Robust sparse principal component analysis
Robust sparse principal component analysis
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DOI：
10.1007/s11432-013-4970-y
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发表时间：
2014-06
期刊：
影响因子：
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通讯作者：
Qian Zhao;Deyu Meng;Zongben Xu
中科院分区：
文献类型：
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作者：
Qian Zhao;Deyu Meng;Zongben Xu
提出了一种提高稀疏主元分析（PCA）鲁棒性的模型。与传统稀疏PCA模型中的12-范数方差不同，该模型最大化了11-范数方差，对噪声和离群点不太敏感。为了保证稀疏性，考虑了比l1-范数更一般、更有效的lp-范数（0 <$p <$1）约束.一个简单而有效的算法是针对所提出的模型。该算法的复杂度与给定数据的大小和维数近似线性增加，这与当前的稀疏PCA方法相当或更好。该算法也被证明是收敛到一个合理的局部最优模型。通过对合成图像数据和数字图像数据的实验，验证了该算法的有效性和鲁棒性。
The model for improving the robustness of sparse principal component analysis (PCA) is proposed in this paper. Instead of thel2-norm variance utilized in the conventional sparse PCA model, the proposed model maximizes thel1-norm variance, which is less sensitive to noise and outlier. To ensure sparsity,lp-norm (0 ⩽p⩽ 1) constraint, which is more general and effective thanl1-norm, is considered. A simple yet efficient algorithm is developed against the proposed model. The complexity of the algorithm approximately linearly increases with both of the size and the dimensionality of the given data, which is comparable to or better than the current sparse PCA methods. The proposed algorithm is also proved to converge to a reasonable local optimum of the model. The efficiency and robustness of the algorithm is verified by a series of experiments on both synthetic and digit number image data.