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2002 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Principal Component Analysis

verfasst von: I. T. Jolliffe

Verlag: Springer New York

Buchreihe : Springer Series in Statistics

Enthalten in: Professional Book Archive

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
1. Introduction
2. Mathematical and Statistical Properties of Population Principal Components
3. Mathematical and Statistical Properties of Sample Principal Components
4. Principal Components as a Small Number of Interpretable Variables: Some Examples
5. Graphical Representation of Data Using Principal Components
6. Choosing a Subset of Principal Components or Variables
7. Principal Component Analysis and Factor Analysis
8. Principal Components in Regression Analysis
9. Principal Components Used with Other Multivariate Techniques
10. Outlier Detection, Influential Observations, Stability, Sensitivity, and Robust Estimation of Principal Components
Concluding Remarks
The topics discussed in this chapter pose difficult problems in data analysis. Much research has been done and is continuing on all of them. It is useful to identify potentially outlying observations, and PCA provides a number of ways of doing so. Similarly, it is important to know which observations have the greatest influence on the results of a PCA.
Identifying potential outliers and influential observations is, however, only part of the problem; the next, perhaps more difficult, task is to decide whether the most extreme or influential observations are sufficiently extreme or influential to warrant further action and, if so, what that action should be. Tests of significance for outliers were discussed only briefly in Section 10.1 because they are usually only approximate, and tests of significance for influential observations in PCA have not yet been widely used. Perhaps the best advice is that observations that are much more extreme or influential than most of the remaining observations in a data set should be thoroughly investigated, and explanations sought for their behaviour. The analysis could also be repeated with such observations omitted, although it may be dangerous to act as if the deleted observations never existed. Robust estimation provides an automatic way of dealing with extreme (or influential) observations but, if at all possible, it should be accompanied by a careful examination of any observations that have been omitted or substantially downweighted by the analysis.
11. Rotation and Interpretation of Principal Components
12. Principal Component Analysis for Time Series and Other Non-Independent Data
13. Principal Component Analysis for Special Types of Data
14. Generalizations and Adaptations of Principal Component Analysis
Concluding Remarks
It has been seen in this book that PCA can be used in a wide variety of different ways. Many of the topics covered, especially in the last four chapters, are of recent origin and it is likely that there will be further advances in the near future that will help to clarify the usefulness, in practice, of some of the newer techniques. Developments range from an increasing interest in model-based approaches on the one hand to the mainly algorithmic ideas of neural networks on the other. Additional uses and adaptations of PCA are certain to be proposed and, given the large number of fields of application in which PCA is employed, it is inevitable that there are already some uses and modifications of which the present author is unaware.
In conclusion, it should be emphasized again that, far from being an old and narrow technique, PCA is the subject of much recent research and has great versatility, both in the ways in which it can be applied, and in the fields of application for which it is useful.
Backmatter
Metadaten
Titel
Principal Component Analysis
verfasst von
I. T. Jolliffe
Copyright-Jahr
2002
Verlag
Springer New York
Electronic ISBN
978-0-387-22440-4
Print ISBN
978-0-387-95442-4
DOI
https://doi.org/10.1007/b98835