Riemannian Multiplicative Update for Sparse Simplex constraint using oblique rotation manifold

We propose a new manifold optimization method to solve low-rank problems with sparse simplex constraints (variables are simultaneous nonnegativity, sparsity, and sum-to-1) that are beneficial in applications. The proposed approach exploits oblique rotation manifolds, rewrite the problem, and introduce a new Riemannian optimization method. Experiments on synthetic datasets compared to the standard Euclidean method show the effectiveness of the proposed method.