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L1-norm-based principal component analysis with adaptive regularization
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DOI：10.1016/j.patcog.2016.07.014.png)
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Abstract
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Recently, some L1-norm-based principal component analysis algorithms with sparsity have been proposed for robust dimensionality reduction and processing multivariate data. The Ll-norm regularization used in these methods encounters stability problems when there are various correlation structures among data. In order to overcome the drawback, in this paper, we propose a novel Li-norm-based principal component analysis with adaptive regularization (PCA-L1/AR) which can consider sparsity and correlation simultaneously. PCA-L1/AR is adaptive to the correlation structure of the training samples and can benefit both from L2-norm and L1-norm. An iterative procedure for solving PCA-Ll/AR is also proposed. The experiment results on some data sets demonstrate the effectiveness of the proposed method. (C) 2016 Elsevier Ltd. All rights reserved.
Keywords:
Principal component analysis
Dimensionality reduction
L1-norm
Trace lasso
L2-norm
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