An Efficient Newton Algorithm for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence
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TL;DR — A new Newton-type optimization algorithm for KL-divergence Nonnegative Matrix Factorization that replaces the standard separable-majorant approach with a second-order Taylor surrogate, improving efficiency while retaining convergence guarantees.
- Targets KL-NMF, the NMF variant best suited to count data (e.g., term-document matrices, images) where samples follow a Poisson distribution.
- Argues that the common approach of minimizing a separable majorant has plateaued, and instead uses the second-order Taylor expansion of the loss for a Newton-type update.
- Minimizes this non-separable surrogate via a generalization of the HALS algorithm, yielding provable convergence.
- Claims competitive-to-favorable performance against state-of-the-art algorithms across a wide range of datasets.
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An Efficient Newton Algorithm for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence
Public signals
N/A
TL;DR — A new Newton-type optimization algorithm for KL-divergence Nonnegative Matrix Factorization that replaces the standard separable-majorant approach with a second-order Taylor surrogate, improving efficiency while retaining convergence guarantees.
- Targets KL-NMF, the NMF variant best suited to count data (e.g., term-document matrices, images) where samples follow a Poisson distribution.
- Argues that the common approach of minimizing a separable majorant has plateaued, and instead uses the second-order Taylor expansion of the loss for a Newton-type update.
- Minimizes this non-separable surrogate via a generalization of the HALS algorithm, yielding provable convergence.
- Claims competitive-to-favorable performance against state-of-the-art algorithms across a wide range of datasets.