Factor Analysis and Dimension Reduction in R

Download Factor Analysis and Dimension Reduction in R PDF Online Free

Author :
Publisher : Taylor & Francis
ISBN 13 : 1000810593
Total Pages : 547 pages
Book Rating : 4.0/5 (8 download)

DOWNLOAD NOW!


Book Synopsis Factor Analysis and Dimension Reduction in R by : G. David Garson

Download or read book Factor Analysis and Dimension Reduction in R written by G. David Garson and published by Taylor & Francis. This book was released on 2022-12-16 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Factor Analysis and Dimension Reduction in R provides coverage, with worked examples, of a large number of dimension reduction procedures along with model performance metrics to compare them. Factor analysis in the form of principal components analysis (PCA) or principal factor analysis (PFA) is familiar to most social scientists. However, what is less familiar is understanding that factor analysis is a subset of the more general statistical family of dimension reduction methods. The social scientist's toolkit for factor analysis problems can be expanded to include the range of solutions this book presents. In addition to covering FA and PCA with orthogonal and oblique rotation, this book’s coverage includes higher-order factor models, bifactor models, models based on binary and ordinal data, models based on mixed data, generalized low-rank models, cluster analysis with GLRM, models involving supplemental variables or observations, Bayesian factor analysis, regularized factor analysis, testing for unidimensionality, and prediction with factor scores. The second half of the book deals with other procedures for dimension reduction. These include coverage of kernel PCA, factor analysis with multidimensional scaling, locally linear embedding models, Laplacian eigenmaps, diffusion maps, force directed methods, t-distributed stochastic neighbor embedding, independent component analysis (ICA), dimensionality reduction via regression (DRR), non-negative matrix factorization (NNMF), Isomap, Autoencoder, uniform manifold approximation and projection (UMAP) models, neural network models, and longitudinal factor analysis models. In addition, a special chapter covers metrics for comparing model performance. Features of this book include: Numerous worked examples with replicable R code Explicit comprehensive coverage of data assumptions Adaptation of factor methods to binary, ordinal, and categorical data Residual and outlier analysis Visualization of factor results Final chapters that treat integration of factor analysis with neural network and time series methods Presented in color with R code and introduction to R and RStudio, this book will be suitable for graduate-level and optional module courses for social scientists, and on quantitative methods and multivariate statistics courses.

Statistics and Data Analysis Through R

Download Statistics and Data Analysis Through R PDF Online Free

Author :
Publisher : Independently Published
ISBN 13 :
Total Pages : 222 pages
Book Rating : 4.5/5 (69 download)

DOWNLOAD NOW!


Book Synopsis Statistics and Data Analysis Through R by : César Pérez López

Download or read book Statistics and Data Analysis Through R written by César Pérez López and published by Independently Published. This book was released on 2020-11-08 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the implementation of statistics and data analysis through R. It deals first with the Exploratory Data Analysis both numerically and graphically, which is always a technique prior to any other statistical analysis. Descriptive statistics and the calculation of probabilities are then developed. Subsequently, the multiple regression model is approached, focusing on the problems of its estimation and diagnosis. It also delves into the generalized linear models and the analysis of variance and covariance models. Dimension reduction techniques are also addressed with special emphasis on principal component analysis and factor analysis. Finally, the segmentation techniques related to hierarchical and non-hierarchical cluster analysis are presented.

Feature Engineering and Selection

Download Feature Engineering and Selection PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1351609467
Total Pages : 266 pages
Book Rating : 4.3/5 (516 download)

DOWNLOAD NOW!


Book Synopsis Feature Engineering and Selection by : Max Kuhn

Download or read book Feature Engineering and Selection written by Max Kuhn and published by CRC Press. This book was released on 2019-07-25 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The process of developing predictive models includes many stages. Most resources focus on the modeling algorithms but neglect other critical aspects of the modeling process. This book describes techniques for finding the best representations of predictors for modeling and for nding the best subset of predictors for improving model performance. A variety of example data sets are used to illustrate the techniques along with R programs for reproducing the results.

Univariate, Bivariate, and Multivariate Statistics Using R

Download Univariate, Bivariate, and Multivariate Statistics Using R PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119549930
Total Pages : 384 pages
Book Rating : 4.1/5 (195 download)

DOWNLOAD NOW!


