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An entropy-based initialization method of K-means clustering on the optimal number of clusters

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Abstract

Clustering is an unsupervised learning approach used to group similar features using specific mathematical criteria. This mathematical criterion is known as the objective function. Any clustering is done depending on some objective function. K-means is one of the widely used partitional clustering algorithms whose performance depends on the initial point and the value of K. In this paper, we have combined both these parameters. We have defined an entropy-based objective function for the initialization process, which is better than other existing initialization methods of K-means clustering. Here, we have also designed an algorithm to calculate the correct number of clusters of datasets using some cluster validity indexes. In this paper, the entropy-based initialization algorithm has been proposed and applied to different 2D and 3D data sets. The comparison with other existing initialization methods has been represented in this paper.

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Notes

  1. COUNT() function gives the count of no. of cluster validity indexes support for a particular K value (no. of clusters). Here, 2, 3, ..., c denote the number of clusters starting from K = 2.

References

  1. Askari G, Li Y, MoezziNasab R (2014) An adaptive polygonal centroidal voronoi tessellation algorithm for segmentation of noisy sar images. Int Arch Photogram Remote Sens Spatial Inf Sci 40(2):65

    Article  Google Scholar 

  2. Astrahan M (1970) Speech analysis by clustering, or the hyperphoneme method. STANFORD UNIV CA DEPT OF COMPUTER SCIENCE, Tech. rep

  3. Bai L, Liang J, Dang C, Cao F (2012) A cluster centers initialization method for clustering categorical data. Expert Syst Appl 39(9):8022–8029

    Article  Google Scholar 

  4. Ball GH, Hall DJ (1965) Isodata, a novel method of data analysis and pattern classification. Tech. rep, Stanford research inst Menlo Park CA

  5. Bordogna G, Pasi G (2011) Soft clustering for information retrieval applications. Wiley Interdiscip Rev Data Min Knowl Discov 1(2):138–146

    Article  Google Scholar 

  6. Bozdogan H (1994) Mixture-model cluster analysis using model selection criteria and a new informational measure of complexity. In: Proceedings of the first US/Japan conference on the frontiers of statistical modeling: an informational approach, Springer, pp 69–113

  7. Cao F, Liang J, Jiang G (2009) An initialization method for the k-means algorithm using neighborhood model. Comput Math Appl 58(3):474–483

    Article  MathSciNet  Google Scholar 

  8. Celebi ME, Kingravi HA, Vela PA (2013) A comparative study of efficient initialization methods for the k-means clustering algorithm. Expert Syst Appl 40(1):200–210

    Article  Google Scholar 

  9. Chaudhuri D, Murthy C, Chaudhuri B (1994) Finding a subset of representative points in a data set. IEEE Trans Syst Man Cybern 24(9):1416–1424

    Article  Google Scholar 

  10. Chen K, Liu L (2005) The “best k” for entropy-based categorical data clustering

  11. Chowdhury K, Chaudhuri D, Pal AK (2018) Seed point selection algorithm in clustering of image data. In: Progress in Intelligent Computing Techniques: Theory, Practice, and Applications, Springer, pp 119–126

  12. Dalhatu K, Sim ATH (2016) Density base k-mean’s cluster centroid initialization algorithm

  13. Dey L, Chakraborty S (2014) Canonical pso based-means clustering approach for real datasets. International scholarly research notices 2014

  14. Evanno G, Regnaut S, Goudet J (2005) Detecting the number of clusters of individuals using the software structure: a simulation study. Mol Ecol 14(8):2611–2620

    Article  Google Scholar 

  15. Forgy EW (1965) Cluster analysis of multivariate data: efficiency versus interpretability of classifications. Biometrics 21:768–769

    Google Scholar 

  16. Gonzalez TF (1985) Clustering to minimize the maximum intercluster distance. Theor Comput Sci 38:293–306

    Article  MathSciNet  Google Scholar 

  17. Jain AK (2010) Data clustering: 50 years beyond k-means. Pattern Recognit Lett 31(8):651–666

    Article  Google Scholar 

  18. Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice-Hall, Inc

  19. Jin Z, Kim DY, Cho J, Lee B (2015) An analysis on optimal cluster ratio in cluster-based wireless sensor networks. IEEE Sens J 15(11):6413–6423

    Article  Google Scholar 

  20. Lu JF, Tang J, Tang ZM, Yang JY (2008) Hierarchical initialization approach for k-means clustering. Pattern Recognit Lett 29(6):787–795

