Automatic Relevance Determination for Nonnegative Matrix Factorization
Vincent Y. F. Tan and Cédric Févotte,
2009 Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS’09), St Malo, France

Apr 6 – Apr 9, 2009

Abstract:

Nonnegative matrix factorization (NMF) has become a popular technique for data analysis and dimensionality reduction. However, it is often assumed that the number of latent dimensions (or components) is given. In practice, one must choose a suitable value depending on the data and/or setting. In this paper, we address this important issue by using a Bayesian approach to estimate the latent dimensionality, or equivalently, select the model order. This is achieved via automatic relevance determination (ARD), a technique that has been employed in Bayesian PCA and sparse Bayesian learning. We show via experiments on synthetic data that our technique is able to recover the correct number of components, while it is also able to recover an effective number of components from real datasets such as the MIT CBCL dataset.

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The associated Matlab code for this paper is available here.

The zip file contains two files: nmf_kl_mos.m is the main function and sc_data_nmf.m is the test file.

Please contact the author if you have any questions. Thanks!