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Block Majorization Minimization with Extrapolation and Application to β-NMF
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DOI：10.1137/24M1660188.png)
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Abstract
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We propose a Block Majorization Minimization method with Extrapolation (BMMe) for solving a class of multiconvex optimization problems. The extrapolation parameters of BMMe are updated using a novel adaptive update rule. By showing that block majorization minimization can be reformulated as a block mirror descent method, with the Bregman divergence adaptively updated at each iteration, we establish subsequential convergence for BMMe. We use this method to design efficient algorithms to tackle nonnegative matrix factorization problems with \beta -divergences (\beta -NMF) for \beta \in [1, 2]. These algorithms, which are multiplicative updates with extrapolation, benefit from our novel results, which offer convergence guarantees. We also empirically illustrate the significant
Keywords:
block majorization minimization
extrapolation
nonnegative matrix factorization
beta-divergences
Kullback-Leibler divergence
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