Robustness analysis of structured matrix factorization via self-dictionary mixed-norm optimization

Xiao Fu, Wing Kin Ma

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We 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.

Original languageEnglish (US)
Article number23895
Pages (from-to)60-64
Number of pages5
JournalIEEE Signal Processing Letters
Issue number1
StatePublished - Jan 2016

Bibliographical note

Publisher Copyright:
© 2015 IEEE.


  • Matrix factorization
  • Performance analysis
  • Selfdictionary sparse optimization


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