鲁棒的稀疏Lp-模主成分分析
发布时间：2018-09-03 14:49
【摘要】：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.
[Abstract]:Principal component Analysis (Principle component analysis,PCA) is a widely used dimensionality reduction method. However, the construction of classical PCA based on L2-norm leads to its sensitivity to outliers and noise points, and the classical PCA does not have the characteristics of sparsity. In order to solve this problem, a sparse principal component analysis (Lp SPCA). LP SPCA) method based on Lp- norm is proposed to minimize the intrinsic variance of Lp- pattern with sparse canonical terms. It can be solved by a simple iterative algorithm, and the convergence of the algorithm can be guaranteed theoretically when p 鈮，
本文编号：2220289
[Abstract]:Principal component Analysis (Principle component analysis,PCA) is a widely used dimensionality reduction method. However, the construction of classical PCA based on L2-norm leads to its sensitivity to outliers and noise points, and the classical PCA does not have the characteristics of sparsity. In order to solve this problem, a sparse principal component analysis (Lp SPCA). LP SPCA) method based on Lp- norm is proposed to minimize the intrinsic variance of Lp- pattern with sparse canonical terms. It can be solved by a simple iterative algorithm, and the convergence of the algorithm can be guaranteed theoretically when p 鈮，
本文编号：2220289
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