    Article  Google Scholar 

  21. MacQueen J et al (1967) Some methods for classification and analysis of multivariate observations. Proc Fifth Berkeley Symp Math Stat Prob Oakland CA USA 1:281–297

    MathSciNet  MATH  Google Scholar 

  22. Mahmud MS, Rahman MM, Akhtar MN (2012) Improvement of k-means clustering algorithm with better initial centroids based on weighted average. In: Electrical & Computer Engineering (ICECE), 2012 7th International Conference on, IEEE, pp 647–650

  23. Milligan GW (1981) A monte carlo study of thirty internal criterion measures for cluster analysis. Psychometrika 46(2):187–199

    Article  Google Scholar 

  24. Nazeer KA, Sebastian M (2009) Improving the accuracy and efficiency of the k-means clustering algorithm. Proc World Congress Eng 1:1–3

    Google Scholar 

  25. Pakhira MK et al (2009) A modified k-means algorithm to avoid empty clusters. Int J Recent Trends Eng 1(1)

  26. Pal SK, Pramanik P (1986) Fuzzy measures in determining seed points in clustering. Pattern Recognit Lett 4(3):159–164

    Article  Google Scholar 

  27. Reddy D, Jana PK, Member IS (2012) Initialization for k-means clustering using voronoi diagram. Proc Technol 4:395–400

    Article  Google Scholar 

  28. Smyth P (1996) Clustering using monte carlo cross-validation. Kdd 1:26–133

    Google Scholar 

  29. Sugar CA, James GM (2003) Finding the number of clusters in a dataset: an information-theoretic approach. J Am Stat Assoc 98(463):750–763

    Article  MathSciNet  Google Scholar 

  30. Suryawanshi R, Puthran S (2016) Review of various enhancement for clustering algorithms in big data mining. Int J Adv Res Comput Sci Softw Eng

  31. Thakare Y, Bagal S (2015) Performance evaluation of k-means clustering algorithm with various distance metrics. Int J Comput Appl 110(11)

  32. Tibshirani R, Walther G, Hastie T (2001) Estimating the number of clusters in a data set via the gap statistic. J R Stat Soc Ser B Stat Methodol 63(2):411–423

    Article  MathSciNet  Google Scholar 

  33. Tzortzis G, Likas A (2014) The minmax k-means clustering algorithm. Pattern Recognit 47(7):2505–2516

    Article  Google Scholar 

  34. Virmani D, Taneja S, Malhotra G (2015) Normalization based k means clustering algorithm. arXiv preprint arXiv:150300900

  35. Wang J (2010) Consistent selection of the number of clusters via crossvalidation. Biometrika 97(4):893–904

    Article  MathSciNet  Google Scholar 

  36. Wang X, Bai Y (2016) A modified minmax-means algorithm based on pso. Comput Intell Neurosci

  37. Wang Y, Li Y, Zhao Q (2016) Coupling regular tessellation with rjmcmc algorithm to segment sar image with unknown number of classes. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, p 7

  38. Xu L (2002) Byy harmony learning, structural rpcl, and topological self-organizing on mixture models. Neural Netw 15(8):1125–1151

    Article  Google Scholar 

  39. Xu S, Qiao X, Zhu L, Zheng H (2010) Deep analysis on mining frequent & maximal reference sequences with generalized suffix tree. J Comput Inf Syst 6(7):2187–2197

    Google Scholar 

  40. Yadav J, Sharma M (2013) Automatic k-detection algorithm. In: 2013 International Conference on Machine Intelligence and Research Advancement (ICMIRA), IEEE, pp 269–273

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Authors and Affiliations

  1. Department of CSE, Indian Institute of Technology (Indian School of Mines) [IIT(ISM)], Dhanbad, Jharkhand, India

    Kuntal Chowdhury & Arup Kumar Pal

  2. Deputy General Manager, DRDO Integration Centre, Panagarh, West Bengal, India

    Debasis Chaudhuri

Authors
  1. Kuntal Chowdhury
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  2. Debasis Chaudhuri
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  3. Arup Kumar Pal
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Correspondence to Kuntal Chowdhury.

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The authors, Kuntal Chowdhury Debasis Chaudhuri Arup Kumar Pal, declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Chowdhury, K., Chaudhuri, D. & Pal, A.K. An entropy-based initialization method of K-means clustering on the optimal number of clusters. Neural Comput & Applic 33, 6965–6982 (2021). https://doi.org/10.1007/s00521-020-05471-9

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  • DOI: https://doi.org/10.1007/s00521-020-05471-9

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