ROBUST PRINCIPAL COMPONENT ANALYSIS BY SELF-ORGANIZING RULES BASED ONSTATISTICAL PHYSICS APPROACH

This paper applies statistical physics to the problem of robust princi pal component analysis (PCA). The commonly used PCA learning rules are first related to energy functions. These functions are generalized by adding a binary decision field with a given prior distribution so tha t outliers in the data are dealt with explicitly in order to make PCB robust. Each of the generalized energy functions is then used to defin e a Gibbs distribution from which a marginal distribution is obtained by summing over the binary decision field. The marginal distribution d efines an effective energy function, from which self-organizing rules have been developed for robust PCA. Under the presence of outliers, bo th the standard PCA methods and the existing self-organizing PCA rules studied in the literature of neural networks perform quite poorly. By contrast, the robust rules proposed here resist outliers well and per form excellently for fulfilling various PCA-like tasks such as obtaini ng the first principal component vector, the first kappa principal com ponent vectors, and directly finding the subspace spanned by the first kappa vector principal component vectors without solving for each vec tor individually. Comparative experiments have been made, and the resu lts show that our robust rules improve the performances of the existin g PCA algorithms significantly when outliers are present.