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Kernel-based multiobjective clustering algorithm with automatic attribute weighting

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Abstract

Clustering algorithms with attribute weighting have gained much attention during the last decade. However, they usually optimize a single-objective function that can be a limitation to cope with different kinds of data, especially those with non-hyper-spherical shapes and/or linearly non-separable patterns. In this paper, the multiobjective optimization approach is introduced into the kernel-based attribute-weighted clustering algorithm, in which two objective functions separately considering the intracluster compactness and intercluster separation are optimized simultaneously. Meanwhile, the sampling operation and efficient clustering ensemble method are incorporated with the projection similarity validity index approach to obtain the clustering solution, which can effectively reduce the computing time especially for large data. Experiments on many data sets demonstrate that, the proposed algorithm in general outperforms the existing attribute-weighted algorithms and the computing efficiency for selection of the final solution is improved by a large margin. Moreover, its merit in terms of the partition and cluster interpretation tools is shown.

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References

  • Alok AK, Saha S, Ekbal A (2016) Multi-objective semi-supervised clustering for automatic pixel classification from remote sensing imagery. Soft Comput 20(12):4733–4751

  • Arthur D, Vassilvitskii S (2007) k-means++: the advantages of careful seeding. In: Proceedings of the 18 annual ACM-SIAM symposium on discrete algorithms, pp 1027–1035

  • Bai L, Liang J (2014) The k-modes type clustering plus between-cluster information for categorical data. Neurocomputing 133:111–121

    Article  Google Scholar 

  • Bai L, Liang J, Dang C, Cao F (2011) A novel attribute weighting algorithm for clustering high-dimensional categorical data. Pattern Recognit 44(12):2843–2861

    Article  MATH  Google Scholar 

  • Bai L, Liang J, Dang C, Cao F (2013) A novel fuzzy clustering algorithm with between-cluster information for categorical data. Fuzzy Sets Syst 215:55–73

    Article  MathSciNet  MATH  Google Scholar 

  • Benaichouche AN, Oulhadj H, Siarry P (2016) Multiobjective improved spatial fuzzy c-means clustering for image segmentation combining Pareto-optimal clusters. J Heuristics 22(4):383–404

  • Capitaine HL, Frlicot C (2011) A cluster-validity index combining an overlap measure and a separation measure based on fuzzy-aggregation operators. IEEE Trans Fuzzy Syst 19(3):580–588

    Article  Google Scholar 

  • Chan EY, Ching WK, Ng MK, Huang JZ (2004) An optimization algorithm for clustering using weighted dissimilarity measures. Pattern Recognit 37(5):943–952

    Article  MATH  Google Scholar 

  • Chang C-C, Lin C-J (2011) LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol: TIST 2(3):1–27

    Article  Google Scholar 

  • Chavent M, de Carvalho FA, Lechevallier Y, Verde R (2006) New clustering methods for interval data. Comput Stat 21(2):211–229

    Article  MathSciNet  MATH  Google Scholar 

  • Coelho AL, Fernandes E, Faceli K (2010) Inducing multi-objective clustering ensembles with genetic programming. Neurocomputing 74(1):494–498

    Article  Google Scholar 

  • de Amorim RC, Mirkin B (2012) Minkowski metric, feature weighting and anomalous cluster initializing in K-means clustering. Pattern Recognit 45(3):1061–1075

    Article  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):97–182

    Article  Google Scholar 

  • Deng Z, Choi K-S, Chung F-L, Wang S (2010) Enhanced soft subspace clustering integrating within-cluster and between-cluster information. Pattern Recognit 43(3):767–781

    Article  MATH  Google Scholar 

  • Faceli K, de Souto MC, de Arajo DS, de Carvalho AC (2009) Multi-objective clustering ensemble for gene expression data analysis. Neurocomputing 72(13):2763–2774

    Article  Google Scholar 

  • Fern XZ, Brodley CE (2004) Solving cluster ensemble problems by bipartite graph partitioning. In: Proceedings of the 21 international conference on Machine learning, pp 1–8

  • Ferreira MR, de Carvalho FA (2014a) Kernel-based hard clustering methods in the feature space with automatic variable weighting. Pattern Recognit 47(9):3082–3095

    Article  MATH  Google Scholar 

  • Ferreira MR, De Carvalho FDA (2014b) Kernel fuzzy c-means with automatic variable weighting. Fuzzy Sets Syst 237:1–46

    Article  MathSciNet  MATH  Google Scholar 

  • Ferreira MR, de Carvalho FDA, Simoes EC (2016) Kernel-based hard clustering methods with kernelization of the metric and automatic weighting of the variables. Pattern Recognit 51:310–321

    Article  Google Scholar 

  • Gan G, Wu J (2008) A convergence theorem for the fuzzy subspace clustering (FSC) algorithm. Pattern Recognit 41(6):1939–1947

