Principal Component Analysis Based on T$\ell_1$-norm Maximization
Yang, Xiang-Fei, Shao, Yuan-Hai, Li, Chun-Na, Liu, Li-Ming, Deng, Nai-Yang
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.
May-23-2020
- Country:
- Asia > China (0.15)
- North America > United States (0.14)
- Genre:
- Research Report (0.65)
- Industry:
- Education (0.46)