鲁棒的稀疏Lp-模主成分分析

Robust Sparse Lp-norm Principal Component Analysis

主成分分析(Principle component analysis,PCA)是一种被广泛应用的降维方法.然而经典PCA的构造基于L2-模导致了其对离群点和噪声点敏感,同时经典PCA也不具备稀疏性的特点.针对此问题,本文提出基于Lp-模的稀疏主成分分析降维方法 (Lp SPCA).Lp SPCA通过极大化带有稀疏正则项的Lp-模样本方差,使得其在降维的同时保证了稀疏性和鲁棒性.Lp SPCA可用简单的迭代算法求解,并且当p≥1时该算法的收敛性可在理论上保证.此外通过选择不同的p值,Lp SPCA可应用于更广泛的数据类型.人工数据及人脸数据上的实验结果表明,本文所提出的Lp SPCA不仅具有较好的降维效果,并且具有较强的抗噪能力.

Principle component analysis（PCA） is a widely applied dimensionality reduction method. However, the construction of classical PCA is based on L2-norm, which leads to its sensitivity to outliers and noises, as well as sparsity. To solve this problem, the paper proposes a sparse principal component analysis method based on Lp-norm for dimensionality reduction（Lp SPCA）. In particular, Lp SPCA maximizes the Lp-norm variance with sparse regularization term, which ensures the sparseness and robustness while reducing dimensions. Lp SPCA can be solved by a simple iterative algorithm,and its convergence is theoretically guaranteed when p ≥ 1. Besides, by choosing a different p, Lp SPCA can be used for more types of data sets. Experimental results on both synthetic and human face data sets demonstrate that the proposed Lp SPCA not only has better dimensionality reduction ability but also has strong anti-noise property.