Projection-Pursuit Approach for Categorical Data
Michael Greenacre, Jorg Blasius · 2006
Principal component analysis (PCA) and related methods, such as correspondence analysis, produce graphical displays for users whose interest focuses primarily on preserving dispersion. Since maximum dispersion is not necessarily equivalent to maximum interest (see the previously mentioned papers), PCA may fail to disclose some of the interesting features of the data set. However, suitably generalized principal component analyses are likely to reveal several kinds of special structures in the data, thus meeting the aims of the exploratory projection-pursuit approach. A generalized PCA is to be understood as a PCA using a special metric on the case space. Proposals for such metrics can be found in Caussinus and Ruiz-Gazen (1995). In that chapter, the authors investigate the properties of their methods for continuous data. They rely basically on a mixture model (18.1) where the “uninteresting noise” is a p -variate normal distribution N , while the (nonnormal) mixing distribution P is the “structure” of interest. P