by using nonlinear PCA. Sparseness and joint dimension reduction and clustering for nonlinear data, the results of recent studies, are extensions obtained by the same matrix operations in nonlinear PCA. Finally, an acceleration algorithm is proposed to reduce the problem of computational cost in the ALS iteration in nonlinear multivariate methods. This book thus presents the usefulness of nonlinear PCA which can be applied to different measurement levels data in diverse fields. As well, it covers the latest topics including the extension of the traditional statistical method, newly proposed nonlinear methods, and computational efficiency in the methods.
Book Synopsis A User's Guide to Principal Components by : J. Edward Jackson
Download or read book A User's Guide to Principal Components written by J. Edward Jackson and published by John Wiley & Sons. This book was released on 2005-01-21 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. From the Reviews of A User’s Guide to Principal Components "The book is aptly and correctly named–A User’s Guide. It is the kind of book that a user at any level, novice or skilled practitioner, would want to have at hand for autotutorial, for refresher, or as a general-purpose guide through the maze of modern PCA." –Technometrics "I recommend A User’s Guide to Principal Components to anyone who is running multivariate analyses, or who contemplates performing such analyses. Those who write their own software will find the book helpful in designing better programs. Those who use off-the-shelf software will find it invaluable in interpreting the results." –Mathematical Geology
Book Synopsis Generalized Structured Component Analysis by : Heungsun Hwang
Download or read book Generalized Structured Component Analysis written by Heungsun Hwang and published by CRC Press. This book was released on 2014-12-11 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed by the authors, generalized structured component analysis is an alternative to two longstanding approaches to structural equation modeling: covariance structure analysis and partial least squares path modeling. Generalized structured component analysis allows researchers to evaluate the adequacy of a model as a whole, compare a model to alternative specifications, and conduct complex analyses in a straightforward manner. Generalized Structured Component Analysis: A Component-Based Approach to Structural Equation Modeling provides a detailed account of this novel statistical methodology and its various extensions. The authors present the theoretical underpinnings of generalized structured component analysis and demonstrate how it can be applied to various empirical examples. The book enables quantitative methodologists, applied researchers, and practitioners to grasp the basic concepts behind this new approach and apply it to their own research. The book emphasizes conceptual discussions throughout while relegating more technical intricacies to the chapter appendices. Most chapters compare generalized structured component analysis to partial least squares path modeling to show how the two component-based approaches differ when addressing an identical issue. The authors also offer a free, online software program (GeSCA) and an Excel-based software program (XLSTAT) for implementing the basic features of generalized structured component analysis.
Book Synopsis Independent Component Analysis by : Aapo Hyvärinen
Download or read book Independent Component Analysis written by Aapo Hyvärinen and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition by : Haruo Yanai
Download or read book Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition written by Haruo Yanai and published by Springer Science & Business Media. This book was released on 2011-04-06 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.
Book Synopsis Principal Component Neural Networks by : K. I. Diamantaras
Download or read book Principal Component Neural Networks written by K. I. Diamantaras and published by Wiley-Interscience. This book was released on 1996-03-08 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Data-Driven and Model-Based Methods for Fault Detection and Diagnosis by : Majdi Mansouri
Download or read book Data-Driven and Model-Based Methods for Fault Detection and Diagnosis written by Majdi Mansouri and published by Elsevier. This book was released on 2020-02-05 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data-Driven and Model-Based Methods for Fault Detection and Diagnosis covers techniques that improve the quality of fault detection and enhance monitoring through chemical and environmental processes. The book provides both the theoretical framework and technical solutions. It starts with a review of relevant literature, proceeds with a detailed description of developed methodologies, and then discusses the results of developed methodologies, and ends with major conclusions reached from the analysis of simulation and experimental studies. The book is an indispensable resource for researchers in academia and industry and practitioners working in chemical and environmental engineering to do their work safely. Outlines latent variable based hypothesis testing fault detection techniques to enhance monitoring processes represented by linear or nonlinear input-space models (such as PCA) or input-output models (such as PLS) Explains multiscale latent variable based hypothesis testing fault detection techniques using multiscale representation to help deal with uncertainty in the data and minimize its effect on fault detection Includes interval PCA (IPCA) and interval PLS (IPLS) fault detection methods to enhance the quality of fault detection Provides model-based detection techniques for the improvement of monitoring processes using state estimation-based fault detection approaches Demonstrates the effectiveness of the proposed strategies by conducting simulation and experimental studies on synthetic data
Book Synopsis Three-mode Principal Component Analysis by : Pieter M. Kroonenberg
Download or read book Three-mode Principal Component Analysis written by Pieter M. Kroonenberg and published by . This book was released on 1983 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Biplots in Practice by : Michael J. Greenacre
Download or read book Biplots in Practice written by Michael J. Greenacre and published by Fundacion BBVA. This book was released on 2010 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Este libro explica las aplicaciones específicas y las interpretaciones del biplot en muchas áreas del análisis multivariante. regresión, modelos lineales generalizados, análisis de componentes principales, análisis de correspondencias y análisis discriminante.
