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 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.

Building Shape Models from Lousy Data

“…Figure 3 clearly shows that in the presence of such outliers, standard PCA will fail. For comparison, we computed a robust PCA using the PCAproj algorithm as provided in the R package pcapp [16]. While the effect of the outlier is reduced, it still influences the model as illustrated in Figure 3(d).…”

Sensor Fault Detection and Isolation by Robust Principal Component Analysis

“…These methods maximize a robust measure of data spread to obtain consecutive directions on which the data points are projected (Croux et al, 2007;Croux & Ruiz-Gazen, 2005;Huber, 1964;Li & Chen, 1985). The main step of these algorithms is then to search for the direction in which the projected observations have the largest robust spread to obtain the first component.…”

Robustified least squares support vector classification

“…Also in the chemometrical literature robust methods, defined in that sense, are already well established and proved to be useful which can be seen by the numerous publications in that field (see e.g. References [12][13][14][15][16][17]). …”