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Connectedness-based subspace clustering

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Abstract

An algorithm for density-based subspace clustering of given data is proposed here. Unlike the existing density-based subspace clustering algorithms which find clusters using spatial proximity, existence of common high-density regions is the condition for grouping of features here. The proposed method is capable of finding subspace clusters based on both linear and nonlinear relationships between features. Unlike existing density-based subspace clustering algorithms, the values of parameters for density estimation need not be provided by the user. These values are calculated for each pair of features using data distribution in space corresponding to the particular pair of features. This allows proposed approach to find subspace clusters where relationship between different features exists at different scales. The performance of proposed algorithm is compared with other subspace clustering methods using artificial and real-life datasets. The proposed method is seen to find subspace clusters embedded in 5 artificial datasets with greater G score. It is also seen that the proposed method is able to find subspace clusters corresponding to known classes in 4 real-life datasets, with greater accuracy.

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References

  1. Aggarwal CC, Wolf JL, Yu PS, Procopiuc C, Park JS (1999) Fast algorithms for projected clustering. SIGMOD Rec. 28(2):61–72. https://doi.org/10.1145/304181.304188

    Article  Google Scholar 

  2. Agrawal R, Gehrke J, Gunopulos D, Raghavan P (1998) Automatic subspace clustering of high dimensional data for data mining applications. SIGMOD Rec. 27(2):94–105. https://doi.org/10.1145/276305.276314

    Article  Google Scholar 

  3. Aguilar-Ruiz JS (2005) Shifting and scaling patterns from gene expression data. Bioinformatics 21(20):3840–3845. https://doi.org/10.1093/bioinformatics/bti641

    Article  Google Scholar 

  4. Ahmed HA, Mahanta P, Bhattacharyya DK, Kalita JK (2014) Shifting-and-scaling correlation based biclustering algorithm. IEEE ACM Trans Comput Biol Bioinform 11(6):1239–1252

    Article  Google Scholar 

  5. Hochreiter S, Bodenhofer U, Heusel M, Mayr A, Mitterecker A, Kasim A, Khamiakova T, Van Sanden S, Lin D, Talloen W, Bijnens L, Ghlmann HWH, Shkedy Z, Clevert D-A (2010) Fabia: factor analysis for bicluster acquisition. Bioinformatics 26:1520

    Article  Google Scholar 

  6. Bergmann S, Ihmels J, Barkai N (2003) Iterative signature algorithm for the analysis of large-scale gene expression. Phys Rev E Stat Nonlinear Soft Matter Phys 67:131902

    Article  Google Scholar 

  7. Carmona-Saez P, Pascual-Marqui RD, Tirado F, Carazo JM, Pascual-Montano A (2006) Biclustering of gene expression data by non-smooth non-negative matrix factorization. BMC Bioinform 7(1):78. https://doi.org/10.1186/1471-2105-7-78

    Article  Google Scholar 

  8. Cheng Y, Church GM (2000) Biclustering of expression data. In: Proceedings of the eighth international conference on intelligent systems for molecular biology. AAAI Press, pp 93–103. http://dl.acm.org/citation.cfm?id=645635.660833

  9. Cheung L, Yip KY, Cheung DW, Kao B, Ng MK (2005) On mining micro-array data by order-preserving submatrix. In: 21st International conference on data engineering workshops (ICDEW’05), pp 1153–1153

  10. Costeira JP, Kanade T (1998) A multibody factorization method for independently moving objects. Int J Comput Vis 29(3):159–179. https://doi.org/10.1023/A:1008000628999

    Article  Google Scholar 

  11. Divina F, Aguilar-Ruiz JS (2006) Biclustering of expression data with evolutionary computation. IEEE Trans Knowl Data Eng 18(5):590–602

    Article  Google Scholar 

  12. Ester M, Kriegel H-P, Sander J, Xu X (1996) A density-based algorithm for discovering clusters a density-based algorithm for discovering clusters in large spatial databases with noise. In: Proceedings of the second international conference on knowledge discovery and data mining, KDD’96. AAAI Press, pp 226–231. http://dl.acm.org/citation.cfm?id=3001460.3001507

  13. Gallo CA, Carballido JA, Ponzoni I (2009) Bihea: a hybrid evolutionary approach for microarray biclustering, In: Guimarães A, Katia S, Panchenko, Przytycka TM (eds) Proceedings of the advances in bioinformatics and computational biology: 4th Brazilian symposium on bioinformatics, BSB 2009, Porto Alegre, Brazil, July 29–31, 2009. Springer, Berlin, pp 36–47. https://doi.org/10.1007/978-3-642-03223-3

  14. Hartigan JA (1972) Direct clustering of a data matrix. J Am Stat Assoc 67(337):123–129

    Article  Google Scholar 

  15. Hassani M, Hansen M (2015) subspace: interface to OpenSubspace. R package version 1.0.4. http://CRAN.R-project.org/package=subspace

  16. Jain N, Murthy CA (2016) A new estimate of mutual information based measure of dependence between two variables: properties and fast implementation. Int J Mach Learn Cybern 7(5):857–875. https://doi.org/10.1007/s13042-015-0418-6

    Article  Google Scholar 

  17. Kailing K, Kriegel H-P, Kröger P (2004) Density-connected subspace clustering for high-dimensional data. In: Proceedings of the SIAM international Conference on data mining (SDM’04), vol 4

