Nonnegative matrix factorization with quadratic programming

Rafal Zdunek, Andrzej Cichocki

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


Nonnegative matrix factorization (NMF) solves the following problem: find such nonnegative matrices A ∈ R+I × J and X ∈ R+J × K that Y ≅ AX, given only Y ∈ RI × K and the assigned index J (K ≫ I ≥ J). Basically, the factorization is achieved by alternating minimization of a given cost function subject to nonnegativity constraints. In the paper, we propose to use quadratic programming (QP) to solve the minimization problems. The Tikhonov regularized squared Euclidean cost function is extended with a logarithmic barrier function (which satisfies nonnegativity constraints), and then using second-order Taylor expansion, a QP problem is formulated. This problem is solved with some trust-region subproblem algorithm. The numerical tests are performed on the blind source separation problems.

Original languageEnglish
Pages (from-to)2309-2320
Number of pages12
Issue number10-12
Publication statusPublished - Jun 2008
Externally publishedYes


  • Blind source separation
  • Nonnegative matrix factorization
  • Quadratic programming


Dive into the research topics of 'Nonnegative matrix factorization with quadratic programming'. Together they form a unique fingerprint.

Cite this