Data Analysis
Abstract
Statistical analysis has traditionally been separated into two phases: an exploratory phase, drawing on a set of descriptive and graphical techniques, and a decisional phase, based on probabilistic models. Some of the tools employed as part of the exploratory phase belong to descriptive statistics, whose elementary exploratory methods consider only a very limited number of variables, while other tools belong to data analysis, the subject matter of this book, which comprises more elaborate exploratory methods to handle multidimensional data, and is often seen as stepping beyond a purely exploratory context. Part One of this book is concerned with methods for obtaining the pertinent dimensions from a collection of data. The variables so obtained provide a synthetic description, often leading to a graphical representation of the data. A considerable number of methods have been developed, adapted to different data types and different analytical goals. Chapters 1 and 2 discuss two reference methods, namely Principal Components Analysis (PCA) and Correspondence Analysis (CA), which we illustrate with examples from statistical process control and sensory analysis. Chapter 3 looks at a family of methods known as Projection Pursuit (less well known, but with a promising future) that can be seen as an extension of PCA and CA that makes it possible to specify the structures that are being sought. Multidimensional positioning methods, discussed in Chapter 4, seek to represent proximity matrix data in low-dimensional Euclidean space. The final chapter of Part One is devoted to functional data analysis, where a function, such as a temperature or rainfall graph, rather than a simple numerical vector, is used to characterize individuals. Part Two is concerned with methods of clustering, which seek to organize data into homogeneous classes. These methods provide an alternative means, often complementary to those discussed in Part One, of synthesizing and analyzing data. In view of the clear link between clustering and discriminant analysis – in pattern recognition the former is termed unsupervised and the latter supervised learning – Chapter 6 gives a general introduction to discriminant analysis. Chapter 7 then provides an overall picture of clustering. The statistical interpretation of clustering in terms of mixtures of probability distributions is discussed in Chapter 8, and the final chapter of Part Two looks at how this approach can be applied to spatial data.