Algorithms for Projection–Pursuit robust principal component analysis

Abstract

The results of a standard principal component analysis (PCA) can be affected by the presence of outliers. Hence robust alternatives to PCA are needed. One of the most appealing robust methods for principal component analysis uses the Projection–Pursuit principle. Here, one projects the data on a lower-dimensional space such that a robust measure of variance of the projected data will be maximized. The Projection–Pursuit-based method for principal component analysis has recently been introduced in the field of chemometrics, where the number of variables is typically large. In this paper, it is shown that the currently available algorithm for robust Projection–Pursuit PCA performs poor in the presence of many variables. A new algorithm is proposed that is more suitable for the analysis of chemical data. Its performance is studied by means of simulation experiments and illustrated on some real data sets.