    Article  MATH  Google Scholar 

  • Gan G, Ng MK-P (2015) Subspace clustering with automatic feature grouping. Pattern Recognit 48(11):3703–3713

    Article  Google Scholar 

  • Garcia-Piquer A, Fornells A, Orriols-Puig A, Corral G, Golobardes E (2012) Data classification through an evolutionary approach based on multiple criteria. Knowl Inf Syst 33(1):35–56

    Article  Google Scholar 

  • Garcia-Piquer A, Fornells A, Bacardit J, Orriols-Puig A, Golobardes E (2014) Large-scale experimental evaluation of cluster representations for multiobjective evolutionary clustering. IEEE Trans Evol Comput 18(1):36–53

    Article  Google Scholar 

  • Graves D, Pedrycz W (2010) Kernel-based fuzzy clustering and fuzzy clustering: a comparative experimental study. Fuzzy Sets Syst 161(4):522–543

    Article  MathSciNet  Google Scholar 

  • Halkidi M, Vazirgiannis M (2001) Clustering validity assessment: finding the optimal partitioning of a data set. In: Proceedings of the 2001 IEEE international conference on data mining, pp 187–194

  • Hancer E, Karaboga D (2017) A comprehensive survey of traditional, merge-split and evolutionary approaches proposed for determination of cluster number. Swarm Evol Comput 32:49–67

  • Handl J, Knowles J (2007) An evolutionary approach to multiobjective clustering. IEEE Trans Evol Comput 11(1):56–76

    Article  Google Scholar 

  • Huang JZ, Ng MK, Rong H, Li Z (2005) Automated variable weighting in k-means type clustering. IEEE Trans Pattern Anal Mach Intell 27(5):657–668

    Article  Google Scholar 

  • Huang X, Ye Y, Zhang H (2014a) Extensions of kmeans-type algorithms: a new clustering framework by integrating intracluster compactness and intercluster separation. IEEE Trans Neural Netw Learn Syst 25(8):1433–1446

    Article  Google Scholar 

  • Huang X, Ye Y, Guo H, Cai Y, Zhang H, Li Y (2014b) DSKmeans: a new kmeans-type approach to discriminative subspace clustering. Knowl Based Syst 70:293–300

    Article  Google Scholar 

  • Jing L, Ng MK, Huang JZ (2007) An entropy weighting k-means algorithm for subspace clustering of high-dimensional sparse data. IEEE Trans Knowl Data Eng 19(8):1026–1041

    Article  Google Scholar 

  • Ji J, Wang K-L (2014) A robust nonlocal fuzzy clustering algorithm with between-cluster separation measure for SAR image segmentation. IEEE J Sel Top Appl Earth Obs Remote Sens 7(12):4929–4936

    Article  Google Scholar 

  • Jos-Garcła A, Gmez-Flores W (2016) Automatic clustering using nature-inspired metaheuristics: a survey. Appl Soft Comput 41:192–213

    Article  Google Scholar 

  • Li Y, Wei Y, Wang Y, Jiao L (2014) Multi-objective evolutionary for synthetic aperture radar image segmentation with non-local means denoising. Nat Comput 13(1):39–53

    Article  MathSciNet  Google Scholar 

  • Liu R, Zhang L, Li B (2015) Synergy of two mutations based immune multi-objective automatic fuzzy clustering algorithm. Knowl Inf Syst 45(1):133–157

    Article  Google Scholar 

  • Ma A, Zhong Y, Zhang L (2015) Adaptive multiobjective memetic fuzzy clustering algorithm for remote sensing imagery. IEEE Trans Geosci Remote Sens 53(8):4202–4217

    Article  Google Scholar 

  • Mukhopadhyay A, Maulik U (2011) A multiobjective approach to MR brain image segmentation. Appl Soft Comput 11(1):872–880

    Article  Google Scholar 

  • Mukhopadhyay A, Maulik U, Bandyopadhyay S (2009) Multiobjective genetic algorithm-based fuzzy clustering of categorical attributes. IEEE Trans Evol Comput 13(5):991–1005

    Article  Google Scholar 

  • Mukhopadhyay A, Maulik U, Bandyopadhyay S (2013) An interactive approach to multiobjective clustering of gene expression patterns. IEEE Trans Biomed Eng 60(1):35–41

    Article  Google Scholar 

  • Mukhopadhyay A, Maulik U, Bandyopadhyay S, Coello CAC (2014) Survey of multiobjective evolutionary algorithms for data mining: part II. IEEE Trans Evol Comput 18(1):20–35

    Article  Google Scholar 

  • Prakash J, Singh P (2015) An effective multiobjective approach for hard partitional clustering. Memet Comput 7(2):93–104

    Article  Google Scholar 

  • Sag T, Cunkas M (2015) Color image segmentation based on multiobjective artificial bee colony optimization. Appl Soft Comput 34:389–401

    Article  Google Scholar 

  • Saha S, Bandyopadhyay S (2013) A generalized automatic clustering algorithm in a multiobjective framework. Appl Soft Comput 13(1):89–108

