Paper Info
Title
A sparse optimization approach to supervised NMF based on convex analytic method
Abstract
In this paper, we propose a novel scheme to supervised nonnegative matrix factorization (NMF). We formulate the supervised NMF as a sparse optimization problem assuming the availability of a set of basis vectors, some of which are irrelevant to a given matrix to be decomposed. The proposed scheme is presented in the context of music transcription and musical instrument recognition. In addition to the nonnegativity constraint, we introduce three regularization terms: (i) a block ℓ1 norm to select relevant basis vectors, and (ii) a temporal-continuity term plus the popular ℓ1 norm to estimate correct activation vectors. We present a state-of-the-art convex-analytic iterative solver which ensures global convergence. The number of basis vectors to be actively used is obtained as a consequence of optimization. Simulation results show the efficacy of the proposed scheme both in the case of perfect/imperfect basis matrices.
Year
DOI
Venue
2013
10.1109/ICASSP.2013.6638832
Acoustics, Speech and Signal Processing
Keywords
Field
DocType
convergence of numerical methods,convex programming,iterative methods,matrix decomposition,music,musical instruments,sparse matrices,convex analytic method-based supervised NMF,convex-analytic iterative solver,global convergence,music transcription,musical instrument recognition,nonnegativity constraint,perfect-imperfect basis matrices,sparse optimization approach,supervised nonnegative matrix factorization,temporal-continuity term,convex analysis,sparse optimization,supervised nonnegative matrix factorization
Mathematical optimization,Computer science,Matrix decomposition,Sparse approximation,Non-negative matrix factorization,Optimization problem,Basis (linear algebra),Convex optimization,Linear matrix inequality,Sparse matrix
Conference
ISSN
Citations 
PageRank 
1520-6149
3
0.45
References 
Authors
5
2
Name
Order
Citations
PageRank
Morikawa, Yu.130.45
Masahiro Yukawa227230.44