Book Synopsis Univariate, Bivariate, and Multivariate Statistics Using R by : Daniel J. Denis

Download or read book Univariate, Bivariate, and Multivariate Statistics Using R written by Daniel J. Denis and published by John Wiley & Sons. This book was released on 2020-04-14 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical source for performing essential statistical analyses and data management tasks in R Univariate, Bivariate, and Multivariate Statistics Using R offers a practical and very user-friendly introduction to the use of R software that covers a range of statistical methods featured in data analysis and data science. The author— a noted expert in quantitative teaching —has written a quick go-to reference for performing essential statistical analyses and data management tasks in R. Requiring only minimal prior knowledge, the book introduces concepts needed for an immediate yet clear understanding of statistical concepts essential to interpreting software output. The author explores univariate, bivariate, and multivariate statistical methods, as well as select nonparametric tests. Altogether a hands-on manual on the applied statistics and essential R computing capabilities needed to write theses, dissertations, as well as research publications. The book is comprehensive in its coverage of univariate through to multivariate procedures, while serving as a friendly and gentle introduction to R software for the newcomer. This important resource: Offers an introductory, concise guide to the computational tools that are useful for making sense out of data using R statistical software Provides a resource for students and professionals in the social, behavioral, and natural sciences Puts the emphasis on the computational tools used in the discovery of empirical patterns Features a variety of popular statistical analyses and data management tasks that can be immediately and quickly applied as needed to research projects Shows how to apply statistical analysis using R to data sets in order to get started quickly performing essential tasks in data analysis and data science Written for students, professionals, and researchers primarily in the social, behavioral, and natural sciences, Univariate, Bivariate, and Multivariate Statistics Using R offers an easy-to-use guide for performing data analysis fast, with an emphasis on drawing conclusions from empirical observations. The book can also serve as a primary or secondary textbook for courses in data analysis or data science, or others in which quantitative methods are featured.

Multiple Factor Analysis by Example Using R

Download Multiple Factor Analysis by Example Using R PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1482205483
Total Pages : 272 pages
Book Rating : 4.4/5 (822 download)

DOWNLOAD NOW!


Book Synopsis Multiple Factor Analysis by Example Using R by : Jérôme Pagès

Download or read book Multiple Factor Analysis by Example Using R written by Jérôme Pagès and published by CRC Press. This book was released on 2014-11-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple factor analysis (MFA) enables users to analyze tables of individuals and variables in which the variables are structured into quantitative, qualitative, or mixed groups. Written by the co-developer of this methodology, Multiple Factor Analysis by Example Using R brings together the theoretical and methodological aspects of MFA. It also inc

Practical Guide To Principal Component Methods in R

Download Practical Guide To Principal Component Methods in R PDF Online Free

Author :
Publisher : STHDA
ISBN 13 : 1975721136
Total Pages : 171 pages
Book Rating : 4.9/5 (757 download)

DOWNLOAD NOW!


Book Synopsis Practical Guide To Principal Component Methods in R by : Alboukadel KASSAMBARA

Download or read book Practical Guide To Principal Component Methods in R written by Alboukadel KASSAMBARA and published by STHDA. This book was released on 2017-08-23 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although there are several good books on principal component methods (PCMs) and related topics, we felt that many of them are either too theoretical or too advanced. This book provides a solid practical guidance to summarize, visualize and interpret the most important information in a large multivariate data sets, using principal component methods in R. The visualization is based on the factoextra R package that we developed for creating easily beautiful ggplot2-based graphs from the output of PCMs. This book contains 4 parts. Part I provides a quick introduction to R and presents the key features of FactoMineR and factoextra. Part II describes classical principal component methods to analyze data sets containing, predominantly, either continuous or categorical variables. These methods include: Principal Component Analysis (PCA, for continuous variables), simple correspondence analysis (CA, for large contingency tables formed by two categorical variables) and Multiple CA (MCA, for a data set with more than 2 categorical variables). In Part III, you'll learn advanced methods for analyzing a data set containing a mix of variables (continuous and categorical) structured or not into groups: Factor Analysis of Mixed Data (FAMD) and Multiple Factor Analysis (MFA). Part IV covers hierarchical clustering on principal components (HCPC), which is useful for performing clustering with a data set containing only categorical variables or with a mixed data of categorical and continuous variables.

Computational Genomics with R

Download Computational Genomics with R PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1498781861
Total Pages : 463 pages
Book Rating : 4.4/5 (987 download)

DOWNLOAD NOW!


