Determining the number of clusters using information entropy for mixed data

In cluster analysis, one of the most challenging and difficult problems is the determination of the number of clusters in a data set, which is a basic input parameter for most clustering algorithms. To solve this problem, many algorithms have been proposed for either numerical or categorical data se...

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Veröffentlicht in:	Pattern recognition Jg. 45; H. 6; S. 2251 - 2265
Hauptverfasser:	Liang, Jiye, Zhao, Xingwang, Li, Deyu, Cao, Fuyuan, Dang, Chuangyin
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Kidlington Elsevier Ltd 01.06.2012 Elsevier
Schlagworte:	Algorithms Applied sciences Cluster validity index Clustering Clusters Complement Entropy (Information theory) Exact sciences and technology Information entropy Information, signal and communications theory k-Prototypes algorithm Mixed data Number of clusters Optimization Pattern recognition Signal and communications theory Signal representation. Spectral analysis Signal, noise Telecommunications and information theory Cluster validity index k-Prototypes algorithm Number of clusters Clustering Information entropy Mixed data Cluster analysis Automatic classification Prototype Similarity Entropy Algorithm Signal classification Algorithm performance Numerical data Renyi theory
ISSN:	0031-3203, 1873-5142
Online-Zugang:	Volltext
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Abstract	In cluster analysis, one of the most challenging and difficult problems is the determination of the number of clusters in a data set, which is a basic input parameter for most clustering algorithms. To solve this problem, many algorithms have been proposed for either numerical or categorical data sets. However, these algorithms are not very effective for a mixed data set containing both numerical attributes and categorical attributes. To overcome this deficiency, a generalized mechanism is presented in this paper by integrating Rényi entropy and complement entropy together. The mechanism is able to uniformly characterize within-cluster entropy and between-cluster entropy and to identify the worst cluster in a mixed data set. In order to evaluate the clustering results for mixed data, an effective cluster validity index is also defined in this paper. Furthermore, by introducing a new dissimilarity measure into the k-prototypes algorithm, we develop an algorithm to determine the number of clusters in a mixed data set. The performance of the algorithm has been studied on several synthetic and real world data sets. The comparisons with other clustering algorithms show that the proposed algorithm is more effective in detecting the optimal number of clusters and generates better clustering results. ► A generalized mechanism is presented using information entropy. ► An effective cluster validity index is developed. ► We redefine the dissimilarity measure used in the k-prototypes algorithm. ► An algorithm is presented to determine the number of clusters for mixed data.
AbstractList	In cluster analysis, one of the most challenging and difficult problems is the determination of the number of clusters in a data set, which is a basic input parameter for most clustering algorithms. To solve this problem, many algorithms have been proposed for either numerical or categorical data sets. However, these algorithms are not very effective for a mixed data set containing both numerical attributes and categorical attributes. To overcome this deficiency, a generalized mechanism is presented in this paper by integrating Renyi entropy and complement entropy together. The mechanism is able to uniformly characterize within-cluster entropy and between-cluster entropy and to identify the worst cluster in a mixed data set. In order to evaluate the clustering results for mixed data, an effective cluster validity index is also defined in this paper. Furthermore, by introducing a new dissimilarity measure into the k-prototypes algorithm, we develop an algorithm to determine the number of clusters in a mixed data set. The performance of the algorithm has been studied on several synthetic and real world data sets. The comparisons with other clustering algorithms show that the proposed algorithm is more effective in detecting the optimal number of clusters and generates better clustering results. In cluster analysis, one of the most challenging and difficult problems is the determination of the number of clusters in a data set, which is a basic input parameter for most clustering algorithms. To solve this problem, many algorithms have been proposed for either numerical or categorical data sets. However, these algorithms are not very effective for a mixed data set containing both numerical attributes and categorical attributes. To overcome this deficiency, a generalized mechanism is presented in this paper by integrating Rényi entropy and complement entropy together. The mechanism is able to uniformly characterize within-cluster entropy and between-cluster entropy and to identify the worst cluster in a mixed data set. In order to evaluate the clustering results for mixed data, an effective cluster validity index is also defined in this paper. Furthermore, by introducing a new dissimilarity measure into the k-prototypes algorithm, we develop an algorithm to determine the number of clusters in a mixed data set. The performance of the algorithm has been studied on several synthetic and real world data sets. The comparisons with other clustering algorithms show that the proposed algorithm is more effective in detecting the optimal number of clusters and generates better clustering results. ► A generalized mechanism is presented using information entropy. ► An effective cluster validity index is developed. ► We redefine the dissimilarity measure used in the k-prototypes algorithm. ► An algorithm is presented to determine the number of clusters for mixed data.
