论文标题
基于t $ \ ell_1 $ -norm最大化的主成分分析
Principal Component Analysis Based on T$\ell_1$-norm Maximization
论文作者
论文摘要
经典的主成分分析（PCA）可能会受到对异常值和噪声的敏感性。因此，已经研究了基于$ \ ell_1 $ -norm和$ \ ell_p $ -norm（$ 0 <p <1 $）的PCA。其中，从稳健性的角度来看，基于$ \ ell_p $ -norm的基于$ \ ell_p $ -norm似乎是最有趣的。但是，它们的数值性能并不令人满意。请注意，尽管T $ \ ell_1 $ -norm类似于$ \ ell_p $ -norm（$ 0 <p <1 $），但它在某种意义上具有更强的抑制作用，对异常值和更好的连续性具有更强的抑制作用。因此，本文提出了基于T $ \ ell_1 $ -norm的PCA。我们的数值实验表明，其性能比PCA优秀 - $ \ ell_p $和$ \ ell_p $ spca以及PCA，PCA-$ \ ell_1 $显然。
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.
