Hierarchical Alternating Least Squares Methods for Quaternion Nonnegative Matrix Factorizations

In this report, we discuss a simple model for RGB color and polarization images under a unified framework of quaternion nonnegative matrix factorization (QNMF) and present a hierarchical nonnegative least squares method to solve the factor matrices. The convergence analysis of the algorithm is discussed as well. We test the proposed method in the polarization image and color facial image representation. Compared to the state-of-the-art methods, the experimental results demonstrate the effectiveness of the hierarchical nonnegative least squares method for the QNMF model.