Author	Zhao, Xingwang Dang, Chuangyin Liang, Jiye Li, Deyu Cao, Fuyuan
Author_xml	– sequence: 1 givenname: Jiye surname: Liang fullname: Liang, Jiye email: ljy@sxu.edu.cn organization: Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, 030006 Shanxi, China – sequence: 2 givenname: Xingwang surname: Zhao fullname: Zhao, Xingwang email: zhaoxw84@163.com organization: Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, 030006 Shanxi, China – sequence: 3 givenname: Deyu surname: Li fullname: Li, Deyu email: lidy@sxu.edu.cn organization: Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, 030006 Shanxi, China – sequence: 4 givenname: Fuyuan surname: Cao fullname: Cao, Fuyuan email: cfy@sxu.edu.cn organization: Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, 030006 Shanxi, China – sequence: 5 givenname: Chuangyin surname: Dang fullname: Dang, Chuangyin email: mecdang@cityu.edu.hk organization: Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Hong Kong
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Cites_doi	10.1109/2.781637 10.1016/j.datak.2008.08.005 10.1023/A:1010924920739 10.1109/TKDE.2002.1019208 10.1109/FUZZ.2002.1004954 10.1002/j.1538-7305.1948.tb01338.x 10.1145/584792.584888 10.1002/widm.47 10.1016/j.patcog.2004.03.012 10.1109/ICECS.2006.379729 10.1080/03081070600687668 10.1109/IJCNN.2010.5596684 10.1023/A:1022852608280 10.1002/widm.33 10.1145/233269.233324 10.1016/j.patcog.2005.01.025 10.1002/widm.15 10.1145/331499.331504 10.1198/016214503000000666 10.1145/276304.276312 10.1016/S0167-8655(99)00008-2 10.1109/TNN.2005.845141 10.1016/j.patrec.2009.09.011 10.1016/B978-012722442-8/50016-1 10.1214/aoms/1177704472 10.1007/s11265-006-9771-8 10.1080/0308107021000013635 10.1016/j.patrec.2007.12.011 10.1145/1497577.1497578 10.1016/S0004-3702(98)00091-5 10.1007/978-3-540-71701-0_129 10.1109/34.982897 10.1016/j.datak.2007.03.016 10.1016/S0167-8655(97)00168-2 10.1016/j.artint.2010.04.018 10.1007/3-540-44533-1_24 10.1016/S0306-4379(00)00022-3 10.1016/S0031-3203(01)00108-X 10.1016/j.fss.2007.03.004 10.1016/j.patcog.2011.04.024 10.1016/j.ins.2007.05.003 10.1016/j.ins.2007.08.010 10.1109/TFUZZ.2010.2050891 10.1109/TKDE.2008.79 10.1023/A:1009769707641 10.1109/TKDE.2008.88 10.1007/978-3-642-20841-6_22 10.1016/j.knosys.2011.02.015 10.1007/BF01908075
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Keywords	Cluster validity index k-Prototypes algorithm Number of clusters Clustering Information entropy Mixed data Cluster analysis Automatic classification Prototype Similarity Entropy Algorithm Signal classification Algorithm performance Numerical data Renyi theory
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References	D. Barbara, Y. Li, J. Couto, Coolcat: an entropy-based algorithm for categorical clustering, in: Proceeding of the 2002 ACM CIKM International Conference on Information and Knowledge Management, 2002, pp. 582–589. Bandyopadhyay, Saha (bib31) 2008; 20 W.D. Zhao, W.H. Dai, C.B. Tang, K-centers algorithm for clustering mixed type data, in: Proceedings of the 11th Pacific-Asia Conference on Knowledge Discovery and Data Mining, 2007, pp. 1140–1147. Düntsch, Gediga (bib42) 1998; 106 Qian, Liang, Li, Zhang, Y Dang (bib49) 2008; 178 Huang (bib13) 1998; 2 UCI Machine Learning Repository Qian, Liang, Pedrycz, Dang (bib48) 2010; 174 for entropy-based categorical clustering, in: Proceeding of the 17th International Conference on Scientific and Statistical Database Management, 2005. Bai, Liang, Dang (bib35) 2011; 24 Yan, Chen, Liu, Bae (bib37) 2009; 68 J.B. MacQueen, Some methods for classification and analysis of multivariate observations, in: Proceeding of the 5th Berkeley Symposium on Mathematical Statistics and Probability, 1967, pp. 281–297. Hsu, Chen, Su (bib20) 2007; 177 Mirkin (bib58) 2001; 45 V. Estivill-Castro, J. Yang, A fast and robust general purpose clustering algorithm, in: Proceeding of 6th Pacific Rim International Conference Artificial Intelligence, Melbourne, Australia, 2000, pp. 208–218. M. Aghagolzadeh, H. Soltanian-Zadeh, B.N. Araabi, A. Aghagolzadeh, Finding the number of clusters in a dataset using an information theoretic hierarchical algorithm, in: Proceedings of the 13th IEEE International Conference on Electronics, Circuits and Systems, 2006, pp. 1336–1339. S. Guha, R. Rastogi, K. Shim, CURE: An efficient clustering algorithm for large databases, in: Proceeding of ACM SIGMOD International Conference Management of Data, 1998, pp. 73–84. Ahmad, Dey (bib12) 2007; 63 Shannon (bib39) 1948; 27 Sun, Wang, Jiang (bib26) 2004; 37 Gluck, Corter (bib55) 1985 Liang, Shi, Li, Wierman (bib51) 2006; 35 Wang, Zhang (bib54) 2007; 158 J. Al-Shaqsi, W.J. Wang, A clustering ensemble method for clustering mixed data, in: The 2010 International Joint Conference on Neural Networks, 2010. A. Renyi, On measures of entropy and information, in: Proceeding of the 4th Berkeley Symposium on Mathematics of Statistics