New Features of Categorical Principal Components Analysis for Complicated Data Sets, Including Data Mining

Abstract

This paper focuses on a technique to perform principal components analysis with nonlinear scaling of variables, and having correspondence analysis features. Special attention will be given to particular properties that make the technique suited for data mining. In addition to fitting of points for individual objects or subjects, additional points may be fitted to identify groups among them. There is a large emphasis on graphical display of the results in biplots (with variables and objects) and triplots (with variables, objects, and groups). The information contained in the biplots and triplots is used to draw special graphs that identify particular groups in the data that stand out on selected variables. Supplementary variables and objects may be used to link different data sets in a single representation. When a fixed configuration of points is given, the technique may be used for property fitting, i.e., fitting external information into the space. The method can be used to analyze very large data sets by assuming that the variables are categorical; when, however, continuous variables are available as well, these can be made discrete by various optimal procedures. Ordered (ordinal) and non-ordered (nominal) data can be handled by the use of monotonic or non-monotonic (spline) transformations. A state-of-the-art computer program (called CATPCA) is available from SPSS Categories 10.0 onwards.