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.
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Keywords
- Regularization Term
- Negative Matrix Factorization
- Cluster Validation Index
- Negative Matrix Factorization
- Multivariate Density Estimation
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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)
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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
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DOI: https://doi.org/10.1007/978-3-319-12640-1_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12639-5
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