and Probability, 1961, pp. 547–561. Kaufman, Rousseeuw (bib17) 1990 Xu, Wunsch II (bib3) 2005; 16 Sugar, James (bib33) 2003; 98 Parzen (bib44) 1962; 33 Leung, Zhang, Xu (bib29) 2000; 22 Rezaee, Lelieveldt, Reiber (bib53) 1998; 19 Höppner, Klawonn, Kruse (bib15) 1999 2011. T. Zhang, R. Ramakrishnan, M. Livny, BIRCH: an efficient data clustering method for very large databases, in: Proceeding of ACM SIGMOD International Conference Management of Data, 1996, pp. 103–114. K. McKusick, K. Thompson, COBWEB/3: A Portable Implementation, Technical Report FIA-90-6-18-2, NASA Ames Research Center, 1990. Kothari, Pitts (bib27) 1999; 20 Liang, Chin, Dang, Yam Richard (bib47) 2002; 31 Gokcay, Principe (bib46) 2002; 24 Halkidi, Vazirgiannis (bib52) 2008; 29 Jenssen, Eltoft, Erdogmus, Principe (bib45) 2006; 49 Kriegel, Kröger, Zimek (bib5) 2009; 3 Hunt, Jorgensen (bib10) 2011; 1 T.K. Xiong, S.R. Wang, A. Mayers, E. Monga, DHCC: Divisive hierarchical clustering of categorical data, Data Mining and Knowledge Discovery, doi R. Jensen, Q. Shen, Fuzzy-rough sets for descriptive dimensionality reduction, in: Proceeding of the 2002 IEEE International Conference on Fuzzy Systems, 2002, pp. 29–34. He, Deng, Xu (bib41) 2005; vol. 3644 Bandyopadhyay, Maulik (bib30) 2002; 35 Bai, Liang, Dang, Cao (bib6) 2011; 44 Cao, Liang, Bai, Zhao, Dang (bib9) 2010; 18 Z.X. Huang, A fast clustering algorithm to cluster very large categorical data sets in data mining, in: Proceeding of the SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery, 1997, pp. 1–8. Karypis, Han, Kumar (bib22) 1999; 32 Bandyopadhyay (bib32) 2011; 1 C.C. Aggarwal, J.W. Han, J.Y. Wang, P.S. Yu, A framework for clustering evolving data streams, in: Proceedings of the 29th VLDB Conference, Berlin, Germany, 2003. Li, Biswas (bib19) 2002; 14 Jain (bib4) 2010; 31 Bezdek (bib61) 1998 Jain, Murty, Flynn (bib2) 1999; 31 Han, Kamber (bib1) 2001 Fisher (bib56) 1987; 2 M. Bohanec, V. Rajkovic, Knowledge acquisition and explanation for multi-attribute decision making, in: Proceeding of the 8th International Workshop on Expert Systems and Their Applications, Avignon, France, 1988, pp. 59–78. K.K. Chen, L. Liu, The best Liang, Li (bib50) 2005 Guha, Rastogi, Shim (bib24) 2000; 25 Hubert, Arabie (bib62) 1985; 2 Mirkin (bib25) 2011; 1 Li, Ng, Cheung, Huang (bib28) 2008; 20 Liao (bib7) 2005; 38 Karypis (10.1016/j.patcog.2011.12.017_bib22) 1999; 32 Shannon (10.1016/j.patcog.2011.12.017_bib39) 1948; 27 Wang (10.1016/j.patcog.2011.12.017_bib54) 2007; 158 10.1016/j.patcog.2011.12.017_bib43 Bandyopadhyay (10.1016/j.patcog.2011.12.017_bib32) 2011; 1 Ahmad (10.1016/j.patcog.2011.12.017_bib12) 2007; 63 10.1016/j.patcog.2011.12.017_bib40 10.1016/j.patcog.2011.12.017_bib38 Liang (10.1016/j.patcog.2011.12.017_bib50) 2005 10.1016/j.patcog.2011.12.017_bib34 10.1016/j.patcog.2011.12.017_bib36 Bai (10.1016/j.patcog.2011.12.017_bib6) 2011; 44 Düntsch (10.1016/j.patcog.2011.12.017_bib42) 1998; 106 Mirkin (10.1016/j.patcog.2011.12.017_bib58) 2001; 45 Cao (10.1016/j.patcog.2011.12.017_bib9) 2010; 18 Guha (10.1016/j.patcog.2011.12.017_bib24) 2000; 25 Hubert (10.1016/j.patcog.2011.12.017_bib62) 1985; 2 Halkidi (10.1016/j.patcog.2011.12.017_bib52) 2008; 29 Gluck (10.1016/j.patcog.2011.12.017_bib55) 1985 Li (10.1016/j.patcog.2011.12.017_bib28) 2008; 20 Bandyopadhyay (10.1016/j.patcog.2011.12.017_bib31) 2008; 20 10.1016/j.patcog.2011.12.017_bib23 Sugar (10.1016/j.patcog.2011.12.017_bib33) 2003; 98 Qian (10.1016/j.patcog.2011.12.017_bib49) 2008; 178 Qian (10.1016/j.patcog.2011.12.017_bib48) 2010; 174 Han (10.1016/j.patcog.2011.12.017_bib1) 2001 Jenssen (10.1016/j.patcog.2011.12.017_bib45) 2006; 49 Gokcay (10.1016/j.patcog.2011.12.017_bib46) 2002; 24 Li (10.1016/j.patcog.2011.12.017_bib19) 2002; 14 Hsu (10.1016/j.patcog.2011.12.017_bib20) 2007; 177 10.1016/j.patcog.2011.12.017_bib63 10.1016/j.patcog.2011.12.017_bib64 10.1016/j.patcog.2011.12.017_bib21 Rezaee (10.1016/j.patcog.2011.12.017_bib53) 1998; 19 Mirkin (10.1016/j.patcog.2011.12.017_bib25) 2011; 1 Jain (10.1016/j.patcog.2011.12.017_bib4) 2010; 31 10.1016/j.patcog.2011.12.017_bib60 10.1016/j.patcog.2011.12.017_bib16 10.1016/j.patcog.2011.12.017_bib18 Bai (10.1016/j.patcog.2011.12.017_bib35) 2011; 24 Kaufman (10.1016/j.patcog.2011.12.017_bib17) 1990 10.1016/j.patcog.2011.12.017_bib57 10.1016/j.patcog.2011.12.017_bib14 10.1016/j.patcog.2011.12.017_bib59 Bezdek (10.1016/j.patcog.2011.12.017_bib61) 1998 Kriegel (10.1016/j.patcog.2011.12.017_bib5) 2009; 3 Sun (10.1016/j.patcog.2011.12.017_bib26) 2004; 37 Huang (10.1016/j.patcog.2011.12.017_bib13) 1998; 2 Liao (10.1016/j.patcog.2011.12.017_bib7) 2005; 38 Fisher (10.1016/j.patcog.2011.12.017_bib56) 1987; 2 Hunt (10.1016/j.patcog.2011.12.017_bib10) 2011; 1 Liang (10.1016/j.patcog.2011.12.017_bib51) 2006; 35 Jain (10.1016/j.patcog.2011.12.017_bib2) 1999; 31 10.1016/j.patcog.2011.12.017_bib11 Leung (10.1016/j.patcog.2011.12.017_bib29) 2000; 22 He (10.1016/j.patcog.2011.12.017_bib41) 2005; vol. 3644 Liang (10.1016/j.patcog.2011.12.017_bib47) 2002; 31 Bandyopadhyay (10.1016/j.patcog.2011.12.017_bib30) 2002; 35 Yan (10.1016/j.patcog.2011.12.017_bib37) 2009; 68 Xu (10.1016/j.patcog.2011.12.017_bib3) 2005; 16 Parzen (10.1016/j.patcog.2011.12.017_bib44) 1962; 33 10.1016/j.patcog.2011.12.017_bib8 Höppner (10.1016/j.patcog.2011.12.017_bib15) 1999 Kothari (10.1016/j.patcog.2011.12.017_bib27) 1999; 20
