This is a book about multidimensional data analysis. Although the word “spatiotemporal” in the title makes the book sound more specialized, many of the techniques described are broadly relevant to all kinds of data analysis. The author mainly focuses on data that possess a well defined covariance matrix and have at least one dimension in which order is important. A vector time series is the most natural example.

The author bases his book on class notes for an upper undergraduate-beginning graduate course in data analysis for students in fields ranging from astronomy to oceanography with widely varying mathematical backgrounds. He writes, “Multidimensional data analysis almost universally boils down to linear algebra.” Yes! Accordingly he devotes about the first third of the book to that subject. Depending on the class, an instructor would probably pick and choose from the topics here. The most important idea from this part is Singular Value Decomposition because it is far and away the most valuable tool and is used extensively throughout the second part of the book.

That second part concentrates on methods of data analysis. Its short introduction hits just the right tone with the title: “The Gray World of Practical Data Analysis”, where vectors may be only sort of orthogonal, matrices almost singular, and quality of the data often at least a little bit doubtful. The topics begin with a little statistics and then go on to autocorrelation, regression and least squares, and finally empirical orthogonal functions.

The author’s terminology is troublesome. He is not careful about definitions, and the meaning of some of the terms is rather slippery. Early on, for example, he discusses eigenvalues and eigenvectors as part of a chapter on “eigenanalysis”. At the end of one of the sections he then writes, “Eigenanalysis is a form of a spectrum”, a strange mangling of process and outcome. He’s not too definite about what he means by “spectrum” either, and says instead that there are various definitions. At another point he refers to a “singular spectrum”, also undefined, that seems to mean a collection of eigenvalues — some of which are zero or nearly zero. “Empirical orthogonal functions” were also a puzzle to me until I realized that the author meant new bases for data vectors, usually eigenvectors of a covariance matrix.

The author prevents examples in image compression, noise filtering, meteorology and climatology. The raw material of the examples is great, the execution less so. The author tends to go through the examples too quickly for a text at this level. I think that the real business of learning data analysis comes in working with real data, and carefully worked-through examples are perhaps the best teaching tools.

I wanted very much to like this book and was progressively disappointed as looked at it more carefully. The author is definitely aimed in the right direction for an introductory course, and he provides a good mixture of theory, technique and street-smarts about data. Nonetheless, the execution still needs a lot of work.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.