  18. Kriegel H-P, Kroger P, Renz M, Wurst S (2005) A generic framework for efficient subspace clustering of high-dimensional data. In: Proceedings of the fifth IEEE international conference on data mining, ICDM ’05. IEEE Computer Society, Washington, DC, USA, pp 250–257. https://doi.org/10.1109/ICDM.2005.5

  19. Kriegel H-P, Kröger P, Zimek A (2009) Clustering high-dimensional data: a survey on subspace clustering, pattern-based clustering, and correlation clustering. ACM Trans. Knowl. Discov. Data 3(1):1:1–1:58. https://doi.org/10.1145/1497577.1497578

    Article  Google Scholar 

  20. Kriegel H-P, Zimek A (2010) Subspace clustering, ensemble clustering, alternative clustering, multiview clustering: what can we learn from each other? In: Proceedings of the 1st international workshop on discovering, summarizing and using multiple clusterings (MultiClust) held in conjunction with KDD

  21. Lazzeroni L, Owen A (2002) Plaid models for gene expression data. Stat Sin 12(1):61–86

    MathSciNet  MATH  Google Scholar 

  22. Li G, Ma Q, Tang H, Paterson AH, Xu Y (2009) Qubic: a qualitative biclustering algorithm for analyses of gene expression data. Nucleic Acids Res 37(15):e101. https://doi.org/10.1093/nar/gkp491

    Article  Google Scholar 

  23. Ling RF (1973) A probability theory of cluster analysis. J Am Stat Assoc 68(341):159–164

    Article  MathSciNet  MATH  Google Scholar 

  24. Madeira SC, Oliveira AL (2004) Biclustering algorithms for biological data analysis: a survey. IEEE ACM Trans Comput Biol Bioinform 1(1):24–45

    Article  Google Scholar 

  25. Mandal DP, Murthy CA (1997) Selection of alpha for alpha-hull in \(\{\text{ R2 }\}\). Pattern Recognit 30(10):1759–1767

    Article  MATH  Google Scholar 

  26. Mitra S, Banka H (2006) Multi-objective evolutionary biclustering of gene expression data. Pattern Recognit 39(12):2464–2477

    Article  MATH  Google Scholar 

  27. Moise G, Sander J, Ester M (2008) Robust projected clustering. Knowl. Inf. Syst. 14(3):273–298. https://doi.org/10.1007/s10115-007-0090-6

    Article  MATH  Google Scholar 

  28. Müller AC, Nowozin S, Lampert CH (2012) Information theoretic clustering using minimum spanning trees. Springer, Berlin, pp 205–215

    Google Scholar 

  29. Parsons L, Haque E, Liu H (2004) Subspace clustering for high dimensional data: a review. SIGKDD Explor. Newsl. 6(1):90–105. https://doi.org/10.1145/1007730.1007731

    Article  Google Scholar 

  30. Parzen E (1962) On estimation of a probability density function and mode. Annals Math Stat 33(3):1065–1076

    Article  MathSciNet  MATH  Google Scholar 

  31. Pontes B, Girldez R, Aguilar-Ruiz JS (2015) Biclustering on expression data: a review. J Biomed Inform 57:163–180

    Article  Google Scholar 

  32. Reshef DN, Reshef YA, Finucane HK, Grossman SR, McVean G, Turnbaugh PJ, Lander ES, Mitzenmacher M, Sabeti PC (2011) Detecting novel associations in large data sets. Science 16:1518–1524

    Article  MATH  Google Scholar 

  33. Selim Jahan EJ (2015) Human development report 2015: work for human development. http://hdr.undp.org/en/content/human-development-report-2015-work-human-development

  34. Seridi K, Jourdan L, Talbi EG (2011) Multi-objective evolutionary algorithm for biclustering in microarrays data. In: 2011 IEEE congress of evolutionary computation (CEC), pp 2593–2599

  35. Sim K, Gopalkrishnan V, Zimek A, Cong G (2013) A survey on enhanced subspace clustering. Data Min Knowl Discov 26(2):332–397

    Article  MathSciNet  MATH  Google Scholar 

  36. Steele JM, Snyder TL (1989) Worst-case growth rates of some classical problems of combinatorial optimization. SIAM J Comput 18(2):278–287. https://doi.org/10.1137/0218019

    Article  MathSciNet  MATH  Google Scholar 

  37. SzéKely GJ, Rizzo ML (2009) Brownian distance covariance. Annals Appl Stat 3(4):1236–1265

    Article  MathSciNet  MATH  Google Scholar 

  38. Tanay A, Sharan R, Shamir R (2002) Discovering statistically significant biclusters in gene expression data. Bioinformatics 18:S136–S144

    Article  Google Scholar 

  39. Wang Z, Li G, Robinson RW, Huang X (2016) Unibic: sequential row-based biclustering algorithm for analysis of gene expression data. Scientific reports. https://doi.org/10.1038/srep23466

  40. Yun T, Yi G-S (2013) Biclustering for the comprehensive search of correlated gene expression patterns using clustered seed expansion. BMC Genom 14:144

    Article  Google Scholar 

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Authors and Affiliations

  1. Machine Intelligence Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata, 700108, India

    Namita Jain & C. A. Murthy

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  1. Namita Jain
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  2. C. A. Murthy
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Correspondence to Namita Jain.

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Jain, N., Murthy, C.A. Connectedness-based subspace clustering. Knowl Inf Syst 58, 9–34 (2019). https://doi.org/10.1007/s10115-018-1181-2

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