Book Synopsis Computational Genomics with R by : Altuna Akalin

Download or read book Computational Genomics with R written by Altuna Akalin and published by CRC Press. This book was released on 2020-12-16 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Genomics with R provides a starting point for beginners in genomic data analysis and also guides more advanced practitioners to sophisticated data analysis techniques in genomics. The book covers topics from R programming, to machine learning and statistics, to the latest genomic data analysis techniques. The text provides accessible information and explanations, always with the genomics context in the background. This also contains practical and well-documented examples in R so readers can analyze their data by simply reusing the code presented. As the field of computational genomics is interdisciplinary, it requires different starting points for people with different backgrounds. For example, a biologist might skip sections on basic genome biology and start with R programming, whereas a computer scientist might want to start with genome biology. After reading: You will have the basics of R and be able to dive right into specialized uses of R for computational genomics such as using Bioconductor packages. You will be familiar with statistics, supervised and unsupervised learning techniques that are important in data modeling, and exploratory analysis of high-dimensional data. You will understand genomic intervals and operations on them that are used for tasks such as aligned read counting and genomic feature annotation. You will know the basics of processing and quality checking high-throughput sequencing data. You will be able to do sequence analysis, such as calculating GC content for parts of a genome or finding transcription factor binding sites. You will know about visualization techniques used in genomics, such as heatmaps, meta-gene plots, and genomic track visualization. You will be familiar with analysis of different high-throughput sequencing data sets, such as RNA-seq, ChIP-seq, and BS-seq. You will know basic techniques for integrating and interpreting multi-omics datasets. Altuna Akalin is a group leader and head of the Bioinformatics and Omics Data Science Platform at the Berlin Institute of Medical Systems Biology, Max Delbrück Center, Berlin. He has been developing computational methods for analyzing and integrating large-scale genomics data sets since 2002. He has published an extensive body of work in this area. The framework for this book grew out of the yearly computational genomics courses he has been organizing and teaching since 2015.

Sufficient Dimension Reduction

Download Sufficient Dimension Reduction PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1498704484
Total Pages : 307 pages
Book Rating : 4.4/5 (987 download)

DOWNLOAD NOW!


Book Synopsis Sufficient Dimension Reduction by : Bing Li

Download or read book Sufficient Dimension Reduction written by Bing Li and published by CRC Press. This book was released on 2018-04-27 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient dimension reduction is a rapidly developing research field that has wide applications in regression diagnostics, data visualization, machine learning, genomics, image processing, pattern recognition, and medicine, because they are fields that produce large datasets with a large number of variables. Sufficient Dimension Reduction: Methods and Applications with R introduces the basic theories and the main methodologies, provides practical and easy-to-use algorithms and computer codes to implement these methodologies, and surveys the recent advances at the frontiers of this field. Features Provides comprehensive coverage of this emerging research field. Synthesizes a wide variety of dimension reduction methods under a few unifying principles such as projection in Hilbert spaces, kernel mapping, and von Mises expansion. Reflects most recent advances such as nonlinear sufficient dimension reduction, dimension folding for tensorial data, as well as sufficient dimension reduction for functional data. Includes a set of computer codes written in R that are easily implemented by the readers. Uses real data sets available online to illustrate the usage and power of the described methods. Sufficient dimension reduction has undergone momentous development in recent years, partly due to the increased demands for techniques to process high-dimensional data, a hallmark of our age of Big Data. This book will serve as the perfect entry into the field for the beginning researchers or a handy reference for the advanced ones. The author Bing Li obtained his Ph.D. from the University of Chicago. He is currently a Professor of Statistics at the Pennsylvania State University. His research interests cover sufficient dimension reduction, statistical graphical models, functional data analysis, machine learning, estimating equations and quasilikelihood, and robust statistics. He is a fellow of the Institute of Mathematical Statistics and the American Statistical Association. He is an Associate Editor for The Annals of Statistics and the Journal of the American Statistical Association.

Machine Learning Techniques for Multimedia

Download Machine Learning Techniques for Multimedia PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3540751718
Total Pages : 297 pages
Book Rating : 4.5/5 (47 download)

DOWNLOAD NOW!


Book Synopsis Machine Learning Techniques for Multimedia by : Matthieu Cord

Download or read book Machine Learning Techniques for Multimedia written by Matthieu Cord and published by Springer Science & Business Media. This book was released on 2008-02-07 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Processing multimedia content has emerged as a key area for the application of machine learning techniques, where the objectives are to provide insight into the domain from which the data is drawn, and to organize that data and improve the performance of the processes manipulating it. Arising from the EU MUSCLE network, this multidisciplinary book provides a comprehensive coverage of the most important machine learning techniques used and their application in this domain.

Large Dimensional Factor Analysis

Download Large Dimensional Factor Analysis PDF Online Free

Author :
Publisher : Now Publishers Inc
ISBN 13 : 1601981449
Total Pages : 90 pages
Book Rating : 4.6/5 (19 download)

DOWNLOAD NOW!


