Robust Tensor Principal Component Analysis Based on F-norm

Abstract

Tensor principal component analysis (TPCA) has been widely used to extract appearance features of colour objects or colour scenes presented in tensor form. Using L 1 -norm as the distance metric, the existing TPCA-L 1 with its greedy (TPCA-L 1 -G) and non-greedy (TPCA-L 1 -NG) algorithms were proposed to reduce the sensitivity to outliers. The two algorithms, however, only derived TPCA solution in a form of two-dimensional matrix without actually extending them to the tensor subspaces and without performing experimental verification for tensor data. Simultaneously, the spatial correlations between pixels of the raw tensor data cannot be effectively preserved. To solve the problems, a robust tensor principal component analysis algorithm based on F-norm distance metric is proposed in this paper, which not only preserves the spatial structure of the raw data, but also reduces the sensitivity to outliers in tensor data. Experiments on reconstruction error and classification rate show that the proposed algorithm is effective and superior to other tensor algorithms in performances.