L. Xu et Al. Yuille, ROBUST PRINCIPAL COMPONENT ANALYSIS BY SELF-ORGANIZING RULES BASED ONSTATISTICAL PHYSICS APPROACH, IEEE transactions on neural networks, 6(1), 1995, pp. 131-143
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.