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Principal Component Analysis (Springer Series in Statistics) Paperback – October 4, 2013

4 customer reviews
ISBN-13: 978-1441929990 ISBN-10: 1441929991 Edition: Softcover reprint of the original 2nd ed. 2002

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Editorial Reviews

Review

From the reviews of the second edition:

TECHNOMETRICS

"Bringing the 1E up to date has added more than 200 pages of additional text. Anyone seriously involved with the application of PCA will certainly want to purchase a copy…Seldom has such a wealth of material on a single topic in statistics appeared in one book…All that material has gotten a whole lot more comprehensive here in this new edition. Goodall (1988) also labeled the book ‘a good read.’ Now it may be a little heavy for that purpose, but it certainly is a fantastic reference book."

ISI SHORT BOOK REVIEWS

"This is the bible of principal component analysis (PCA). This second edition of the book is nearly twice the length of the first. [Short Book Reviews, Vol.6, p.45] New material includes discussion of ordination methods linked to PCA, including biplots, determining the number of components to retain, extended discussion of outlier detection, stability, and sensitivity, simplifying PCAs to aid interpretation, time series data, size/shape data, and nonlinear PCA, including the Gifi system and neural networks, and other topics. As can be seen from this, the book is not a narrow discussion of PCA, but links it effectively and in an illuminating way to a wide variety of other multivariate statistical tools.

Principal component analysis is the empirical manifestation of the eigen value-decomposition of a correlation or covariance matrix. The fact that a book of nearly 500 pages can be written on this, and noting the author's comment that 'it is certain that I have missed some topics, and my coverage of others will be too brief for the taste of some readers' drives home the extent to whch statistics exceeds mere mathematics.

This book is an invaluable reference work and I am pleased to have it on my shelves. My only regret is that I probably will not have time to read it from cover to cover with the attention it deserves."

JOURNAL OF CLASSIFICATION

"This revised edition presents much new information on methods developed since the 1986 edition. Some of these newer parts include the expanded discussion of ordination and scaling methods (e.g., biplots), selection of the number of components to retain, canonical correlation for comparing groups of variables, independent correlation analysis for non-normal data, and principal curves."

"This book is one of the very few texts entirely devoted to principal component analysis (PCA). The second edition is usefully expanded and updated from the first edition; thus it is very well worth considering this edition, even if one is familiar with the first. … Very nice features are the carefully discussed links between PCA and related techniques … . Throughout, numerous references to relevant literature are provided. This book will be useful as an introduction to PCA as well as a reference." (Marieke E. Timmerman, Journal of the American Statistical Association, 2004)

"This is another volume in the Springer Series in Statistics … which has consistently produced books of high quality and generally advanced treatment of the topic. This revised edition presents much new information on methods developed since the 1986 edition, and these are well described … ." (William Shannon, Journal of Classification, Vol. 21 (1), 2004)

"The first edition of this book (IE), published in 1986, was the first book devoted entirely to principal component analysis (PCA). … Bringing the IE up to date has added more than 200 pages of additional text. Anyone seriously involved with the application of PCA will certainly want to purchase a copy. … Seldom has such a wealth of material on a single topic in statistics appeared in one book. … it certainly is a fantastic reference book." (Technometrics, Vol. 45 (3), 2003)

"This is the Bible of principle components analysis (PCA). This second edition of the book is nearly twice the length of the first. … The book is an invaluable reference work and I am pleased to have it on my shelves." (D. J. Hand, Short Book Reviews, Issue 2, 2003)

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Product Details

  • Series: Springer Series in Statistics
  • Paperback: 488 pages
  • Publisher: Springer; Softcover reprint of the original 2nd ed. 2002 edition (December 1, 2010)
  • Language: English
  • ISBN-10: 1441929991
  • ISBN-13: 978-1441929990
  • Product Dimensions: 6.1 x 1.2 x 9.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #2,637,870 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

