Abstract
Non-negative Matrix Factorization (NMF) is a technique for factorizing a non-negative matrix into the products of non-negative component matrices and has been used in such applications as air pollution analysis. In order to make NMF robust against noise, noise clustering-based approach was proposed with least square criterion, where NMF model estimation was performed in conjunction with noise rejection under the iterative optimization principle. In this paper, another robust NMF model was proposed supported by I-divergence criterion, which considers asymmetric distance measures rather than symmetric ones in the least square model. The updating formula of fuzzy memberships for non-noise degrees of objects are also constructed based on I-divergence criterion. The characteristic features of the proposed method are compared with the conventional one through numerical experiments using an artificial dataset.
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References
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788–791 (1999)
Lee, D.D., Seung, H.S.: Algorithms for nonnegative matrix factorization. Adv. Neural Inf. Process. Syst. 13, 556–562 (2000)
Févotte, C., Bertin, N., Durrieu, J.-L.: Nonnegative matrix factorization with the Itakura-Saito divergence. With application to music analysis. Neural Comput. 21(3), 793–830 (2009)
Zhang, L., Chen, Z., Zheng, M., He, X.: Robust non-negative matrix factorization. Front. Electr. Electron. Eng. China 6, 192–200 (2011). https://doi.org/10.1007/s11460-011-0128-0
Shen, B., Liu, B., Wang, Q., Ji, R.: Robust nonnegative matrix factorization via \(L_1\) norm regularization by multiplicative updating rules. In: Proceedings of 2014 IEEE International Conference on Image Processing, pp. 5282–5286 (2014)
Ueno, M., Honda, K., Ubukata, S., Notsu, A.: Robust non-negative matrix factorization based on noise fuzzy clustering mechanism. In: Proceedings of 2019 2nd Artificial Intelligence and Cloud Computing Conference and 2019 Asia Digital Image Processing Conference, pp. 1–5 (2019)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Miyamoto, S., Ichihashi, H., Honda, K.: Algorithms for Fuzzy Clustering. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78737-2
Davé, R.N.: Characterization and detection of noise in clustering. Pattern Recognit. Lett. 12(11), 657–664 (1991)
Davé, R.N., Krishnapuram, R.: Robust clustering methods: a unified view. IEEE Trans. Fuzzy Syst. 5, 270–293 (1997)
Holland, P.W., Welsch, R.E.: Robust regression using iteratively reweighted least-squares. Commun. Stat. A6(9), 813–827 (1977)
Honda, K., Notsu, A., Ichihashi, H.: Fuzzy PCA-guided robust \(k\)-means clustering. IEEE Trans. Fuzzy Syst. 18(1), 67–79 (2010)
Honda, K., Ichihashi, H.: Linear fuzzy clustering techniques with missing values and their application to local principal component analysis. IEEE Trans. Fuzzy Syst. 12(2), 183–193 (2004)
MacQueen, J. B.: Some methods of classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297 (1967)
Honda, K., Ueno, M., Ubukata, S., Notsu, A.: Robust non-negative matrix factorization based on noise fuzzy clustering mechanism and application to environmental observation data analysis. J. Japan Soc. Fuzzy Theory Intell. Inform. 33(2), 593–599 (2021). (in Japanese)
Acknowledgment
This work was supported in part by JSPS KAKENHI Grant Number JP18K11474.
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Okabe, A., Honda, K., Ubukata, S. (2022). Noise Fuzzy Clustering-Based Robust Non-negative Matrix Factorization with I-divergence Criterion. In: Honda, K., Entani, T., Ubukata, S., Huynh, VN., Inuiguchi, M. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2022. Lecture Notes in Computer Science(), vol 13199. Springer, Cham. https://doi.org/10.1007/978-3-030-98018-4_21
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DOI: https://doi.org/10.1007/978-3-030-98018-4_21
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