Visualization

The first and most obvious difficulty we face with multivariate data is visualization. If we want to explore the association between variables, one possibility is to draw scatterplots for each pair of them; for instance, if we have 4 variables, we may draw a matrix of scatterplots, like the one illustrated in Fig. 15.1. The matrix of plots is symmetric, and the histograms of each single variable are displayed on the diagonal. Clearly, this is a rather partial view, even though it can help in spotting pairwise relationships. Many fancy methods have been proposed to obtain a more complete picture of multivariate data, such as drawing human faces, whose features are related to data characteristics; however, they may be rather hard to interpret. A less trivial approach is based on data reduction. Quite often, even though there are many variables, we may take linear combinations of them in such a way that a limited number of such transformations includes most of the really interesting information. Such an approach is principal component analysis,