{"references": ["R. Agrawal, J. Gehrke, D. Gunopulos, and P. Raghavan, \"Automatic\nsubspace slustering of high dimensional data for data mining\napplications,\" In Proc. ACM SIGMOD International Conference on\nManagement of Data, Seattle, Washington, June 1998, pp. 94-105.", "J. S. Aguilar, R. Ruiz, J. C. Riquelme, and R. Giraldez, \"SNN: A\nsupervised clustering algorithm,\" In Proc. 14th International Conference\non Industrial & Engineering Applications of Artificial Intelligence &\nExpert Systems (IEA/AIE 2001)", "S. H. Al-Harbi, and V. J. Rayward-Smith, \"Adaptive k-means for\nsupervised clustering,\" Applied Intelligence, Volume 24, Number 3, pp.\n219-226(8), June 2006.", "T. Finley and T. Joachims, \"Supervised clustering with support vector\nmachines,\" In Proc. International conference on Machine learning,\nBonn, Germany, August 07 - 11, 2005, pp. 217-224.", "A. Jirayusakul, \"Supervised growing neural gas algorithm in clustering\nanalysis,\" Ph.D. dissertation, School of Applied Statistics, National\nInstitute of Development Administration, Thailand, 2007, unpublised.", "A. Jirayusakul, and S. Auwatanamongkol, \"A supervised growing neural\ngas algorithm for cluster analysis,\" International Journal of Hybrid\nIntelligent Systems, Vol. 4, No.2, 2007.", "S. B. Kotsiantis and P. E. Pintelas, \"Recent Advances in Clustering: A\nBrief Survey,\" Transactions on Information Science and Applications,\n2004,1(1):73-81.", "X. Li and N. Ye, \"Grid-and Dummy-Cluster-Based Learning of Normal\nand Intrusive Clusters of Computer Intrusion Detection,\" Journal of\nQuality and Reliability Engineering International, Vol. 18, No. 3, pp.\n231-242.", "X. Li and N. Ye, \"A Supervised Clustering Algorithm for Computer\nIntrusion Detection,\" Knowledge and Information Systems, Vol. 8,\nNo.4, pp. 498-509.\n[10] X. Li and N. Ye, \"A Supervised Clustering and Classification Algorithm\nfor Mining Data With Mixed Variables,\" IEEE Transactions on Systems,\nMan, and Cybernetics-Part A, Vol. 36, No. 2, pp. 396-406.\n[11] N. H. Park and W. S. Lee, \"Statistical Grid-based Clustering over Data\nStreams,\" SIGMODD Record, Vol.33, No.1, March 2004.\n[12] L. Parsans, E. Haque, and H. Liu, \"Subspace Clustering for High\nDimensional Data: A Review,\" ACM SIGKDD Explorations Newsletter,\n6(1):90-105, June 2004.\n[13] C. M. Procopiuc, 1997, \"Clustering Problems and their Applications (a\nSurvey),\" Available: http://www.cs.duke.edu/~magda.\n[14] G. Sheikholeslami, S. Chatterjee, and A. Zhang, \"WaveCluster: A Multi-\nResolution Clustering Approach for Very Large Spatial Databases,\" In\nProc. International Conference on Very Large Databases, New York\nCity, August 24-27, 1998.\n[15] J. Sinkkonen, S. Kaski, and J. Nikkila, \"Discriminative Clustering:\nOptimal Contingency Tables by Learning Metrics,\" In Proc. European\nConference on Machine Learning (ECML-02), Springer-Veriag,\nLondon, pp. 418-430.\n[16] N. Slonim and N. Tishby, \"Agglomerative Information Bottleneck,\" In\nProc. Neural Information Processing Systems, pp. 617-623, 1999.\n[17] P-N. Tan, M. Steinbach, and V. Kumar, \"Introduction to Data Mining.\nBoston: Pearson Education, Inc., pp. 604-608.\n[18] N. Tishby, F. C. Pereira, and W. Bialek, \"The Information Bottleneck\nMethod,\" In Proceedings of the Allerton Conference on\nCommunication and Computation, 1999.\n[19] Y. Qu and Z. Xu, \"Supervised Clustering Analysis for Microarray Data\nBased on Multivariate Gauussian Mixture,\" Bioinformatics. 20 (Aug) :\n1275-1288.\n[20] University of California at Irving, Machine Learning Repository.\nAvailable: http:/www.ics.edu/~mlearn/MLRepository.html\n[21] N. Ye and X. Li, \"A Scalable Clustering Technique for Intrusion\nSignature Recognition,\" In Proc. The 2001 IEEE Workshop on\nInformation Assurance and Security United States Military Academy,\nWest Point, NY, 5-6 June, 2001.\n[22] N. Ye and X. Li, 2005, \"Method for Classifying Data using Clustering\nand Classification Algorithm Supervised,\" Available:\nhttp://www.patentstorm.us/patents/6907436/fulltext.html.\n[23] N. Zeidat, C. F. Eick, and Z. Zhao, \"Supervised Clustering: Algorithms\nand Applications,\" Available:\nhttp://www2.cs.uh.edu/~ceick/kdd/ZEZ06.pdf."]}

This paper presents a supervised clustering algorithm, namely Grid-Based Supervised Clustering (GBSC), which is able to identify clusters of any shapes and sizes without presuming any canonical form for data distribution. The GBSC needs no prespecified number of clusters, is insensitive to the order of the input data objects, and is capable of handling outliers. Built on the combination of grid-based clustering and density-based clustering, under the assistance of the downward closure property of density used in bottom-up subspace clustering, the GBSC can notably reduce its search space to avoid the memory confinement situation during its execution. On two-dimension synthetic datasets, the GBSC can identify clusters with different shapes and sizes correctly. The GBSC also outperforms other five supervised clustering algorithms when the experiments are performed on some UCI datasets.