ROBPCA: A New Approach to Robust Principal Component Analysis

In this paper we introduce a new method for robust principal component analysis. Classical PCA is based on the empirical covariance matrix of the data and hence it is highly sensitive to outlying observations. In the past, two robust approaches have been developed. The first is based on the eigenvectors of a robust scatter matrix such as the MCD or an S-estimator, and is limited to relatively low-dimensional data. The second approach is based on projection pursuit and can handle high-dimensional data. Here, we propose the ROBPCA approach which combines projection pursuit ideas with robust scatter matrix estimation. It yields more accurate estimates at non-contaminated data sets and more robust estimates at contaminated data. ROBPCA can be computed fast, and is able to detect exact fit situations. As a byproduct, ROBPCA produces a diagnostic plot which displays and classifies the outliers. The algorithm is applied to several data sets from chemometrics and engineering.