Robustness Analysis of Structured Matrix Factorization via Self-Dictionary Mixed-Norm Optimization
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AbstractWe are interested in a low-rank matrix factorization problem where one of the matrix factors has a special structure; specifically, its columns live in the unit simplex. This problem finds applications in diverse areas such as hyperspectral unmixing, video summarization, spectrum sensing, and blind speech separation. Prior works showed that such a factorization problem can be formulated as a self-dictionary sparse optimization problem under some assumptions that are considered realistic in many applications, and convex mixed norms were employed as optimization surrogates to realize the factorization in practice. Numerical results have shown that the mixed-norm approach demonstrates promising performance. In this letter, we conduct performance analysis of the mixed-norm approach under noise perturbations. Our result shows that using a convex mixed norm can indeed yield provably good solutions. More importantly, we also show that using nonconvex mixed (quasi) norms is more advantageous in terms of robustness against noise.
All Author(s) ListFu X, Ma WK
Journal nameIEEE Signal Processing Letters
Volume Number23
Issue Number1
Pages60 - 64
LanguagesEnglish-United Kingdom
KeywordsMatrix factorization; performance analysis; self-dictionary sparse optimization
Web of Science Subject CategoriesEngineering; Engineering, Electrical & Electronic

Last updated on 2020-25-11 at 02:10