    Article  Google Scholar 

  • Saha I, Maulik U (2014) Incremental learning based multiobjective fuzzy clustering for categorical data. Inf Sci 267:35–57

    Article  MathSciNet  Google Scholar 

  • Saha I, Maulik U, Plewczynski D (2011) A new multi-objective technique for differential fuzzy clustering. Appl Soft Comput 11(2):2765–2776

    Article  Google Scholar 

  • Saha S, Ekbal A, Gupta K, Bandyopadhyay S (2013) Gene expression data clustering using a multiobjective symmetry based clustering technique. Comput Biol Med 43(11):1965–1977

    Article  Google Scholar 

  • Saha S, Spandana R, Ekbal A, Bandyopadhyay S (2015) Simultaneous feature selection and symmetry based clustering using multiobjective framework. Appl Soft Comput 29:479–486

    Article  Google Scholar 

  • Saha S, Alok AK, Ekbal A (2016) Brain image segmentation using semi-supervised clustering. Expert Syst Appl 52(15):50–63

    Article  Google Scholar 

  • Shen H, Yang J, Wang S, Liu X (2006) Attribute weighted mercer kernel based fuzzy clustering algorithm for general non-spherical datasets. Soft Comput 10(11):1061–1073

    Article  Google Scholar 

  • Strehl A, Ghosh J (2003) Cluster ensembles—a knowledge reuse framework for combining multiple partitions. J Mach Learn Res 3:583–617

    MathSciNet  MATH  Google Scholar 

  • 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  MATH  Google Scholar 

  • Wang J, Deng Z, Choi K-S, Jiang Y, Luo X, Chung F-L, Wang S (2016) Distance metric learning for soft subspace clustering in composite kernel space. Pattern Recognit 52:113–134

    Article  Google Scholar 

  • Wikaisuksakul S (2014) A multi-objective genetic algorithm with fuzzy c-means for automatic data clustering. Appl Soft Comput 24:679–691

    Article  Google Scholar 

  • Wu K-L, Yu J, Yang M-S (2005) A novel fuzzy clustering algorithm based on a fuzzy scatter matrix with optimality tests. Pattern Recogn Lett 26(5):639–652

    Article  Google Scholar 

  • Wu C, Ouyang C, Chen L, Lu L (2014) A new fuzzy clustering validity index with a median factor for centroid-based clustering. IEEE Trans Fuzzy Syst 23(3):701–718

    Article  Google Scholar 

  • Xia H, Zhuang J, Yu D (2013) Novel soft subspace clustering with multi-objective evolutionary approach for high-dimensional data. Pattern Recognit 46(9):2562–2575

    Article  MATH  Google Scholar 

  • Yang D, Jiao L, Gong M, Liu F (2011) Artificial immune multi-objective SAR image segmentation with fused complementary features. Inf Sci 181(13):2797–2812

    Article  Google Scholar 

  • Yang C-L, Kuo R, Chien C-H, Quyen NTP (2015) Non-dominated sorting genetic algorithm using fuzzy membership chromosome for categorical data clustering. Appl Soft Comput 18(1):20–35

    Google Scholar 

  • Zhao F, Liu H, Fan J (2015) A multiobjective spatial fuzzy clustering algorithm for image segmentation. Appl Soft Comput 30:48–57

    Article  Google Scholar 

  • Zhong Y, Zhang S, Zhang L (2013) Automatic fuzzy clustering based on adaptive multi-objective differential evolution for remote sensing imagery. IEEE J Sel Top Appl Earth Obs Remote Sens 6(99):1–12

    Google Scholar 

  • Zhou J, Chen L, Chen CLP, Zhang Y, Li H (2016) Fuzzy clustering with the entropy of attribute weights. Neurocomputing 198:34–125

    Article  Google Scholar 

  • Zhu L, Cao L, Yang J (2012) Multiobjective evolutionary algorithm-based soft subspace clustering. In: Proceedings of the 2012 IEEE international conference on Evolutionary Computation, pp 1–8

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Acknowledgements

This study was funded by the Natural Science Foundation of China (Grant No. 61373126) and the Fundamental Research Funds for the Central Universities of China (Grant No. JUSRP51510).

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Authors and Affiliations

  1. Engineering Research Center of Internet of Things Technology Applications Ministry of Education, Jiangnan University, Wuxi, 214122, Jiangsu, China

    Zhiping Zhou

  2. College of Electronics and Information Engineering, Tongji University, Shanghai, 201804, China

    Shuwei Zhu

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  1. Zhiping Zhou
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Correspondence to Shuwei Zhu.

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Communicated by V. Loia.

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Zhou, Z., Zhu, S. Kernel-based multiobjective clustering algorithm with automatic attribute weighting. Soft Comput 22, 3685–3709 (2018). https://doi.org/10.1007/s00500-017-2590-y

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