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About this paper
Sinan Yildirim, A. Taylan Cemgil, Sumeetpal S. Singh
An online Expectation-Maximization (EM) algorithm is introduced for Nonnegative Matrix Factorization (NMF) by framing it as a Maximum Likelihood Estimation problem within a Hidden Markov Model (HMM) framework. This approach, implemented with Sequential Monte Carlo (SMC) methods, facilitates scalable and theoretically grounded estimation of NMF basis matrices from streaming data, demonstrating convergence in numerical examples.
Key insights
- Framing NMF within an HMM-MLE paradigm provides a robust theoretical foundation for online estimation, leveraging established asymptotic properties of MLE in HMMs.
- The introduction of an auxiliary latent integer matrix allows for a tractable closed-form E-step, which is crucial for applying the EM algorithm effectively in the NMF context.
- Online EM, approximated by SMC, offers a scalable and principled method for NMF that can adapt to streaming data and explicitly model dynamic latent factor behavior.
Summary by alphaXiv.
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