L1-norm-based principal component analysis with adaptive regularization

• 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.

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.