The classical principal component analysis (PCA) is not sparse enough since it is based on the L2-norm that is also prone to be adversely affected by the presence of outliers and noises. In order to address the problem, a sparse robust PCA framework is proposed based on the min of zero-norm regularization and the max of Lp-norm (0 < p ≤ 2) PCA. Furthermore, we developed a continuous optimization method, DC (difference of convex functions) programming algorithm (DCA), to solve the proposed problem. The resulting algorithm (called DC-LpZSPCA) is convergent linearly. In addition, when choosing different p values, the model can keep robust and is applicable to different data types. Numerical simulations are simulated in artificial data sets and Yale face data sets. Experiment results show that the proposed method can maintain good sparsity and anti-outlier ability.

中文翻译：

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直流编程算法的鲁棒稀疏主成分分析

经典的主成分分析（PCA）不够稀疏，因为它基于L2范数，并且容易受到异常值和噪声的影响。为了解决该问题，提出了一种基于零范数正则化最小值和Lp范数最大值（0 <p≤2）PCA的稀疏鲁棒PCA框架。此外，我们开发了一种连续优化方法，即DC（凸函数差）编程算法（DCA），以解决所提出的问题。生成的算法（称为DC-LpZSPCA）是线性收敛的。另外，选择不同的P值时，该模型能够保持强劲，适用于不同的数据类型。在人工数据集和耶鲁人脸数据集中模拟了数值模拟。