L1-norm-based principal component analysis with adaptive regularization. (December 2016)

• Record Type: Journal Article
• Authors: Lu, Gui-Fu; Zou, Jian; Wang, Yong; Wang, Zhongqun
• Is Part Of: Pattern recognition. Volume 60(2016:Dec.)
• Page Start: 901
• Page End: 907
• Publication Date: 2016-12
• Subjects: Principal component analysis -- Dimensionality reduction -- L1-norm -- Trace lasso -- L2-norm; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2016.07.014
• Languages: English
• ISSNs: 0031-3203

Abstract

Abstract: Recently, some L1-norm-based principal component analysis algorithms with sparsity have been proposed for robust dimensionality reduction and processing multivariate data. The L1-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 L1-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-L1/AR is also proposed. The experiment results on some data sets demonstrate the effectiveness of the proposed method. Highlights: We propose a L1-norm-based principal component analysis with adaptive regularization. We use trace Lasso to regularize the projection vectors. Our mode can simultaneously consider the sparsity and correlation.