Supervised nonnegative matrix factorization via minimization of regularized Moreau-envelope of divergence function with application to music transcription

Masahiro Yukawa, Hideaki Kagami

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We propose a convex-analytic approach to supervised nonnegative matrix factorization (NMF), using the Moreau envelope, a smooth approximation, of the β-divergence as a loss function. The supervised NMF problem is cast as minimization of the loss function penalized by four terms: (i) a time-continuity enhancing regularizer, (ii) the indicator function enforcing the nonnegativity, (iii) a basis-vector selector (a block ℓ1 norm), and (iv) a sparsity-promoting regularizer. We derive a closed-form expression of the proximity operator of the sum of the three non-differentiable penalty terms (ii)–(iv). The optimization problem can thus be solved numerically by the proximal forward–backward splitting method, which requires no auxiliary variable and is therefore free from extra errors. The source number is automatically attained as an outcome of optimization. The simulation results show the efficacy of the proposed method in an application to polyphonic music transcription.

Original languageEnglish
Pages (from-to)2041-2066
Number of pages26
JournalJournal of the Franklin Institute
Volume355
Issue number4
DOIs
Publication statusPublished - 2018 Mar 1

Fingerprint

Moreau Envelope
Non-negative Matrix Factorization
Transcription
Loss Function
Factorization
Music
Divergence
Smooth Approximation
Indicator function
Selector
Auxiliary Variables
Splitting Method
Nonnegativity
Term
Sparsity
Proximity
Penalty
Efficacy
Closed-form
Optimization Problem

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics

Cite this

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