Book Synopsis Large Dimensional Factor Analysis by : Jushan Bai

Download or read book Large Dimensional Factor Analysis written by Jushan Bai and published by Now Publishers Inc. This book was released on 2008 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large Dimensional Factor Analysis provides a survey of the main theoretical results for large dimensional factor models, emphasizing results that have implications for empirical work. The authors focus on the development of the static factor models and on the use of estimated factors in subsequent estimation and inference. Large Dimensional Factor Analysis discusses how to determine the number of factors, how to conduct inference when estimated factors are used in regressions, how to assess the adequacy pf observed variables as proxies for latent factors, how to exploit the estimated factors to test unit root tests and common trends, and how to estimate panel cointegration models.

Robust Methods for Data Reduction

Download Robust Methods for Data Reduction PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 9780367783518
Total Pages : 0 pages
Book Rating : 4.7/5 (835 download)

DOWNLOAD NOW!


Book Synopsis Robust Methods for Data Reduction by : Alessio Farcomeni

Download or read book Robust Methods for Data Reduction written by Alessio Farcomeni and published by CRC Press. This book was released on 2021-03-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust Methods for Data Reduction gives a non-technical overview of robust data reduction techniques, encouraging the use of these important and useful methods in practical applications. The main areas covered include principal components analysis, sparse principal component analysis, canonical correlation analysis, factor analysis, clustering, double clustering, and discriminant analysis. The first part of the book illustrates how dimension reduction techniques synthesize available information by reducing the dimensionality of the data. The second part focuses on cluster and discriminant analysis. The authors explain how to perform sample reduction by finding groups in the data. Despite considerable theoretical achievements, robust methods are not often used in practice. This book fills the gap between theoretical robust techniques and the analysis of real data sets in the area of data reduction. Using real examples, the authors show how to implement the procedures in R. The code and data for the examples are available on the book's CRC Press web page.

DATA STATISTICAL ANALYSIS WITH R

Download DATA STATISTICAL ANALYSIS WITH R PDF Online Free

Author :
Publisher : CESAR PEREZ
ISBN 13 : 1008971162
Total Pages : 222 pages
Book Rating : 4.0/5 (89 download)

DOWNLOAD NOW!


Book Synopsis DATA STATISTICAL ANALYSIS WITH R by : CESAR PEREZ LOPEZ

Download or read book DATA STATISTICAL ANALYSIS WITH R written by CESAR PEREZ LOPEZ and published by CESAR PEREZ. This book was released on with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: R is a program focused primarily on statistical data analysis. This book deals with the most important facets of data analysis applied with R, including exploratory data analysis, descriptive statistics, graphs, regression models, generalized linear models, analysis of variance models, dimension reduction techniques, principal components, factor analysis, cluster analysis and other topics of multivariate data analysis

Data Science and Predictive Analytics

Download Data Science and Predictive Analytics PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3031174836
Total Pages : 940 pages
Book Rating : 4.0/5 (311 download)

DOWNLOAD NOW!


Book Synopsis Data Science and Predictive Analytics by : Ivo D. Dinov

Download or read book Data Science and Predictive Analytics written by Ivo D. Dinov and published by Springer Nature. This book was released on 2023-02-16 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook integrates important mathematical foundations, efficient computational algorithms, applied statistical inference techniques, and cutting-edge machine learning approaches to address a wide range of crucial biomedical informatics, health analytics applications, and decision science challenges. Each concept in the book includes a rigorous symbolic formulation coupled with computational algorithms and complete end-to-end pipeline protocols implemented as functional R electronic markdown notebooks. These workflows support active learning and demonstrate comprehensive data manipulations, interactive visualizations, and sophisticated analytics. The content includes open problems, state-of-the-art scientific knowledge, ethical integration of heterogeneous scientific tools, and procedures for systematic validation and dissemination of reproducible research findings. Complementary to the enormous challenges related to handling, interrogating, and understanding massive amounts of complex structured and unstructured data, there are unique opportunities that come with access to a wealth of feature-rich, high-dimensional, and time-varying information. The topics covered in Data Science and Predictive Analytics address specific knowledge gaps, resolve educational barriers, and mitigate workforce information-readiness and data science deficiencies. Specifically, it provides a transdisciplinary curriculum integrating core mathematical principles, modern computational methods, advanced data science techniques, model-based machine learning, model-free artificial intelligence, and innovative biomedical applications. The book’s fourteen chapters start with an introduction and progressively build foundational skills from visualization to linear modeling, dimensionality reduction, supervised classification, black-box machine learning techniques, qualitative learning methods, unsupervised clustering, model performance assessment, feature selection strategies, longitudinal data analytics, optimization, neural networks, and deep learning. The second edition of the book includes additional learning-based strategies utilizing generative adversarial networks, transfer learning, and synthetic data generation, as well as eight complementary electronic appendices. This textbook is suitable for formal didactic instructor-guided course education, as well as for individual or team-supported self-learning. The material is presented at the upper-division and graduate-level college courses and covers applied and interdisciplinary mathematics, contemporary learning-based data science techniques, computational algorithm development, optimization theory, statistical computing, and biomedical sciences. The analytical techniques and predictive scientific methods described in the book may be useful to a wide range of readers, formal and informal learners, college instructors, researchers, and engineers throughout the academy, industry, government, regulatory, funding, and policy agencies. The supporting book website provides many examples, datasets, functional scripts, complete electronic notebooks, extensive appendices, and additional materials.

