Abstract
The clustering is one of the fundamental steps in the field of data mining. This is widely used in various real-life applications for realizing potential information from the datasets. However, this particular procedure is intensive in term of computation. So, the clustering procedure is preferred with the optimal number of clusters. In this paper, the authors have suggested a novel objective function which is more effective in clustering with the optimal number of clusters detected through cluster validity indices. The proposed objective function based clustering approach is implemented on different types of images and the outcomes depict effective performance in terms of cluster quality based on segmentation entropy, and cluster partitioning time. The results are comparable with other related works and the satisfactory outcome is attained.
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References
A. Ben-Dor, R. Shamir, Z. Yakhini, Clustering gene expression patterns. J. Comput. Biol. 6(3–4), 281–297 (1999)
H. Bozdogan, 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, Berlin, 1994), pp. 69–113
T. Caliński, J. Harabasz, A dendrite method for cluster analysis. Commun. Stat. Theory Methods 3(1), 1–27 (1974)
D. Chaudhuri, A. Agrawal, Split-and-merge procedure for image segmentation using bimodality detection approach. Def. Sci. J. 60(3), 290 (2010)
D.L. Davies, D.W. Bouldin, A cluster separation measure. IEEE Trans. Pattern Anal. Mach. Intell. 2, 224–227 (1979)
J.C. Dunn, Well-separated clusters and optimal fuzzy partitions. J. Cybern. 4(1), 95–104 (1974)
G. Evanno, S. Regnaut, J. Goudet, Detecting the number of clusters of individuals using the software structure: a simulation study. Mol. Ecol. 14(8), 2611–2620 (2005)
S. Haifeng, L. Lanlan, Clustering color image segmentation based on maximum entropy, in The 2nd International Conference on Computer Applications and System Modeling (2012), pp. 1466–1468
E. Hancer, D. Karaboga, A comprehensive survey of traditional, merge-split and evolutionary approaches proposed for determination of cluster number. Swarm Evol. Comput. 32, 49–67 (2017)
E. Hancer, C. Ozturk, D. Karaboga, Artificial bee colony based image clustering method, in 2012 IEEE Congress on Evolutionary Computation (CEC) (IEEE, 2012), pp. 1–5
P. Hansen, B. Jaumard, Cluster analysis and mathematical programming. Math. Program. 79(1–3), 191–215 (1997)
J.A. Hartigan, Clustering Algorithms (1975)
X. Hu, L. Xu, Investigation on several model selection criteria for determining the number of cluster. Neural Inf. Process. Lett. Rev. 4(1), 1–10 (2004)
A.K. Jain, R.C. Dubes, Algorithms for Clustering Data (1988)
A.K. Jain, M.N. Murty, P.J. Flynn, Data clustering: a review. ACM Comput. Surv. (CSUR) 31(3), 264–323 (1999)
J.N. Kapur, P.K. Sahoo, A.K. Wong, A new method for gray-level picture thresholding using the entropy of the histogram. Comput. Vis. Graph. Image Process. 29(3), 273–285 (1985)
T.M. Kodinariya, P.R. Makwana, Review on determining number of cluster in k-means clustering. Int. J. 1(6), 90–95 (2013)
R. Liscano, A. Wong, A Study into Entropy-Based Thresholding for Image Edge Detection (1995)
G.W. Milligan, A monte carlo study of thirty internal criterion measures for cluster analysis. Psychometrika 46(2), 187–199 (1981)
P.J. Rousseeuw, Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987)
P. Smyth, Clustering using monte carlo cross-validation. Kdd 1, 26–133 (1996)
C.A. Sugar, G.M. James, Finding the number of clusters in a dataset: An information-theoretic approach. J. Am. Stat. Assoc. 98(463), 750–763 (2003)
J. Wang, Consistent selection of the number of clusters via crossvalidation. Biometrika 97(4), 893–904 (2010)
I.H. Witten, E. Frank, M.A. Hall, C.J. Pal, Data Mining: Practical Machine Learning Tools and Techniques (Morgan Kaufmann, USA, 2016)
L. Xu, Byy harmony learning, structural rpcl, and topological self-organizing on mixture models. Neural Netw. 15(8–9), 1125–1151 (2002)
X. Xu, M. Ester, H.P. Kriegel, J. Sander, A distribution-based clustering algorithm for mining in large spatial databases, in Proceedings of the 14th International Conference on Data Engineering (IEEE, 1998), pp. 324–331
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Chowdhury, K., Chaudhuri, D., Pal, A.K. (2018). A Novel Objective Function Based Clustering with Optimal Number of Clusters. In: Mandal, J., Mukhopadhyay, S., Dutta, P., Dasgupta, K. (eds) Methodologies and Application Issues of Contemporary Computing Framework. Springer, Singapore. https://doi.org/10.1007/978-981-13-2345-4_3
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DOI: https://doi.org/10.1007/978-981-13-2345-4_3
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