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SPARCL: an effective and efficient algorithm for mining arbitrary shape-based clusters

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Abstract

Clustering is one of the fundamental data mining tasks. Many different clustering paradigms have been developed over the years, which include partitional, hierarchical, mixture model based, density-based, spectral, subspace, and so on. The focus of this paper is on full-dimensional, arbitrary shaped clusters. Existing methods for this problem suffer either in terms of the memory or time complexity (quadratic or even cubic). This shortcoming has restricted these algorithms to datasets of moderate sizes. In this paper we propose SPARCL, a simple and scalable algorithm for finding clusters with arbitrary shapes and sizes, and it has linear space and time complexity. SPARCL consists of two stages—the first stage runs a carefully initialized version of the Kmeans algorithm to generate many small seed clusters. The second stage iteratively merges the generated clusters to obtain the final shape-based clusters. Experiments were conducted on a variety of datasets to highlight the effectiveness, efficiency, and scalability of our approach. On the large datasets SPARCL is an order of magnitude faster than the best existing approaches.

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References

  1. Astrahan MM (1970) Speech analysis by clustering, or the hyperphoneme method. Stanford A.I. Project Memo, Stanford University

  2. Aupetit M (2003) Robust topology representing networks. In: Proceedings of the European symposium on artificial neural networks, Bruges, Belgium, pp 45–50

  3. Arthur D, Vassilvitskii S (2007) k-means++: the advantages of careful seeding. In: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, New Orleans, Louisiana, 2007, pp 1027–1035

  4. Ball GH, Hall DJ (1967) PROMENADE—an online pattern recognition system. Stanford Research Institute, Stanford University

  5. Bradley PS, Fayyad UM (1998) Refining initial points for k-means clustering. In: Proceedings of the fifteenth international conference on machine learning Madison, Wisconsin, pp 91–99

  6. Breunig MM, Kriegel H, Ng RT, Sander J (2000) LOF: identifying density-based local outliers. In: Proceedings of 2000 ACM-SIGMOD international conference on management of data, Dallas, Texas, 2000, pp 93–104

  7. Chazelle B, Palios L (1994) Decomposition algorithms in geometry. In: Bajaj C (eds) Algebraic geometry and its applications. Springer, Berlin, pp 419–447

    Google Scholar 

  8. Cormen TH, Leiserson CE, Rivest RL, Stein C (2005) Introduction to algorithms, 2nd edn. MIT Press, Cambridge

    Google Scholar 

  9. Dasgupta S, Schulman LJ (2000) A two-round variant of EM for Gaussian mixtures. In: Proceedings of the 16th conference on uncertainty in artificial intelligence, Stanford, CA, June 2000, pp 152–159

  10. Dhillon IS, Guan Y, Julis B (2004) Kernel k-means, spectral clustering and normalized cuts. In: Proceedings of the tenth international conference on knowledge discovery and data mining, Seattle, WA, August 2004, pp 551–556

  11. Domeniconi C, Gunopulos D (2004) An efficient density-based approach for data mining tasks. Knowl Inform Syst 6(6): 750–770

    Article  Google Scholar 

  12. Duda RO, Hart PE, Stork DG (2000) Pattern classification, 2nd edn. Wiley-Interscience, New York

    Google Scholar 

  13. Ester M, Kriegel H-P, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: Proceedings of ACM SIGKDD international conference on knowledge discovery and data mining, 1996, pp 226–231

  14. García JA, Fdez-Valdivia J, Cortijo FJ, Molina R (1995) A dynamic approach for clustering data. Signal Process 44(2): 181–196

    Article  Google Scholar 

  15. Gao BJ, Ester M, Cai J-Y, Schulte O, Xiong H (2007) The minimum consistent subset cover problem and its applications in data mining. In: Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining San Jose, California, USA, 2007, pp 310–319

  16. Guha S, Rastogi R, Shim K (1998) CURE: an efficient clustering algorithm for large databases. In: ACM SIGMOD international conference on management of data, Seattle, WA, pp 73–84

  17. Hasan MA, Chaoji V, Salem S, Zaki MJ (2008) Robust partitional clustering by outlier and density insensitive seeding. Technical Report 08-04, RPI Computer Science

  18. Hinneburg A, Gabriel H-H (2007) DENCLUE 2.0: fast clustering based on kernel density estimation. In: International symposium on intelligent data analysis, pp 70–80

  19. Hinneburg A, Keim DA (2003) A general approach to clustering in large databases with noise. Knowl Inform Syst 5(4): 387–415

    Article  Google Scholar 

  20. Hinneburg A, Keim DA (1998) An efficient approach to clustering in multimedia databases with noise. In: Proceedings of 4th international conference on knowledge discovery and data mining. AAAI Press, New York

  21. Hu X, Pan Y (2007) Knowledge discovery in bioinformatics: techniques, methods, and applications (Wiley Series in Bioinformatics). Wiley, New York

