Three-Mode Fuzzy Co-Clustering Based on Probabilistic Concept and Comparison with FCM-Type Algorithms
Katsuhiro Honda, Issei Hayashi, Seiki Ubukata, and Akira Notsu
Osaka Prefecture University
1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan
Three-mode fuzzy co-clustering is a promising technique for analyzing relational co-occurrence information among three mode elements. The conventional FCM-type algorithms achieved simultaneous fuzzy partition of three mode elements based on the fuzzy c-means (FCM) concept, and then, they often suffer from careful tuning of three independent fuzzification parameters. In this paper, a novel three-mode fuzzy co-clustering algorithm is proposed by modifying the conventional aggregation criterion of three elements based on a probabilistic concept. The fuzziness degree of three-mode partition can be easily tuned only with a single parameter under the guideline of the probabilistic standard. The characteristic features of the proposed method are compared with the conventional algorithms through numerical experiments using an artificial dataset and are demonstrated in application to a real world dataset of MovieLens movie evaluation data.
-  K. Kummamuru, A. Dhawale, and R. Krishnapuram, “Fuzzy co-clustering of documents and keywords,” Proc. of the 12th IEEE Int. Conf. on Fuzzy Systems, pp. 772-777, 2003.
-  W.-C. Tjhi and L. Chen, “A partitioning based algorithm to fuzzy co-cluster documents and words,” Pattern Recognition Letters, Vol.27, pp. 151-159, 2006.
-  K. Honda, A. Notsu, and H. Ichihashi, “Collaborative filtering by sequential user-item co-cluster extraction from rectangular relational data,” Int. J. of Knowledge Engineering and Soft Data Paradigms, Vol.2, No.4, pp. 312-327, 2010.
-  C.-H. Oh, K. Honda, and H. Ichihashi, “Fuzzy clustering for categorical multivariate data,” Proc. of Joint 9th IFSA World Congress and 20th NAFIPS Int. Conf., pp. 2154-2159, 2001.
-  J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, 1981.
-  K. Honda, S. Oshio, and A. Notsu, “Fuzzy co-clustering induced by multinomial mixture models,” J. Adv. Comput. Intell. Intell. Inform., Vol.19, No.6, pp. 717-726, doi: 10.20965/jaciii.2015.p0717, 2015.
-  L. Rigouste, O. Cappé, and F. Yvon, “Inference and evaluation of the multinomial mixture model for text clustering,” Information Processing and Management, Vol.43, No.5, pp. 1260-1280, 2007.
-  S. Bickel and T. Scheffer, “Multi-view clustering,” Proc. the 4th IEEE Int. Conf. on Data Mining, pp. 19-26, 2004.
-  Y.-M. Xu, C.-D. Wang, and J.-H. Lai, “Weighted multi-view clustering with feature reduction,” Pattern Recognition, Vol.53, pp. 25–35, 2016.
-  Y. Yang and H. Wang, “Multi-view clustering: A survey,” Big Data Mining and Analytics, Vol.1, No.2, pp. 83-107, 2018.
-  T. Iwasaki and T. Furukawa, “Tensor SOM and tensor GTM: nonlinear tensor analysis by topographic mappings,” Neural Networks, Vol.77, pp. 107-125, 2016.
-  T.-C. T. Chen and K. Honda, “Fuzzy Collaborative Forecasting and Clustering: Methodology, System Architecture, and Applications,” SpringerBriefs in Applied Sciences and Technology, Springer, 2019.
-  K. Honda, Y. Suzuki, S. Ubukata, and A. Notsu, “FCM-type fuzzy coclustering for three-mode cooccurrence data: 3FCCM and 3Fuzzy CoDoK,” Advances in Fuzzy Systems, Vol.2017, No.9842127, pp. 1-8, 2017.
-  K. Honda, I. Hayashi, S. Ubukata, and A. Notsu, “A comparative study on three-mode fuzzy co-clustering based on co-occurrence aggregation criteria,” Proc. of 2020 Int. Symp. on Community-centric Systems (CcS), #88, pp. 1-6, 2020.
-  MovieLens Web Page, http://www.movielens.org/ [accessed February 25, 2021]
-  S. Miyamoto and M. Mukaidono, “Fuzzy c-means as a regularization and maximum entropy approach,” Proc. of the 7th Int. Fuzzy Systems Association World Congress, Vol.2, pp 86-92, 1997.
-  S. Miyamoto, H. Ichihashi, and K. Honda, “Algorithms for Fuzzy Clustering,” Springer, 2008.
-  S. Miyamoto and K. Umayahara, “Fuzzy clustering by quadratic regularization,” Proc. 1998 IEEE Int. Conf. Fuzzy Systems and IEEE World Congress Computational Intelligence, Vol.2, pp. 1394-1399, 1998.
-  A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. of the Royal Statistical Society, Series B, Vol.39, pp. 1-38, 1977.
-  J. A. Konstan, B. N. Miller, D. Maltz, J. L. Herlocker, L. R. Gardon, and J. Riedl, “Grouplens: applying collaborative filtering to usenet news,” Communications of the ACM, Vol.40, No.3, pp. 77-87, 1997.
-  K. Rose, E. Gurewitz, and G. Fox, “A deterministic annealing approach to clustering,” Pattern Recognition Letters, Vol.11, pp. 589-594, 1990.
-  T. Goshima, K. Honda, S. Ubukata, and A. Notsu, “Deterministic annealing process for pLSA-induced fuzzy co-clustering and cluster splitting characteristics,” Int. J. of Approximate Reasoning, Vol.95, pp. 185-193, 2018.
-  K. Honda, N. Yamamoto, S. Ubukata, and A. Notsu, “Noise rejection in MMMs-induced fuzzy co-clustering,” J. Adv. Comput. Intell. Intell. Inform., Vol.21, No.7, pp. 1144-1151, doi: 10.20965/jaciii.2017.p1144, 2017.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.