References_xml	– volume: 20 start-page: 405 year: 1999 end-page: 416 ident: bib27 article-title: On finding the number of clusters publication-title: Pattern Recognition Letters – volume: 31 start-page: 331 year: 2002 end-page: 342 ident: bib47 article-title: A new method for measuring uncertainly and fuzziness in rough set theory publication-title: International Journal of General Systems – volume: 158 start-page: 2095 year: 2007 end-page: 2117 ident: bib54 article-title: On fuzzy cluster validity indices publication-title: Fuzzy Sets and Systems – volume: 3 start-page: 1 year: 2009 end-page: 58 ident: bib5 article-title: Clustering high-dimensional data: a survey on subspace clustering, pattern-based clustering and correlation clustering publication-title: ACM Transactions on Knowledge Discovery from Data – volume: 63 start-page: 503 year: 2007 end-page: 527 ident: bib12 article-title: A publication-title: Data & Knowledge Engineering – volume: 35 start-page: 1197 year: 2002 end-page: 1208 ident: bib30 article-title: Genetic clustering for automatic evolution of clusters and application to image classification publication-title: Pattern Recognition – reference: T.K. Xiong, S.R. Wang, A. Mayers, E. Monga, DHCC: Divisive hierarchical clustering of categorical data, Data Mining and Knowledge Discovery, doi: – volume: 1 start-page: 524 year: 2011 end-page: 531 ident: bib32 article-title: Genetic algorithms for clustering and fuzzy clustering publication-title: WIREs Data Mining and Knowledge Discovery – reference: A. Renyi, On measures of entropy and information, in: Proceeding of the 4th Berkeley Symposium on Mathematics of Statistics and Probability, 1961, pp. 547–561. – reference: J.B. MacQueen, Some methods for classification and analysis of multivariate observations, in: Proceeding of the 5th Berkeley Symposium on Mathematical Statistics and Probability, 1967, pp. 281–297. – reference: K. McKusick, K. Thompson, COBWEB/3: A Portable Implementation, Technical Report FIA-90-6-18-2, NASA Ames Research Center, 1990. – volume: 18 start-page: 872 year: 2010 end-page: 882 ident: bib9 article-title: A framework for clustering categorical time-evolving data publication-title: IEEE Transactions on Fuzzy Systems – volume: 68 start-page: 28 year: 2009 end-page: 48 ident: bib37 article-title: Determining the best publication-title: Data & Knowledge Engineering – volume: 98 start-page: 750 year: 2003 end-page: 763 ident: bib33 article-title: Finding the number of clusters in a data set: an information theoretic approach publication-title: Journal of the American Statistical Association – volume: 35 start-page: 641 year: 2006 end-page: 654 ident: bib51 article-title: The information entropy, rough entropy and knowledge granulation in incomplete information system publication-title: International Journal of General Systems – volume: 32 start-page: 68 year: 1999 end-page: 75 ident: bib22 article-title: Chameleon: hierarchical clustering using dynamic modeling publication-title: IEEE Computer – start-page: 283 year: 1985 end-page: 287 ident: bib55 article-title: Information, uncertainty, and the utility of categories publication-title: Proceeding of the 7th Annual Conference of the Cognitive Science Society – reference: Z.X. Huang, A fast clustering algorithm to cluster very large categorical data sets in data mining, in: Proceeding of the SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery, 1997, pp. 1–8. – volume: 22 start-page: 1394 year: 2000 end-page: 1410 ident: bib29 article-title: Clustering by scale-space filtering publication-title: IEEE Transactions on Pattern Analysis and Machine Intelligence – volume: 2 start-page: 193 year: 1985 end-page: 218 ident: bib62 article-title: Comparing partitions publication-title: Journal of Classification – reference: D. Barbara, Y. Li, J. Couto, Coolcat: an entropy-based algorithm for categorical clustering, in: Proceeding of the 2002 ACM CIKM International Conference on Information and Knowledge Management, 2002, pp. 582–589. – reference: W.D. Zhao, W.H. Dai, C.B. Tang, K-centers algorithm for clustering mixed type data, in: Proceedings of the 11th Pacific-Asia Conference on Knowledge Discovery and Data Mining, 2007, pp. 1140–1147. – volume: 16 start-page: 645 year: 2005 end-page: 678 ident: bib3 article-title: Survey of clustering algorithms publication-title: IEEE Transactions on Neural Networks – volume: 45 start-page: 219 