Abstract
In this paper we study the effect of regularization on clustering results provided by Non-negative Matrix Factorization (NMF). Different kinds of regularization terms were previously added to the NMF objective function in order to produce sparser results and thus to obtain a more qualitative partition of data. We would like to propose the general framework for regularized NMF based on Schatten p-norms. Experimental results show the effectiveness of our approach on different data sets.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arabie, P., Hubert, L.J.: An overview of combinatorial data analysis. World Scientific Publishing Co. (1996)
Duda, R., Hart, P.: Pattern Classification and Scene Analysis (1973)
Jain, A.K., Flynn, P.J.: Image segmentation using clustering. In: Advances in Image Understanding: A Festschrift for Azriel Rosenfeld, pp. 65–83. IEEE Press (1966)
Scott, D.W.: Multivariate Density Estimation. Wiley, New York (1992)
Gersho, A., Gray.: Vector Quantization and Signal Compression. Communications and Information Theory. Kluwer Academic Publishers (1992)
Han, J., Kamber, M.: Data Mining. Morgan Kaufmann Publishers (2001)
Galen, A., Jianfeng, G.: Scalable training of l1-regularized log-linear models. In: Proceedings of the 24th International Conference on Machine Learning, pp. 788–791 (2007)
Tsuruoka, Y., Tsujii, J., Ananiadou, S.: Stochastic gradient descent training for l1-regularized log-linear models with cumulative penalty. In: Proceedings of the AFNLP/ACL, pp. 788–791 (2009)
Cichocki, A., Phan, A.H., Zdunek, R.: Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley (2009)
Nie, F., Huang, H., Ding, C.: Low-Rank Matrix Recovery via Efficient Schatten p-Norm Minimization. In: AAAI Conference on Artificial Intelligence (2012)
Nie, F., Wang, H., Cai, X., Huang, H., Ding, C.: Low-Rank Matrix Recovery via Efficient Schatten p-Norm Minimization. In: ICDM, pp. 566–574 (2012)
Lefkimmiatis, S., Ward, J.P., Unser, M.: Hessian Schatten-Norm Regularization for Linear Inverse Problems. IEEE Transactions on Image Processing 22(5), 1873–1888 (2013)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)
Argyriou, A., Micchelli, C.A., Pontil, M.: On Spectral Learning. Journal of Machine Learning Research 11, 935–953 (2010)
Rendon, E., Abundez, I., Arizmendi, A., Quiroz, E.M.: Internal versus external cluster validation indexes. International Journal of Computers and Communications 5(1) (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Redko, I., Bennani, Y. (2014). Non-negative Matrix Factorization with Schatten p-norms Reguralization. In: Loo, C.K., Yap, K.S., Wong, K.W., Teoh, A., Huang, K. (eds) Neural Information Processing. ICONIP 2014. Lecture Notes in Computer Science, vol 8835. Springer, Cham. https://doi.org/10.1007/978-3-319-12640-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-12640-1_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12639-5
Online ISBN: 978-3-319-12640-1
eBook Packages: Computer ScienceComputer Science (R0)