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Self-Organizing Rules for Robust Principal Component Analysis

In the presence of outliers, the existing self-organizing rules for Principal Component Analysis (PCA) perform poorly. Using statistical 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 component vector, the first k principal component vectors, and directly finding the subspace spanned by the first k vector principal component vectors without solving for each vector individually. Comparative experiments have shown that the proposed robust rules improve the performances of the existing PCA algorithms significantly when outliers are present.