Riemannian Multiplicative Update for Sparse Simplex constraint using oblique rotation manifold

• URL: http://arxiv.org/abs/2503.24075v1
• Date: Mon, 31 Mar 2025 13:31:05 GMT
• Title: Riemannian Multiplicative Update for Sparse Simplex constraint using oblique rotation manifold
• Authors: Flavia Esposito, Andersen Ang,
• Abstract summary: We propose a new manifold optimization method to solve low-rank problems with sparse simplex constraints.<n> Experiments on synthetic datasets compared to the standard Euclidean method show the effectiveness of the proposed method.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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