year: 2001 end-page: 228 ident: bib58 article-title: Reinterpreting the category utility function publication-title: Machine Learning – year: 1998 ident: bib61 article-title: Pattern Recognition in Handbook of Fuzzy Computation – reference: V. Estivill-Castro, J. Yang, A fast and robust general purpose clustering algorithm, in: Proceeding of 6th Pacific Rim International Conference Artificial Intelligence, Melbourne, Australia, 2000, pp. 208–218. – reference: UCI Machine Learning Repository – reference: M. Aghagolzadeh, H. Soltanian-Zadeh, B.N. Araabi, A. Aghagolzadeh, Finding the number of clusters in a dataset using an information theoretic hierarchical algorithm, in: Proceedings of the 13th IEEE International Conference on Electronics, Circuits and Systems, 2006, pp. 1336–1339. – reference: C.C. Aggarwal, J.W. Han, J.Y. Wang, P.S. Yu, A framework for clustering evolving data streams, in: Proceedings of the 29th VLDB Conference, Berlin, Germany, 2003. – year: 1999 ident: bib15 article-title: Fuzzy Cluster Analysis: Methods for Classification, Data Analysis, and Image Recognition – reference: R. Jensen, Q. Shen, Fuzzy-rough sets for descriptive dimensionality reduction, in: Proceeding of the 2002 IEEE International Conference on Fuzzy Systems, 2002, pp. 29–34. – volume: 37 start-page: 2027 year: 2004 end-page: 2037 ident: bib26 article-title: FCM-based model selection algorithms for determining the number of clusters publication-title: Pattern Recognition – volume: 2 start-page: 283 year: 1998 end-page: 304 ident: bib13 article-title: Extensions to the publication-title: Data Mining and Knowledge Discovery – volume: 33 start-page: 1065 year: 1962 end-page: 1076 ident: bib44 article-title: On the estimation of a probability density function and the mode publication-title: Annals of Mathematical Statistics – volume: 178 start-page: 181 year: 2008 end-page: 202 ident: bib49 article-title: Measures for evaluating the decision performance of a decision table in rough set theory publication-title: Information Sciences – reference: K.K. Chen, L. Liu, The best – reference: M. Bohanec, V. Rajkovic, Knowledge acquisition and explanation for multi-attribute decision making, in: Proceeding of the 8th International Workshop on Expert Systems and Their Applications, Avignon, France, 1988, pp. 59–78. – reference: , 2011. – volume: 25 start-page: 345 year: 2000 end-page: 366 ident: bib24 article-title: ROCK: a robust clustering algorithm for categorical attributes publication-title: Information Systems – volume: 44 start-page: 2843 year: 2011 end-page: 2861 ident: bib6 article-title: A novel attribute weighting algorithm for clustering high-dimensional categorical data publication-title: Pattern Recognition – volume: 49 start-page: 49 year: 2006 end-page: 65 ident: bib45 article-title: Some equivalences between kernel methods and information theoretic methods publication-title: Journal of VLSI Signal Processing Systems – volume: 174 start-page: 597 year: 2010 end-page: 618 ident: bib48 article-title: Positive approximation: an accelerator for attribute reduction in rough set theory publication-title: Artificial Intelligence – volume: 31 start-page: 264 year: 1999 end-page: 323 ident: bib2 article-title: Data clustering: a review publication-title: ACM Computing Surveys – reference: for entropy-based categorical clustering, in: Proceeding of the 17th International Conference on Scientific and Statistical Database Management, 2005. – year: 1990 ident: bib17 article-title: Finding Groups in Data: An Introduction to Cluster Analysis – reference: S. Guha, R. Rastogi, K. Shim, CURE: An efficient clustering algorithm for large databases, in: Proceeding of ACM SIGMOD International Conference Management of Data, 1998, pp. 73–84. – volume: 24 start-page: 158 year: 2002 end-page: 171 ident: bib46 article-title: Information theoretic clustering publication-title: IEEE Transactions on Pattern Analysis and Machine Intelligence – volume: 1 start-page: 352 year: 2011 end-page: 361 ident: bib10 article-title: Clustering mixed data publication-title: WIREs Data Mining and Knowledge Discovery – volume: 14 start-page: 673 year: 2002 end-page: 690 ident: bib19 article-title: Unsupervised learning with mixed numeric and nominal data publication-title: IEEE Transactions on Knowledge and Data Engineering – volume: 31 start-page: 651 year: 2010 end-page: 666 ident: bib4 article-title: Data clustering: 50 years beyond publication-title: Pattern Recognition Letters – volume: 20 start-page: 1519 year: 2008 end-page: 1534 ident: bib28 article-title: Agglomerative fuzzy publication-title: IEEE Transactions on Knowledge and Data Engineering – volume: 2 start-page: 139 year: 1987 end-page: 172 ident: bib56 article-title: Knowledge acquisition via incremental conceptual clustering publication-title: Machine Learning – volume: 29 start-page: 773 year: 2008 end-page: 786 