A Modified Frank-wolfe Algorithm for Tensor Factorization with Unimodal Signals

Abstract

Unimodality-constrained matrix or tensor factorization has applications in various domains, such as non-parametric source localization and data clustering, where the signals of interest are unimodal. Such factorizations are challenged by the non-convex nature of unimodality constraints. This paper develops a modified Frank-Wolfe algorithm with a successive programming technique, which produces a sequence of linear subproblems with modified and adaptive constraints. The algorithm is proven to converge and the subproblems are shown to be solved easily. In an application example of solving unimodality-constrained tensor factorization problems, the proposed algorithm demonstrates substantial complexity reduction while achieving the same convergence performance as compared to a brute-force projected gradient algorithm.