Abstract
Nonnegative Matrix Factorization (NMF) is an important tool in machine learning for blind source separation and latent factor extraction. Most of existing NMF algorithms assume a specific noise kernel, which is insufficient to deal with complex noise in real scenarios. In this study, we present a hierarchical nonparametric nonnegative matrix factorization (NPNMF) model in which the Gaussian mixture model is used to approximate the complex noise distribution. The model is cast in the nonparametric Bayesian framework by using Dirichlet process mixture to infer the necessary number of Gaussian components. We derive a mean-field variational inference algorithm for the proposed nonparametric Bayesian model. Experimental results on both synthetic data and electroencephalogram (EEG) demonstrate that NPNMF performs better in extracting the latent nonnegative factors in comparison with state-of-the-art methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Blankertz, B., et al.: The BCI competition 2003: progress and perspectives in detection and discrimination of EEG single trials. IEEE Trans. Biomed. Eng. 51(6), 1044–1051 (2004). https://doi.org/10.1109/TBME.2004.826692
Blei, D.M., Jordan, M.I., et al.: Variational inference for Dirichlet process mixtures. Bayesian Anal. 1(1), 121–143 (2006)
Cemgil, A.T.: Bayesian inference for nonnegative matrix factorisation models. Computational Intelligence and Neuroscience 2009 (2009)
Fu, X., Huang, K., Sidiropoulos, N.D., Ma, W.K.: Nonnegative matrix factorization for signal and data analytics: Identifiability, algorithms, and applications. IEEE Signal Process. Mag. 36, 59–80 (2019)
Guan, N., Tao, D., Luo, Z., Shawe-Taylor, J.: MahNMF: Manhattan non-negative matrix factorization. ArXiv abs/1207.3438 (2012)
Hinrich, J.L., Mørup, M.: Probabilistic sparse non-negative matrix factorization. In: Deville, Y., Gannot, S., Mason, R., Plumbley, M.D., Ward, D. (eds.) LVA/ICA 2018. LNCS, vol. 10891, pp. 488–498. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93764-9_45
Hoyer, P.O.: Non-negative matrix factorization with sparseness constraints. J. Mach. Learn. Res. 5(Nov), 1457–1469 (2004)
Huang, K., Sidiropoulos, N.D.: Putting nonnegative matrix factorization to the test: a tutorial derivation of pertinent Cramer-Rao bounds and performance benchmarking. IEEE Signal Process. Mag. 31(3), 76–86 (2014)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788 (1999)
Maz’ya, V., Schmidt, G.: On approximate approximations using Gaussian kernels. IMA J. Numer. Anal. 16(1), 13–29 (1996)
Renkens, V., et al.: Automatic relevance determination for nonnegative dictionary learning in the Gamma-Poisson model. Sig. Process. 132, 121–133 (2017)
Schachtner, R., Po, G., Tomé, A.M., Puntonet, C.G., Lang, E.W., et al.: A new Bayesian approach to nonnegative matrix factorization: Uniqueness and model order selection. Neurocomputing 138, 142–156 (2014)
Wang, Y.X., Zhang, Y.J.: Nonnegative matrix factorization: a comprehensive review. IEEE Trans. Knowl. Data Eng. 25(6), 1336–1353 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Xie, HB., Li, C., Mengersen, K., Wang, S., Xu, R.Y.D. (2020). Nonparametric Bayesian Nonnegative Matrix Factorization. In: Torra, V., Narukawa, Y., Nin, J., Agell, N. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2020. Lecture Notes in Computer Science(), vol 12256. Springer, Cham. https://doi.org/10.1007/978-3-030-57524-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-57524-3_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-57523-6
Online ISBN: 978-3-030-57524-3
eBook Packages: Computer ScienceComputer Science (R0)