ident: bib52 article-title: A density-based cluster validity approach using multi-representatives publication-title: Pattern Recognition Letters – volume: 106 start-page: 109 year: 1998 end-page: 137 ident: bib42 article-title: Uncertainty measures of rough set prediction publication-title: Artificial Intelligence – year: 2001 ident: bib1 article-title: Data Mining Concepts and Techniques – reference: T. Zhang, R. Ramakrishnan, M. Livny, BIRCH: an efficient data clustering method for very large databases, in: Proceeding of ACM SIGMOD International Conference Management of Data, 1996, pp. 103–114. – volume: 1 start-page: 252 year: 2011 end-page: 260 ident: bib25 article-title: Choosing the number of clusters publication-title: WIREs Data Mining and Knowledge Discovery – volume: 24 start-page: 785 year: 2011 end-page: 795 ident: bib35 article-title: An initialization method to simultaneously find initial cluster centers and the number of clusters for clustering categorical data publication-title: Knowledge-Based Systems – year: 2005 ident: bib50 article-title: Uncertainty and Knowledge Acquisition in Information Systems – volume: 19 start-page: 237 year: 1998 end-page: 346 ident: bib53 article-title: A new cluster validity index for the fuzzy c-mean publication-title: Pattern Recognition Letters – volume: 177 start-page: 4474 year: 2007 end-page: 4492 ident: bib20 article-title: Hierarchical clustering of mixed data based on distance hierarchy publication-title: Information Sciences – volume: vol. 3644 start-page: 400 year: 2005 end-page: 409 ident: bib41 article-title: An optimization model for outlier detection in categorical data publication-title: Lecture Notes in Computer Science – reference: 2011. – volume: 20 start-page: 1441 year: 2008 end-page: 1457 ident: bib31 article-title: A point symmetry-based clustering technique for automatic evolution of clusters publication-title: IEEE Transactions on Knowledge and Data Engineering – volume: 38 start-page: 1857 year: 2005 end-page: 1874 ident: bib7 article-title: Clustering of time series data survey publication-title: Pattern Recognition – volume: 27 start-page: 379 year: 1948 end-page: 423 ident: bib39 article-title: A mathematical theory of communication publication-title: Bell Systems Technical Journal – reference: J. Al-Shaqsi, W.J. Wang, A clustering ensemble method for clustering mixed data, in: The 2010 International Joint Conference on Neural Networks, 2010. – volume: 32 start-page: 68 issue: 8 year: 1999 ident: 10.1016/j.patcog.2011.12.017_bib22 article-title: Chameleon: hierarchical clustering using dynamic modeling publication-title: IEEE Computer doi: 10.1109/2.781637 – volume: 68 start-page: 28 issue: 1 year: 2009 ident: 10.1016/j.patcog.2011.12.017_bib37 article-title: Determining the best k for clustering transactional datasets: a coverage density-based approach publication-title: Data & Knowledge Engineering doi: 10.1016/j.datak.2008.08.005 – volume: 45 start-page: 219 issue: 2 year: 2001 ident: 10.1016/j.patcog.2011.12.017_bib58 article-title: Reinterpreting the category utility function publication-title: Machine Learning doi: 10.1023/A:1010924920739 – ident: 10.1016/j.patcog.2011.12.017_bib43 – volume: 14 start-page: 673 issue: 4 year: 2002 ident: 10.1016/j.patcog.2011.12.017_bib19 article-title: Unsupervised learning with mixed numeric and nominal data publication-title: IEEE Transactions on Knowledge and Data Engineering doi: 10.1109/TKDE.2002.1019208 – ident: 10.1016/j.patcog.2011.12.017_bib38 doi: 10.1109/FUZZ.2002.1004954 – year: 1998 ident: 10.1016/j.patcog.2011.12.017_bib61 – ident: 10.1016/j.patcog.2011.12.017_bib14 – volume: 27 start-page: 379 issue: 3-4 year: 1948 ident: 10.1016/j.patcog.2011.12.017_bib39 article-title: A mathematical theory of communication publication-title: Bell Systems Technical Journal doi: 10.1002/j.1538-7305.1948.tb01338.x – ident: 10.1016/j.patcog.2011.12.017_bib40 doi: 10.1145/584792.584888 – volume: 1 start-page: 524 issue: 6 year: 2011 ident: 10.1016/j.patcog.2011.12.017_bib32 article-title: Genetic algorithms for clustering and fuzzy clustering publication-title: WIREs Data Mining and Knowledge Discovery doi: 10.1002/widm.47 – ident: 10.1016/j.patcog.2011.12.017_bib57 – volume: 37 start-page: 2027 issue: 10 year: 2004 ident: 10.1016/j.patcog.2011.12.017_bib26 article-title: FCM-based model selection algorithms for determining the number of clusters publication-title: Pattern Recognition doi: 10.1016/j.patcog.2004.03.012 – year: 2005 ident: 10.1016/j.patcog.2011.12.017_bib50 – ident: 10.1016/j.patcog.2011.12.017_bib34 doi: 10.1109/ICECS.2006.379729 – volume: 35 start-page: 641 issue: 6 year: 2006 ident: 10.1016/j.patcog.2011.12.017_bib51 article-title: The information entropy, rough entropy and knowledge granulation in incomplete information system publication-title: International Journal of General Systems doi: 