Block principal component analysis with L1-norm for image analysis

Block principal component analysis (BPCA) is an important subspace learning method in modern image analysis. The utilization of the L2-norm, however, makes it sensitive to outliers. In this paper, we propose an L1-norm-based BPCA (BPCA-L1) as a robust alternative to BPCA. We show the equivalence between the L1-norm-based two-dimensional principal component analysis (2DPCA-L1) and the L1-norm-based principal component analysis (PCA-L1), both of which can be formulated as special cases of BPCA-L1. Experiments of image reconstruction and classification on benchmark image sets show the effectiveness of the proposed method.

► A new L1-norm-based block principle component analysis is proposed.
► Equivalence between 2DPCA-L1 and PCA-L1 is clarified.
► Both 2DPCA-L1 and PCA-L1 can be formulated as special cases of BPCA-L1.
► BPCA-L1 is a robust version of BPCA as a result of the employment of L1-norm.
► BPCA-L1 avoids construction of covariance matrix and intensive eigen-decomposition.