Principal Component Analysis Based on Tℓ_1-norm Maximization

05/23/2020

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by   Xiang-Fei Yang, et al.

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Classical principal component analysis (PCA) may suffer from the sensitivity to outliers and noise. Therefore PCA based on ℓ_1-norm and ℓ_p-norm (0 < p < 1) have been studied. Among them, the ones based on ℓ_p-norm seem to be most interesting from the robustness point of view. However, their numerical performance is not satisfactory. Note that, although Tℓ_1-norm is similar to ℓ_p-norm (0 < p < 1) in some sense, it has the stronger suppression effect to outliers and better continuity. So PCA based on Tℓ_1-norm is proposed in this paper. Our numerical experiments have shown that its performance is superior than PCA-ℓ_p and ℓ_pSPCA as well as PCA, PCA-ℓ_1 obviously.