Self-Organizing Rules for Robust Principal Component Analysis

Abstract

In the presence of outliers, the existing self-organizing rules for Principal Component Analysis (PCA) perform poorly. Using sta(cid:173) tistical physics techniques including the Gibbs distribution, binary decision fields and effective energies, we propose self-organizing PCA rules which are capable of resisting outliers while fulfilling various PCA-related tasks such as obtaining the first principal com(cid:173) ponent vector, the first k principal component vectors, and directly finding the subspace spanned by the first k vector principal com(cid:173) ponent vectors without solving for each vector individually. Com(cid:173) parative experiments have shown that the proposed robust rules improve the performances of the existing PCA algorithms signifi(cid:173) cantly when outliers are present.