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Author : I.T. Jolliffe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Download 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.
Author : George H. Dunteman
language : en
Release Date : 1989-05-01
Download Principal Components Analysis written by George H. Dunteman and has been published by SAGE this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-05-01 with Mathematics categories.
For anyone in need of a concise, introductory guide to principal components analysis, this book is a must. Through an effective use of simple mathematical-geometrical and multiple real-life examples (such as crime statistics, indicators of drug abuse, and educational expenditures) -- and by minimizing the use of matrix algebra -- the reader can quickly master and put this technique to immediate use.
Author : Giovanni Di Franco
language : en
Release Date : 2013-11-25T00:00:00+01:00
Download Factor Analysis And Principal Component Analysis written by Giovanni Di Franco and has been published by FrancoAngeli this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-25T00:00:00+01:00 with Social Science categories.
Author : Judson Gary Isebrands
language : en
Release Date : 1975
Download Introduction To Uses And Interpretation Of Principal Component Analysis In Forest Biology written by Judson Gary Isebrands and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Nature categories.
Author : René Vidal
language : en
Release Date : 2016-04-11
Download 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.
Author : Walter Theodore Federer
language : en
Release Date : 1987
Download Illustrative Examples Of Principal Component Analysis Using Systat Factor written by Walter Theodore Federer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
In order to provide a deeper understanding of the workings of principal components, four data sets were constructed by taking linear combinations of values of two correlated variables to form the X-variates for the principal component analysis. The examples highlight some of the properties and limitations of principal component analysis. This is part of a continuing project that produces annotated computer output for principal component analysis. The complete project will involve processing four examples on SAS/PRINCOMP, BMDP/4M, SPSS-X/FACTOR, GENSTAT / PCP, and SYSTAT / FACTOR. We show here the results from SYSTAT/FACTOR, Version 3. (Author).
Author : Yuichi Mori
language : en
Release Date : 2016-12-09
Download Nonlinear Principal Component Analysis And Its Applications written by Yuichi Mori and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-09 with Mathematics categories.
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.