There is no doubt about the importance of visual data analysis in today’s society. From scientists working on complex phenomena to social scientists investigating the distribution of populations, visually analyzing a problem enables key insights to be gained. One of the problems often faced in such situations is the inherent high dimensionality of the data. Many observations may be taken for each sample, meaning that traditional visualization methods simply won’t suffice. The desire to develop methods to aid in the visual analysis of large, often high-dimensional datasets has attracted much research over the years and gaining a perspective on the landscape can be difficult. This book introduces the diverse field of multidimensional data visualization and aims to explore it in an easily accessible manner.

The book is split into five chapters, with the bulk of the work in chapters 3 and 4. As with most books in this field, the opening chapter gently introduces the key concepts involved in visualization and details the goals for its use. The second chapter provides an analytical review of methods for multidimensional data visualization, so-called direct visualization methods, such as scatter plot matrices, Andrews curves, and dimensionality reduction. Throughout this chapter, and indeed throughout the book, excellent visual examples accompany the discussion. This is one of the key strengths of the book: the application of visualization techniques is never far from the theory. Examples help the reader appreciate how certain techniques work and judge for themselves how effective they are.

As mentioned previously, the bulk of the work is located in the third and fourth chapters, including multidimensional scaling (MDS) and artificial neural networks (ANNs), which are combined to form a powerful visualization tool. MDS is a method of projecting data into a low-dimensional space while retaining pairwise distances. Chapter 3 discusses MDS and outlines different strategies for optimization. The final section of this chapter looks at using different distance metrics with MDS. This is one of the most intriguing parts of the book, addressing an often-overlooked problem in dimensionality reduction. Traditionally, all spaces are assumed to be Euclidean, but employing different distance metrics can overcome some problems often associated with Euclidean distances. This section provides a brief insight into these problems, but unfortunately only for MDS. I think it would be interesting to extend the discussion to other mapping methods such as principal component analysis or isomaps.

Chapter 4 combines ANNs with MDS to exploit the strengths of both methods. Again, through the liberal use of examples, the authors show how to use such methods and highlight various pitfalls to avoid. This hints at the other key strength of this book: the excellent use of pseudocode examples. For those unfamiliar with the field, particularly optimization, it is sometimes difficult to get a handle on how the theory relates to an actual computer program. The use of pseudocode for the main algorithms in this book provides a bridge between the two without being tied down to a specific programming language. This simple addition vastly improves the readability and usefulness of this book.

The final chapter provides worked examples using multidimensional data visualization methods to solve real problems. Each problem is outlined and the visualization-based solution is worked through, showing readers how to interpret the results. As a matter of style, it might have been more beneficial to have these examples throughout the book rather than grouped in a separate chapter. However, it is still refreshing to have a book that seeks to provide the reader with a means for using the described methods in a real-world setting.

Overall, this interesting book provides practical help for those wishing to use visualization as a data analysis tool. There are, however, two caveats. First, this book is quite narrow in its focus. Although various multidimensional data visualizations are mentioned, they are not discussed in the same amount of detail as MDS and ANNs are. So, in effect, this book is more about using MDS and ANNs to analyze high-dimensional data than it is about multidimensional data visualization in general. Second, in places, the rigorous mathematics could deter the nontechnical reader. That said, the problem is somewhat alleviated by the use of pseudocode and examples.

Overall, I recommend this book as a useful resource for anyone wishing to understand and apply specific visualization algorithms to their problem domain.