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Article overview
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Block Coordinate Descent for Sparse NMF | | Vamsi K. Potluru
; Sergey M. Plis
; Jonathan Le Roux
; Barak A. Pearlmutter
; Vince D. Calhoun
; Thomas P. Hayes
; | | Date: |
16 Jan 2013 | | Abstract: | Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data
analysis. An important variant is the sparse NMF problem which arises when we
explicitly require the learnt features to be sparse. A natural measure of
sparsity is the L$_0$ norm, however its optimization is NP-hard. Mixed norms,
such as L$_1$/L$_2$ measure, have been shown to model sparsity robustly, based
on intuitive attributes that such measures need to satisfy. This is in contrast
to computationally cheaper alternatives such as the plain L$_1$ norm. However,
present algorithms designed for optimizing the mixed norm L$_1$/L$_2$ are slow
and other formulations for sparse NMF have been proposed such as those based on
L$_1$ and L$_0$ norms. Our proposed algorithm allows us to solve the mixed norm
sparsity constraints while not sacrificing computation time. We present
experimental evidence on real-world datasets that shows our new algorithm
performs an order of magnitude faster compared to the current state-of-the-art
solvers optimizing the mixed norm and is suitable for large-scale datasets. | | Source: | arXiv, 1301.3527 | | Services: | Forum | Review | PDF | Favorites | |
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