Principal Components Analysis
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Principal Components Analysis
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.
Principal Component Analysis
Author: I.T. Jolliffe
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-05-09
Principal component analysis is central to the study of multivariate data. Although one of the earliest multivariate techniques, it continues to be the subject of much research, ranging from new model-based approaches to algorithmic ideas from neural networks. It is extremely versatile, with applications in many disciplines. The first edition of this book was the first comprehensive text written solely on principal component analysis. The second edition updates and substantially expands the original version, and is once again the definitive text on the subject. It includes core material, current research and a wide range of applications. Its length is nearly double that of the first edition. Researchers in statistics, or in other fields that use principal component analysis, will find that the book gives an authoritative yet accessible account of the subject. It is also a valuable resource for graduate courses in multivariate analysis. The book requires some knowledge of matrix algebra. Ian Jolliffe is Professor of Statistics at the University of Aberdeen. He is author or co-author of over 60 research papers and three other books. His research interests are broad, but aspects of principal component analysis have fascinated him and kept him busy for over 30 years.
Principal Components Analysis
Principal component analysis (PCA) is a technique that essentially converts observed correlated variables into unobserved uncorrelated components. This enables a data set containing many individual variables to be described using a small number of components that capture much of the variation in the data set. PCA has a long history in statistics and has been applied in many disciplines including biology, astronomy, geography, social sciences, meteorology and management. In addition to reducing the number of variables required to describe a data set, PCA can also identify underlying mechanisms that may have played a role in determining the structure in the data (i.e., the underlying "Bcauses"). The reduction of a large number of variables to a relatively small number of components also enables a data set to be more easily analysed and described using other techniques. In particular, as the components identified by PCA are uncorrelated, many of the problems associated with multicollinearity are alleviated, enabling regression models to be more easily interpreted. This entry provides a relatively nontechnical and practical introduction to the application of PCA using a readily available data set and open-source software.