10.1080/03081070600687668 – ident: 10.1016/j.patcog.2011.12.017_bib59 doi: 10.1109/IJCNN.2010.5596684 – volume: 2 start-page: 139 issue: 2 year: 1987 ident: 10.1016/j.patcog.2011.12.017_bib56 article-title: Knowledge acquisition via incremental conceptual clustering publication-title: Machine Learning doi: 10.1023/A:1022852608280 – volume: 1 start-page: 352 issue: 4 year: 2011 ident: 10.1016/j.patcog.2011.12.017_bib10 article-title: Clustering mixed data publication-title: WIREs Data Mining and Knowledge Discovery doi: 10.1002/widm.33 – ident: 10.1016/j.patcog.2011.12.017_bib23 doi: 10.1145/233269.233324 – volume: 38 start-page: 1857 issue: 11 year: 2005 ident: 10.1016/j.patcog.2011.12.017_bib7 article-title: Clustering of time series data survey publication-title: Pattern Recognition doi: 10.1016/j.patcog.2005.01.025 – volume: 1 start-page: 252 issue: 3 year: 2011 ident: 10.1016/j.patcog.2011.12.017_bib25 article-title: Choosing the number of clusters publication-title: WIREs Data Mining and Knowledge Discovery doi: 10.1002/widm.15 – volume: 31 start-page: 264 issue: 3 year: 1999 ident: 10.1016/j.patcog.2011.12.017_bib2 article-title: Data clustering: a review publication-title: ACM Computing Surveys doi: 10.1145/331499.331504 – volume: 98 start-page: 750 issue: 463 year: 2003 ident: 10.1016/j.patcog.2011.12.017_bib33 article-title: Finding the number of clusters in a data set: an information theoretic approach publication-title: Journal of the American Statistical Association doi: 10.1198/016214503000000666 – volume: vol. 3644 start-page: 400 year: 2005 ident: 10.1016/j.patcog.2011.12.017_bib41 article-title: An optimization model for outlier detection in categorical data – ident: 10.1016/j.patcog.2011.12.017_bib21 doi: 10.1145/276304.276312 – volume: 20 start-page: 405 issue: 4 year: 1999 ident: 10.1016/j.patcog.2011.12.017_bib27 article-title: On finding the number of clusters publication-title: Pattern Recognition Letters doi: 10.1016/S0167-8655(99)00008-2 – volume: 16 start-page: 645 issue: 3 year: 2005 ident: 10.1016/j.patcog.2011.12.017_bib3 article-title: Survey of clustering algorithms publication-title: IEEE Transactions on Neural Networks doi: 10.1109/TNN.2005.845141 – volume: 31 start-page: 651 issue: 8 year: 2010 ident: 10.1016/j.patcog.2011.12.017_bib4 article-title: Data clustering: 50 years beyond k-means publication-title: Pattern Recognition Letters doi: 10.1016/j.patrec.2009.09.011 – ident: 10.1016/j.patcog.2011.12.017_bib8 doi: 10.1016/B978-012722442-8/50016-1 – ident: 10.1016/j.patcog.2011.12.017_bib16 – volume: 33 start-page: 1065 issue: 3 year: 1962 ident: 10.1016/j.patcog.2011.12.017_bib44 article-title: On the estimation of a probability density function and the mode publication-title: Annals of Mathematical Statistics doi: 10.1214/aoms/1177704472 – volume: 49 start-page: 49 issue: 1–2 year: 2006 ident: 10.1016/j.patcog.2011.12.017_bib45 article-title: Some equivalences between kernel methods and information theoretic methods publication-title: Journal of VLSI Signal Processing Systems doi: 10.1007/s11265-006-9771-8 – volume: 31 start-page: 331 issue: 4 year: 2002 ident: 10.1016/j.patcog.2011.12.017_bib47 article-title: A new method for measuring uncertainly and fuzziness in rough set theory publication-title: International Journal of General Systems doi: 10.1080/0308107021000013635 – volume: 29 start-page: 773 issue: 6 year: 2008 ident: 10.1016/j.patcog.2011.12.017_bib52 article-title: A density-based cluster validity approach using multi-representatives publication-title: Pattern Recognition Letters doi: 10.1016/j.patrec.2007.12.011 – year: 2001 ident: 10.1016/j.patcog.2011.12.017_bib1 – volume: 3 start-page: 1 issue: 1 year: 2009 ident: 10.1016/j.patcog.2011.12.017_bib5 article-title: Clustering high-dimensional data: a survey on subspace clustering, pattern-based clustering and correlation clustering publication-title: ACM Transactions on Knowledge Discovery from Data doi: 10.1145/1497577.1497578 – volume: 22 start-page: 1394 issue: 12 year: 2000 ident: 10.1016/j.patcog.2011.12.017_bib29 article-title: Clustering by scale-space filtering publication-title: IEEE Transactions on Pattern Analysis and Machine Intelligence – volume: 106 start-page: 109 issue: 1 year: 1998 ident: 10.1016/j.patcog.2011.12.017_bib42 article-title: Uncertainty measures of rough set prediction publication-title: Artificial Intelligence doi: 10.1016/S0004-3702(98)00091-5 – ident: 10.1016/j.patcog.2011.12.017_bib60 doi: 10.1007/978-3-540-71701-0_129 – ident: 10.1016/j.patcog.2011.12.017_bib36 – volume: 24 start-page: 158 issue: 2 year: 2002 ident: 10.1016/j.patcog.2011.12.017_bib46 article-title: Information theoretic clustering publication-title: IEEE Transactions on Pattern Analysis and Machine Intelligence doi: 10.1109/34.982897 – ident: 10.1016/j.patcog.2011.12.017_bib64 – volume: 63 start-page: 503 issue: 2 year: 2007 