    Book  Google Scholar 

  22. Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice-Hall, Upper Saddle River

    MATH  Google Scholar 

  23. Klaus J (2003) Clustering intrusion detection alarms to support root cause analysis. ACM Trans Inform Syst Secur 6(4): 443–471

    Article  Google Scholar 

  24. Karypis G, Han E-H, Kumar V (1999) Chameleon: hierarchical clustering using dynamic modeling. Computer 32(8): 68–75

    Article  Google Scholar 

  25. Katsavounidis I, Kuo CCJ, Zhen Z (1994) A new initialization technique for generalized Lloyd iteration. IEEE Signal Process Lett 1(10): 144–146

    Article  Google Scholar 

  26. Kaufman, L Rousseeuw, PJ (1990) Finding groups in data: An introduction to cluster analysis. Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics, New York

  27. Koga H, Ishibashi T, Watanabe T (2007) Fast agglomerative hierarchical clustering algorithm using Locality-Sensitive Hashing. Knowl Inform Syst 12(1): 25–53

    Article  Google Scholar 

  28. Lee J, Verleysen M (2007) Nonlinear dimensionality reduction. Springer, Berlin

    Book  MATH  Google Scholar 

  29. Martinetz T, Schulten K (1994) Topology representing networks. Neural Netw 7(3): 507–522

    Article  Google Scholar 

  30. Meila M, Shi J (2001) A random walks view of spectral segmentation. AI and Statistics (AISTATS)

  31. Miller HJ, Han J (2001) Geographic data mining and knowledge discovery. Taylor & Francis, Bristol

    Google Scholar 

  32. Ng AY, Jordan M, Weiss Y (2001) On spectral clustering: analysis and an algorithm. In: Advances in neural information processing systems, vol 14

  33. Okabe A, Boots B, Sugihara K (1992) Spatial tessellations: concepts and applications of voronoi diagrams. Wiley, New York

    MATH  Google Scholar 

  34. Punj G, Stewart DW (1983) Cluster analysis in marketing research: review and suggestions for application. J Mark Res 20(2): 134–148

    Article  Google Scholar 

  35. Sack JR, Urrutia J (2000) Handbook of computational geometry. North-Holland, Amsterdam

    MATH  Google Scholar 

  36. Shawe-Taylor J, Cristianini N (2004) Kernel methods for pattern analysis. Cambridge University Press, Cambridge

    Google Scholar 

  37. Sheikholeslami G, Chatterjee S, Zhang A (1998) WaveCluster: a multi-resolution clustering approach for very large spatial databases. In: Proceedings of 24th international conference on very large data bases, pp 428–439

  38. Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22(8): 888–905

    Article  Google Scholar 

  39. Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500): 2319–2323

    Article  Google Scholar 

  40. Vennam JR, Vadapalli S (2005) SynDECA: a tool to generate synthetic datasets for evaluation of clustering algorithms. In: 11th international conference on management of data

  41. Wu X, Kumar V, Ross Q, Ghosh J, Yang Q, Motoda H, McLachlan GJ, Ng A, Liu B, Yu PS, Zhou Z-H, Steinbach M, Hand DJ, Steinberg D (2008) Top 10 algorithms in data mining. Knowl Inform Syst 14(1): 1–37

    Article  Google Scholar 

  42. Zelnik-Manor L, Perona P (2004) Self-tuning spectral clustering. In: Proceedings of 18th annual conference on neural information processing systems

  43. Zeng H-J, He Q-C, Chen Z, Ma W-Y, Ma J (2004) Learning to cluster web search results. In: Proceedings of the 27th annual international ACM SIGIR conference on Research and development in information retrieval, New York, NY, pp 210–217

  44. Zhang T, Ramakrishnan R, Livny M (1997) BIRCH: a new data clustering algorithm and its applications. Data Min Knowl Discov 1(2): 141–182

    Article  Google Scholar 

  45. Zhao Y, Karypis G (2005) Hierarchical clustering algorithms for document datasets. Data Min Knowl Discov 10(2): 141–168

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Computer Science Department, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Vineet Chaoji, Mohammad Al Hasan, Saeed Salem & Mohammed J. Zaki

Authors
  1. Vineet Chaoji
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  2. Mohammad Al Hasan
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  3. Saeed Salem
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  4. Mohammed J. Zaki
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Corresponding author

Correspondence to Vineet Chaoji.

Additional information

This work was supported in part by NSF Grants EMT-0829835, and CNS-0103708, and NIH Grant 1R01EB0080161-01A1.

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Chaoji, V., Al Hasan, M., Salem, S. et al. SPARCL: an effective and efficient algorithm for mining arbitrary shape-based clusters. Knowl Inf Syst 21, 201–229 (2009). https://doi.org/10.1007/s10115-009-0216-0

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