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.

Principal Component Analysis (PCA) is an essential technique for data compression and feature extraction, and has been widely used in statistical data analysis, communication theory, pattern recognition and image processing. In the neural network literature, a lot of studies have been made on learning rules for implementing PCA or on networks closely related to PCA (see Xu & Yuille, 1993 for a detailed reference list which contains more than 30 papers related to these issues).

Principal Component Analysis (PCA) is an essential technique for data compression and feature extraction, and has been widely used in statistical data analysis, communication theory, pattern recognition and image processing. In the neural network literature, a lot of studies have been made on learning rules for implementing PCA or on networks closely related to PCA (see Xu & Yuille, 1993 for a detailed reference list which contains more than 30 papers related to these issues).

Using statistical physicstechniques 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 component vector,the first k principal component vectors, and directly finding the subspace spanned by the first k vector principal component vectorswithout solving for each vector individually. Comparative experimentshave shown that the proposed robust rules improve the performances of the existing PCA algorithms significantly whenoutliers are present.