  Classical principal component analysis (PCA) may suffer from the sensitivity
to 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 $\ell_p$-norm
seem to be most interesting from the robustness point of view. However, their
numerical performance is not satisfactory. Note that, although T$\ell_1$-norm
is similar to $\ell_p$-norm ($0 < p < 1$) in some sense, it has the stronger
suppression effect to outliers and better continuity. So PCA based on
T$\ell_1$-norm is proposed in this paper. Our numerical experiments have shown
that its performance is superior than PCA-$\ell_p$ and $\ell_p$SPCA as well as
PCA, PCA-$\ell_1$ obviously.
