Sparse non-negative tensor factorization using columnwise coordinate descent

Many applications in computer vision, biomedical informatics, and graphics deal with data in the matrix or tensor form. Non-negative matrix and tensor factorization, which extract data-dependent non-negative basis functions, have been commonly applied for the analysis of such data for data compression, visualization, and detection of hidden information (factors). In this paper, we present a fast and flexible algorithm for sparse non-negative tensor factorization (SNTF) based on columnwise coordinate descent (CCD). Different from the traditional coordinate descent which updates one element at a time, CCD updates one column vector simultaneously. Our empirical results on higher-mode images, such as brain MRI images, gene expression images, and hyperspectral images show that the proposed algorithm is 12 orders of magnitude faster than several state-of-the-art algorithms.