Exploratory Factor Analysis

Download Exploratory Factor Analysis PDF Online Free

Author :
Publisher : Oxford University Press
ISBN 13 : 0199734178
Total Pages : 170 pages
Book Rating : 4.1/5 (997 download)

DOWNLOAD NOW!


Book Synopsis Exploratory Factor Analysis by : Leandre R. Fabrigar

Download or read book Exploratory Factor Analysis written by Leandre R. Fabrigar and published by Oxford University Press. This book was released on 2012-01-12 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a non-mathematical introduction to the theory and application of Exploratory Factor Analysis. Among the issues discussed are the use of confirmatory versus exploratory factor analysis, the use of principal components analysis versus common factor analysis, and procedures for determining the appropriate number of factors.

Advanced R Statistical Programming and Data Models

Download Advanced R Statistical Programming and Data Models PDF Online Free

Author :
Publisher : Apress
ISBN 13 : 1484228723
Total Pages : 649 pages
Book Rating : 4.4/5 (842 download)

DOWNLOAD NOW!


Book Synopsis Advanced R Statistical Programming and Data Models by : Matt Wiley

Download or read book Advanced R Statistical Programming and Data Models written by Matt Wiley and published by Apress. This book was released on 2019-02-20 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carry out a variety of advanced statistical analyses including generalized additive models, mixed effects models, multiple imputation, machine learning, and missing data techniques using R. Each chapter starts with conceptual background information about the techniques, includes multiple examples using R to achieve results, and concludes with a case study. Written by Matt and Joshua F. Wiley, Advanced R Statistical Programming and Data Models shows you how to conduct data analysis using the popular R language. You’ll delve into the preconditions or hypothesis for various statistical tests and techniques and work through concrete examples using R for a variety of these next-level analytics. This is a must-have guide and reference on using and programming with the R language. What You’ll LearnConduct advanced analyses in R including: generalized linear models, generalized additive models, mixed effects models, machine learning, and parallel processing Carry out regression modeling using R data visualization, linear and advanced regression, additive models, survival / time to event analysis Handle machine learning using R including parallel processing, dimension reduction, and feature selection and classification Address missing data using multiple imputation in R Work on factor analysis, generalized linear mixed models, and modeling intraindividual variability Who This Book Is For Working professionals, researchers, or students who are familiar with R and basic statistical techniques such as linear regression and who want to learn how to use R to perform more advanced analytics. Particularly, researchers and data analysts in the social sciences may benefit from these techniques. Additionally, analysts who need parallel processing to speed up analytics are given proven code to reduce time to result(s).

Connect the Dots

Download Connect the Dots PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (113 download)

DOWNLOAD NOW!


Book Synopsis Connect the Dots by :

Download or read book Connect the Dots written by and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Factor extraction using PCA in Excel, R and Python About This Video Understanding principal components Eigen values and Eigen vectors Eigenvalue decomposition Using principal components for dimensionality reduction and exploratory factor analysis. Implementing PCA in Excel, R and Python Apply PCA to explain the returns of a technology stock like Apple Find the principal components and use them to build a regression model In Detail Factor analysis helps to cut through the clutter when you have a lot of correlated variables to explain a single effect. This course will help you understand Factor analysis and it's link to linear regression. See how Principal Components Analysis is a cookie cutter technique to solve factor extraction and how it relates to Machine learning.

Principal Component Analysis

Download Principal Component Analysis PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1475719043
Total Pages : 283 pages
Book Rating : 4.4/5 (757 download)

DOWNLOAD NOW!


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.