Abstract
Constrained clustering - finding clusters that satisfy user-specified constraints - aims at providing more relevant clusters by adding constraints enforcing required properties. Leveraging the recent progress in declarative and constraint-based pattern mining, we propose an effective constraint-clustering approach handling a large set of constraints which are described by a generic constraint-based language. Starting from an initial solution, queries can easily be refined in order to focus on more interesting clustering solutions. We show how each constraint (and query) is encoded in SAT and solved by taking benefit from several features of SAT solvers. Experiments performed using MiniSat on several datasets from the UCI repository show the feasibility and the advantages of our approach.
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
Bailleux, O., Boufkhad, Y.: Efficient CNF Encoding of Boolean Cardinality Constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 108–122. Springer, Heidelberg (2003)
Banerjee, A., Ghosh, J.: Scalable clustering algorithms with balancing constraints. Data Min. Knowl. Discov. 13(3), 365–395 (2006)
Basu, S., Davidson, I., Wagstaff, K.L.: Constrained Clustering: Advances in Algorithms, Theory, and Applications. Chapman & Hall (2008)
Batcher, K.E.: Sorting networks and their applications. In: AFIPS Spring Joint Computing Conference. AFIPS Conference Proceedings, vol. 32, pp. 307–314. Thomson Book Company, Washington, D.C (1968)
Berkhin, P.: Survey of clustering data mining techniques. Technical report, Accrue Software, San Jose, CA, USA (2002)
Coquery, E., Jabbour, S., Sais, L.: A constraint programming approach for enumerating motifs in a sequence. In: Workshop on Declarative Pattern Mining, ICDM 2011, Vancouver, Canada, pp. 1091–1097 (December 2011)
Davidson, I., Ravi, S.: Clustering with constraints: Feasibility issues and the k-means algorithm. In: SDM (2005)
Davidson, I., Ravi, S.: Using instance-level constraints in agglomerative hierarchical clustering: theoretical and empirical results. Data Min. Knowl. Discov. 18(2), 257–282 (2009)
Davidson, I., Ravi, S., Shamis, L.: A SAT-based framework for efficient constrained clustering. In: SDM, pp. 94–105. SIAM (2010)
Eén, N., Sörensson, N.: An Extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into SAT. JSAT 2(1-4), 1–26 (2006)
Fisher, D.H.: Knowledge acquisition via incremental conceptual clustering. Machine Learning 2(2), 139–172 (1987)
Gilpin, S., Davidson, I.: Incorporating SAT solvers into hierarchical clustering algorithms: an efficient and flexible approach. In: KDD 2011, pp. 1136–1144 (2011)
Guns, T., Nijssen, S., De Raedt, L.: Itemset mining: A constraint programming perspective. Artif. Intell. 175(12-13), 1951–1983 (2011)
Khiari, M., Boizumault, P., Crémilleux, B.: Constraint Programming for Mining n-ary Patterns. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 552–567. Springer, Heidelberg (2010)
MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press (1967)
Métivier, J.-P., Boizumault, P., Crémilleux, B., Khiari, M., Loudni, S.: A constraint-based language for declarative pattern discovery. In: 27th Annual ACM Symposium on Applied Computing (SAC 2012), March 2012, pp. 438–444 (2012)
Sinz, C.: Towards an Optimal CNF Encoding of Boolean Cardinality Constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005)
Tung, A.K.H., Han, J., Lakshmanan, L.V.S., Ng, R.T.: Constraint-Based Clustering in Large Databases. In: Van den Bussche, J., Vianu, V. (eds.) ICDT 2001. LNCS, vol. 1973, pp. 405–419. Springer, Heidelberg (2000)
Wagstaff, K., Cardie, C.: Clustering with instance-level constraints. In: ICML 2000, pp. 1103–1110. M. Kaufmann (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Métivier, JP., Boizumault, P., Crémilleux, B., Khiari, M., Loudni, S. (2012). Constrained Clustering Using SAT. In: Hollmén, J., Klawonn, F., Tucker, A. (eds) Advances in Intelligent Data Analysis XI. IDA 2012. Lecture Notes in Computer Science, vol 7619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34156-4_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-34156-4_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34155-7
Online ISBN: 978-3-642-34156-4
eBook Packages: Computer ScienceComputer Science (R0)