Abstract
We consider the balanced bi-clustering problem for a given data set, where the number of entities in each cluster is bounded, and its special case where the number of entities in each cluster is fixed. Several algorithms to attack these problems are proposed. In particular, a novel and efficient heuristic, in which we first reformulate the constrained bi-clustering problem into a quadratic programming(QP) problem and then try to solve it by optimization technique, is proposed. We prove that our algorithm can provide a 2-approximate solution to the original problem. Promising numerical results are reported.
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Aggarwal, C., Kaplan, H., Orlin, J., Tarjan, R.: A Faster Primal Network Simplex Algorithm. Operations Research Center, Massachusetts Institute of Technology. OR 315-96 (1996)
Asano, T.: Effective Use of Geometric Properties for Clustering. In: Akiyama, J., Kano, M., Urabe, M. (eds.) JCDCG 1998. LNCS, vol. 1763, pp. 30–46. Springer, Heidelberg (2000)
Batagelj, V., Ferligoj, A.: Constrained Clustering Problems. In: Proc. of IFCS 1998 (1998)
Bradley, P., Bennet, K., Demiriz, A.: Constrained K-Means Clustering. MSRTR- 2000-65, Microsoft Research (2000)
Hasegawa, S., Imai, H., Inaba, M.: Efficient Algorithms for Variance-Based kclustering. In: First Pacific Conf. on Comp. Graph. and Appl. (1993)
Hansen, P., Jaumard, B.: Clustering analysis and mathematical programming. Math. Prog. B. 79, 191–215 (1997)
Hansen, P., Mladenovic, N.: J-means: a new local search heuristic for minimum sum-of-squares clustering. Pattern Recog. 34, 405–413 (2001)
He, J., Lan, M., Tan, C., Sung, S., Low, H.: Initialization of clusters refinement algorithms: a review and comparative study. In: International Joint Conf. on Neural Networks, IJCNN, pp. 25–29 (2004)
Inaba, M., Katoh, N., Imai, H.: Applications of Weighted Voronoi Diagrams and Randomization to Variance-Based k-clustering. In: Proc. of 10th ACM Symp. on Comp. Geo., pp. 332–339 (1994)
Jain, A.K., Murty, N.M., Flynn, P.J.: Data Clustering: A Review. ACM Comput. Surveys 31(1999), 264–323 (1999)
Matoušek, J.: On Approximate Geometric k-clustering. Dis. and Comput. Geo. 24, 61–84 (2000)
Michalski, R.S., Chilausky, R.L.: Learning by being told and learning from examples: An experimental comparison of the two methods of knowledge acquisition in the context of developing an expert system for soybean disease diagnosis. International Journal of Policy Analysis and Information Systems 4(2), 125–161 (1980)
Späth, H.: Cluster analysis Algorithms for Data Reduction and Classification of Objects. John Wiley and Sons, Ellis Horwood (1980)
Tung, A., Ng, R., Lakshmanan, L., Han, J.: Constraint-Based Clustering in Large Databases. In: Proc. of the 8th Inter. Conf. on Database Theory, pp. 405–419 (2001)
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Ma, G., Peng, J., Wei, Y. (2005). On Approximate Balanced Bi-clustering. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_67
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DOI: https://doi.org/10.1007/11533719_67
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
Online ISBN: 978-3-540-31806-4
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