Non-negative Matrix Semi-tensor Factorization for Image Feature Extraction and Clustering

Non-negative Matrix Factorization (NMF) has been frequently applied to image feature extraction and clustering. Especially in image clustering tasks, it can achieve the similar or better performance than most of the matrix factorization algorithms due to its parts-based representations in the brain. However, the features extracted by NMF are not sparse and localized enough and the error of factorization is not small enough. Semi-tensor product of matrices (STP) is a novel operation of matrix multiplication, it is a generalization of the conventional matrix product for allowing the dimensions of factor matrices to be unequal. STP can manage the data hierarchically and the inverse process of STP can separate the data hierarchically. Based on this character of STP, we propose the Non-Negative Matrix Semi-Tensor Factorization (NMSTF). In this algorithm, we use the inverse process of Semi-Tensor Product of matrices for non-negative matrix factorization. This algorithm effectively optimizes the above two problems in NMF. While achieving similar even better performance on image clustering tasks, the size of features extracted by STNMF is at least 50% smaller than the ones' extracted by NMF and the error of factorization reduces 30% in average.