Generalized Principal Component Analysis
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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.
Generalized Principal Component Analysis Gpca
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Author : René Esteban Vidal
language : en
Publisher:
Release Date : 2003
Generalized Principal Component Analysis Gpca written by René Esteban Vidal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Advances In Principal Component Analysis
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Author : Ganesh R. Naik
language : en
Publisher: Springer
Release Date : 2017-12-11
Advances In Principal Component Analysis written by Ganesh R. Naik and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-11 with Technology & Engineering categories.
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.
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.
Generalized Structured Component Analysis
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Author : Heungsun Hwang
language : en
Publisher: CRC Press
Release Date : 2014-12-11
Generalized Structured Component Analysis written by Heungsun Hwang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-11 with Mathematics categories.
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.
Generalized Low Rank Models
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Author : Madeleine Udell
language : en
Publisher:
Release Date : 2016-05-03
Generalized Low Rank Models written by Madeleine Udell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-03 with categories.
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.
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.
The Gini Methodology
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Author : Shlomo Yitzhaki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-13
The Gini Methodology written by Shlomo Yitzhaki 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 2012-11-13 with Mathematics categories.
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.
A User S Guide To Principal Components
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Author : J. Edward Jackson
language : en
Publisher: John Wiley & Sons
Release Date : 2005-01-21
A User S Guide To Principal Components written by J. Edward Jackson 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 2005-01-21 with Mathematics categories.
WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selectedbooks that have been made more accessible to consumers in an effortto increase global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. From the Reviews of A User’s Guide to PrincipalComponents "The book is aptly and correctly named–A User’sGuide. It is the kind of book that a user at any level, novice orskilled practitioner, would want to have at hand for autotutorial,for refresher, or as a general-purpose guide through the maze ofmodern PCA." –Technometrics "I recommend A User’s Guide to Principal Components toanyone who is running multivariate analyses, or who contemplatesperforming such analyses. Those who write their own software willfind the book helpful in designing better programs. Those who useoff-the-shelf software will find it invaluable in interpreting theresults." –Mathematical Geology
Biplots In Practice
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Author : Michael J. Greenacre
language : en
Publisher: Fundacion BBVA
Release Date : 2010
Biplots In Practice written by Michael J. Greenacre and has been published by Fundacion BBVA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Fishes categories.
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.