Principal Component Analysis Based on T_1-norm Maximization

Abstract

Classical principal component analysis (PCA) may suffer from the sensitivity to outliers and noise. Therefore PCA based on _1-norm and _p-norm (0 < p < 1) have been studied. Among them, the ones based on _p-norm seem to be most interesting from the robustness point of view. However, their numerical performance is not satisfactory. Note that, although T_1-norm is similar to _p-norm (0 < p < 1) in some sense, it has the stronger suppression effect to outliers and better continuity. So PCA based on T_1-norm is proposed in this paper. Our numerical experiments have shown that its performance is superior than PCA-_p and _pSPCA as well as PCA, PCA-_1 obviously.

Tasks

Reproductions