ident: 10.1016/j.patcog.2011.12.017_bib12 article-title: A k-mean clustering algorithm for mixed numeric and categorical data publication-title: Data & Knowledge Engineering doi: 10.1016/j.datak.2007.03.016 – volume: 19 start-page: 237 issue: 3-4 year: 1998 ident: 10.1016/j.patcog.2011.12.017_bib53 article-title: A new cluster validity index for the fuzzy c-mean publication-title: Pattern Recognition Letters doi: 10.1016/S0167-8655(97)00168-2 – volume: 174 start-page: 597 issue: 9–10 year: 2010 ident: 10.1016/j.patcog.2011.12.017_bib48 article-title: Positive approximation: an accelerator for attribute reduction in rough set theory publication-title: Artificial Intelligence doi: 10.1016/j.artint.2010.04.018 – ident: 10.1016/j.patcog.2011.12.017_bib11 doi: 10.1007/3-540-44533-1_24 – volume: 25 start-page: 345 issue: 5 year: 2000 ident: 10.1016/j.patcog.2011.12.017_bib24 article-title: ROCK: a robust clustering algorithm for categorical attributes publication-title: Information Systems doi: 10.1016/S0306-4379(00)00022-3 – year: 1999 ident: 10.1016/j.patcog.2011.12.017_bib15 – volume: 35 start-page: 1197 issue: 6 year: 2002 ident: 10.1016/j.patcog.2011.12.017_bib30 article-title: Genetic clustering for automatic evolution of clusters and application to image classification publication-title: Pattern Recognition doi: 10.1016/S0031-3203(01)00108-X – volume: 158 start-page: 2095 issue: 19 year: 2007 ident: 10.1016/j.patcog.2011.12.017_bib54 article-title: On fuzzy cluster validity indices publication-title: Fuzzy Sets and Systems doi: 10.1016/j.fss.2007.03.004 – volume: 44 start-page: 2843 issue: 12 year: 2011 ident: 10.1016/j.patcog.2011.12.017_bib6 article-title: A novel attribute weighting algorithm for clustering high-dimensional categorical data publication-title: Pattern Recognition doi: 10.1016/j.patcog.2011.04.024 – volume: 177 start-page: 4474 issue: 20 year: 2007 ident: 10.1016/j.patcog.2011.12.017_bib20 article-title: Hierarchical clustering of mixed data based on distance hierarchy publication-title: Information Sciences doi: 10.1016/j.ins.2007.05.003 – volume: 178 start-page: 181 issue: 1 year: 2008 ident: 10.1016/j.patcog.2011.12.017_bib49 article-title: Measures for evaluating the decision performance of a decision table in rough set theory publication-title: Information Sciences doi: 10.1016/j.ins.2007.08.010 – year: 1990 ident: 10.1016/j.patcog.2011.12.017_bib17 – volume: 18 start-page: 872 issue: 5 year: 2010 ident: 10.1016/j.patcog.2011.12.017_bib9 article-title: A framework for clustering categorical time-evolving data publication-title: IEEE Transactions on Fuzzy Systems doi: 10.1109/TFUZZ.2010.2050891 – volume: 20 start-page: 1441 issue: 11 year: 2008 ident: 10.1016/j.patcog.2011.12.017_bib31 article-title: A point symmetry-based clustering technique for automatic evolution of clusters publication-title: IEEE Transactions on Knowledge and Data Engineering doi: 10.1109/TKDE.2008.79 – volume: 2 start-page: 283 issue: 3 year: 1998 ident: 10.1016/j.patcog.2011.12.017_bib13 article-title: Extensions to the k-means algorithm for clustering large data sets with categorical values publication-title: Data Mining and Knowledge Discovery doi: 10.1023/A:1009769707641 – start-page: 283 year: 1985 ident: 10.1016/j.patcog.2011.12.017_bib55 article-title: Information, uncertainty, and the utility of categories – volume: 20 start-page: 1519 issue: 11 year: 2008 ident: 10.1016/j.patcog.2011.12.017_bib28 article-title: Agglomerative fuzzy k-means clustering algorithm with selection of number of clusters publication-title: IEEE Transactions on Knowledge and Data Engineering doi: 10.1109/TKDE.2008.88 – ident: 10.1016/j.patcog.2011.12.017_bib18 doi: 10.1007/978-3-642-20841-6_22 – ident: 10.1016/j.patcog.2011.12.017_bib63 – volume: 24 start-page: 785 issue: 6 year: 2011 ident: 10.1016/j.patcog.2011.12.017_bib35 article-title: An initialization method to simultaneously find initial cluster centers and the number of clusters for clustering categorical data publication-title: Knowledge-Based Systems doi: 10.1016/j.knosys.2011.02.015 – volume: 2 start-page: 193 issue: 1 year: 1985 ident: 10.1016/j.patcog.2011.12.017_bib62 article-title: Comparing partitions publication-title: Journal of Classification doi: 10.1007/BF01908075
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SubjectTerms	Algorithms Applied sciences Cluster validity index Clustering Clusters Complement Entropy (Information theory) Exact sciences and technology Information entropy Information, signal and communications theory k-Prototypes algorithm Mixed data Number of clusters Optimization Pattern recognition Signal and communications theory Signal representation. Spectral analysis Signal, noise Telecommunications and information theory
Title	Determining the number of clusters using information entropy for mixed data
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