21 of 25 people found the following review helpful By Abstract Space on December 17, 2002
Format: Hardcover
The first edition of this book was the most authoritative book on this subject 15 years ago. Now the author has provided us with a much-needed second edition since there are many developments since. Principal components related techniques are the main dimension-reduction methods in analysis of multivariate data. Since there is much redundancy with high throughput measurements such as spatial, spectra, or image data, thus the need to compress or decompose data. Related but somewhat different techniques include SVD, singular spectrum analysis (SSA0, PC regression, shrinkage, EoF, etc.
Main consumers of PCA-related methods include chemometrics, climate analysis, and image analysis A very nice book in the
area of climate analysis is Principal Component Analysis in Meteorology and Oceanography (Developments in Atmospheric Sciences).
The area of SSA has been developing fast and several
monographs have appeared already, e.g. Analysis of Time Series Structure: SSA and Related Techniques. The area of indpedent component analysis is another one that has attracted increasing
attention in recent years, Independent Component Analysis. Most of these recent developments have been covered and more. With this, I strongly recommend this book for readers who use multivariate analysis extensively and who need to keep abreast of the fast growing PCA tools which are as important as ever!
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5 of 5 people found the following review helpful By EB on February 8, 2009
Format: Hardcover
Although it may sound strange, multivariate analysis is a sort of "philosophy of life", and Principal Component is its systemic perspective of the reality. Needless to say, this book is a guide to the development of such perception. Both the numerical background and its practical interpretations are discussed taking care of the many different situations in which multivariate approaches are often applied. In this sense, this book is a tool for experts in numerical modelling as well as for those people lacking deep numerical knowledge. I think that there is still a certain gap between theory and application of multivariate statistics, and this may be the main reason for which many different sources are needed to shape a "personal" multivariate perspective. Nonetheless, this book definitely represents a barycentre.
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4 of 4 people found the following review helpful By Liang X. on July 19, 2010
Format: Paperback
I use this book as my guide for PCA-related topics and studies.

The math level required for this books is merely being familiar with linear algebra and any matrix operations as well as basic statistics concepts, and should be suitable to any senior level or graduate level students, or application researchers in various fields. In contrast to those full of mathematical formula and symbols, this book is a pleasure to read yet it doesn't sacrifice mathematical rigor.

I like the broadness and depth of this book. It covers almost all major aspects of PCA related topics and a wide range of real applications. The theories and applications are made clear enough for anyone to understand the materials yet it doesn't go very deep, so that readers need to explore the cited works for further indepth study. I personally like this style because it is a good balance of theory and application and it actually serves as a road map for anyone who have further interests in specific topics.

In the future editions, I hope the author can put even more weight on developments of recent decade, such as its application in data mining.
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6 of 10 people found the following review helpful By Academic Book Reviewer on April 30, 2010
Format: Paperback
I once gave 4 stars to this book. But after reading more, I believe that it deserves 3 stars for its poor presentation in at least the following aspects.

Each chapter should be written in a more self contained way so that the readers don't have to jump back and forth to look for definitions of symbols. For example, no explanation of x is given under eq (2.1.1) z=A'x. I have to go to page 2 to figure out that "x is a vector of p random variables". Another example on page 92, the matrix S is mentioned in the first paragraph in the same page without mathematical definition until at the end of the page (after eq(5.3.6)). The authors should clear state the mathematically definition of S first.

The authors should just write the mathematical definition of a variable rather than using plain English to define it. For example, it says on page 1, "alpha1 is a vector of p constants alpha11, alpha12, . . . , alpha1p". It can be easily written as "alpha1 = (alpha11, alpha12, . . . , alpha1p), a constant vector". When you glimpse through the book, it is much easier to see what alpha1 is by the second form. Another example on page 92, "The product $\boldsymbol{h}_j'\boldsymbol{h}_k$ is therefore equal to (n - 1) multiplied by the covariance $s_{jk}$ between the jth
and kth variables, and h_j^*' h_k^* ...". I think that this could be simply explained by changing the formula at the top of the page to (n-1)S=X'X=....=HH'.

It says on pape 14 "A corollary of the spectral decomposition of Sigma concerns the conditional distribution of x, given the first q PCs, zq ...". Why not just write "Corollary 1: blah blah blah" and boldface "Corollary 1" such that reader immediately follow that it is a corollary? It also gives a reference to the theorem (Mardia et al., 1979, Theorem 3.2.4).
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