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Classical principal component analysis (PCA) may suffer from the sensitivityto outliers and noise. Therefore PCA based on $\ell_1$-norm and $\ell_p$-norm($0 < p < 1$) have been studied. Among them, the ones based on $\ell_p$-normseem to be most interesting from the robustness point of view. However, theirnumerical performance is not satisfactory. Note that, although T$\ell_1$-normis similar to $\ell_p$-norm ($0 < p < 1$) in some sense, it has the strongersuppression effect to outliers and better continuity. So PCA based onT$\ell_1$-norm is proposed in this paper. Our numerical experiments have shownthat its performance is superior than PCA-$\ell_p$ and $\ell_p$SPCA as well asPCA, PCA-$\ell_1$ obviously.

Principal Component Analysis Based on T$\ell_1$-norm Maximization