Customer Reviews

Principal Component Analysis

5 star:		(1)
4 star:		(2)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

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!

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.

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.

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). I would suggest that the author simply show the proof of this theorem for the convenience of the readers, because the readers may not have access to Mardia's book. The author should make the book self contained.

The author tend to compare different methods without actually discussion what the methods are first. In section 5.3, it talks a lot above the history before the actually showing what biplot is (5.3.1). Since this is a textbook, I don't recommend this way of writing. The author should assume the readers know nothing and gradually introduce the topic.

I hope that the author will improve the presentation in the book in future editions.