Book Synopsis The Gini Methodology by : Shlomo Yitzhaki
Download or read book The Gini Methodology written by Shlomo Yitzhaki and published by Springer Science & Business Media. This book was released on 2012-11-13 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gini's mean difference (GMD) was first introduced by Corrado Gini in 1912 as an alternative measure of variability. GMD and the parameters which are derived from it (such as the Gini coefficient or the concentration ratio) have been in use in the area of income distribution for almost a century. In practice, the use of GMD as a measure of variability is justified whenever the investigator is not ready to impose, without questioning, the convenient world of normality. This makes the GMD of critical importance in the complex research of statisticians, economists, econometricians, and policy makers. This book focuses on imitating analyses that are based on variance by replacing variance with the GMD and its variants. In this way, the text showcases how almost everything that can be done with the variance as a measure of variability, can be replicated by using Gini. Beyond this, there are marked benefits to utilizing Gini as opposed to other methods. One of the advantages of using Gini methodology is that it provides a unified system that enables the user to learn about various aspects of the underlying distribution. It also provides a systematic method and a unified terminology. Using Gini methodology can reduce the risk of imposing assumptions that are not supported by the data on the model. With these benefits in mind the text uses the covariance-based approach, though applications to other approaches are mentioned as well.
Download or read book Comprehensive Chemometrics written by and published by Elsevier. This book was released on 2009-03-09 with total page 2880 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed to serve as the first point of reference on the subject, Comprehensive Chemometrics presents an integrated summary of the present state of chemical and biochemical data analysis and manipulation. The work covers all major areas ranging from statistics to data acquisition, analysis, and applications. This major reference work provides broad-ranging, validated summaries of the major topics in chemometrics—with chapter introductions and advanced reviews for each area. The level of material is appropriate for graduate students as well as active researchers seeking a ready reference on obtaining and analyzing scientific data. Features the contributions of leading experts from 21 countries, under the guidance of the Editors-in-Chief and a team of specialist Section Editors: L. Buydens; D. Coomans; P. Van Espen; A. De Juan; J.H. Kalivas; B.K. Lavine; R. Leardi; R. Phan-Tan-Luu; L.A. Sarabia; and J. Trygg Examines the merits and limitations of each technique through practical examples and extensive visuals: 368 tables and more than 1,300 illustrations (750 in full color) Integrates coverage of chemical and biological methods, allowing readers to consider and test a range of techniques Consists of 2,200 pages and more than 90 review articles, making it the most comprehensive work of its kind Offers print and online purchase options, the latter of which delivers flexibility, accessibility, and usability through the search tools and other productivity-enhancing features of ScienceDirect
Book Synopsis Applying Generalized Linear Models by : James K. Lindsey
Download or read book Applying Generalized Linear Models written by James K. Lindsey and published by Springer Science & Business Media. This book was released on 2008-01-15 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes how generalised linear modelling procedures can be used in many different fields, without becoming entangled in problems of statistical inference. The author shows the unity of many of the commonly used models and provides readers with a taste of many different areas, such as survival models, time series, and spatial analysis, and of their unity. As such, this book will appeal to applied statisticians and to scientists having a basic grounding in modern statistics. With many exercises at the end of each chapter, it will equally constitute an excellent text for teaching applied statistics students and non- statistics majors. The reader is assumed to have knowledge of basic statistical principles, whether from a Bayesian, frequentist, or direct likelihood point of view, being familiar at least with the analysis of the simpler normal linear models, regression and ANOVA.
