Evaluation of Different Algorithms of Nonnegative Matrix Factorization in Temporal Psychovisual Modulation

Temporal psychovisual modulation (TPVM) is a newly proposed information display paradigm, which can be implemented by nonnegative matrix factorization (NMF) with additional upper bound constraints on the variables. In this paper, we study all the state-of-the-art algorithms in NMF, extend them to incorporate the upper bounds and discuss their potential use in TPVM. By comparing all the NMF algorithms with their extended versions, we find that: 1) the factorization error of the truncated alternating least squares algorithm always fluctuates throughout the iterations, 2) the alternating nonnegative least squares based algorithms may slow down dramatically under the upper bound constraints, and 3) the hierarchical alternating least squares (HALS) algorithm converges the fastest and its final factorization error is often the smallest among all the algorithms. Based on the experimental results of the HALS, we propose a guideline of determining the parameter setting of TPVM, that is, the number of viewers to support and the scaling factor for adjusting the light intensity of the images formed by TPVM. This paper will facilitate the applications of TPVM.