Two-dimensional principal component analysis based on Schatten p-norm for image feature extraction

• A Schatten p-norm-based 2DPCA (2DPCA-Sp) method is proposed.
• The proposed 2DPCA-Sp method is used for extracting features from images.
• An iterative algorithm is derived to solve the optimization problem of 2DPCA-Sp.
• 2DPCA-Sp with 0

In this paper, we propose a novel Schatten p-norm-based two-dimensional principal component analysis (2DPCA) method, which is named after 2DPCA-Sp, for image feature extraction. Different from the conventional 2DPCA that is based on Frobenius-norm, 2DPCA-Sp learns an optimal projection matrix by maximizing the total scatter criterion based on Schatten p-norm in the low-dimensional feature space. Since p   can take different values, 2DPCA-Sp is regarded as a general framework of 2DPCA. We also propose an iterative algorithm to solve the optimization problem of 2DPCA-Sp with 0