{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T10:50:58Z","timestamp":1776855058681,"version":"3.51.2"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,1,26]],"date-time":"2008-01-26T00:00:00Z","timestamp":1201305600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Pattern Anal Applic"],"published-print":{"date-parts":[[2009,2]]},"DOI":"10.1007\/s10044-007-0099-1","type":"journal-article","created":{"date-parts":[[2008,1,25]],"date-time":"2008-01-25T06:38:01Z","timestamp":1201243081000},"page":"79-98","source":"Crossref","is-referenced-by-count":28,"title":["Development of assessment criteria for clustering algorithms"],"prefix":"10.1007","volume":"12","author":[{"given":"Sameh A.","family":"Salem","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Asoke K.","family":"Nandi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,1,26]]},"reference":[{"key":"99_CR1","doi-asserted-by":"crossref","unstructured":"Webb AR (2003) Statistical pattern recognition. Wiley, New York","DOI":"10.1002\/0470854774"},{"key":"99_CR2","doi-asserted-by":"crossref","unstructured":"Theodoridis S, Koutroubas K (2003) Pattern recognition. Academic Press, New York","DOI":"10.1016\/B0-12-227240-4\/00132-5"},{"issue":"2","key":"99_CR3","first-page":"40","volume":"31","author":"M Halkidi","year":"2002","unstructured":"Halkidi M, Batistakis Y, Vazirgiannis M (2002) Cluster validity methods: Part I, SIGMOD. Record 31(2):40\u201345","journal-title":"Record"},{"issue":"3","key":"99_CR4","first-page":"19","volume":"31","author":"M Halkidi","year":"2002","unstructured":"Halkidi M, Batistakis Y, Vazirgiannis M (2002) Cluster validity methods: Part II, SIGMOD. Record 31(3):19\u201327","journal-title":"Record"},{"key":"99_CR5","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1109\/TPAMI.1979.4766909","volume":"1","author":"DL Davies","year":"1979","unstructured":"Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Anal Mach Intell 1:224\u2013227","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"99_CR6","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1080\/01969727308546046","volume":"3","author":"JC Dunn","year":"1973","unstructured":"Dunn JC (1973) A fuzzy relative of ISODATA process and its use in detecting compact well-separated clusters. J Cybern 3:32\u201357","journal-title":"J Cybern"},{"key":"99_CR7","first-page":"1","volume":"3","author":"RB Calinski","year":"1974","unstructured":"Calinski RB, Harabasz J (1974) A dendrite method for cluster analysis. Commun Stat 3:1\u201327","journal-title":"Commun Stat"},{"issue":"12","key":"99_CR8","doi-asserted-by":"crossref","first-page":"1650","DOI":"10.1109\/TPAMI.2002.1114856","volume":"24","author":"U Maulik","year":"2002","unstructured":"Maulik U, Bandyopadhyay S (2002) Performance evaluation of some clustering algorithms and validity indices. IEEE Trans Pattern Anal Mach Intell 24(12):1650\u20131654","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"2","key":"99_CR9","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/BF02294245","volume":"50","author":"GW Milligan","year":"1985","unstructured":"Milligan GW, Cooper C (1985) An examination of procedures for determining the number of clusters in a data set. Psychometrika 50(2):159\u2013179","journal-title":"Psychometrika"},{"issue":"8","key":"99_CR10","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1093\/comjnl\/41.8.578","volume":"41","author":"C Fraley","year":"1998","unstructured":"Fraley C, Raftery AE (1998) How many clusters? Which clustering method? Answers via model-based cluster analysis. Comput J 41(8):578\u2013588","journal-title":"Comput J"},{"issue":"3","key":"99_CR11","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/3477.678624","volume":"28","author":"JC Bezdek","year":"1998","unstructured":"Bezdek JC, Pal NR (1998) Some new indexes of cluster validity. IEEE Trans Syst Man Cybern Part B 28(3):301\u2013315","journal-title":"IEEE Trans Syst Man Cybern Part B"},{"key":"99_CR12","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1109\/34.85677","volume":"13","author":"XL Xie","year":"1991","unstructured":"Xie XL, Beni G (1991) A validity measure for fuzzy clustering. IEEE Trans Pattern Anal Mach Intell 13:841\u2013847","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"99_CR13","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s10044-004-0218-1","volume":"7","author":"C Chou","year":"2004","unstructured":"Chou C, Su M, Lai E (2004) A new cluster validity measure and its application to image compression. Pattern Anal Appl 7:205\u2013220","journal-title":"Pattern Anal Appl"},{"issue":"2","key":"99_CR14","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1111\/1467-9868.00293","volume":"63","author":"R Tibshirani","year":"2001","unstructured":"Tibshirani R, Walther G, Hastie T (2001) Estimating the number of clusters via the gap statistic. J R Stat Soc B 63(2):411\u2013423","journal-title":"J R Stat Soc B"},{"key":"99_CR15","volume-title":"Algorithms for clustering data","author":"AK Jain","year":"1988","unstructured":"Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice-Hall, Englewood Cliffs"},{"key":"99_CR16","unstructured":"Law MH, Jain AK (2003) Cluster validity by bootstrapping partitions. Technical report MSU-CSE-03-5, Department of Computer Science and Engineering, Michigan State University"},{"key":"99_CR17","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1162\/089976604773717621","volume":"16","author":"T Lange","year":"2004","unstructured":"Lange T, Braun M, Buhmann JM (2004) Stability-based validation of clustering solutions. Neural Comput 16:1299\u20131323","journal-title":"Neural Comput"},{"key":"99_CR18","unstructured":"Ben-Hur A, Elisseeff A, Guyon I (2002) A stability based method for discovering structure in clustered data. In: Pacific symposium on biocomputing. World Scientific, Singapore, pp 6\u201317"},{"key":"99_CR19","doi-asserted-by":"crossref","first-page":"2573","DOI":"10.1162\/089976601753196030","volume":"13","author":"E Levine","year":"2001","unstructured":"Levine E, Domany E (2001) Resampling method for unsupervised estimation of cluster validity. Neural Comput 13:2573\u20132593","journal-title":"Neural Comput"},{"key":"99_CR20","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1016\/0031-3203(87)90081-1","volume":"20","author":"A Jain","year":"1987","unstructured":"Jain A, Morean J (1987) Bootstrap techniques in cluster analysis. Pattern Recognit 20:547\u2013568","journal-title":"Pattern Recognit"},{"key":"99_CR21","unstructured":"Tibshirani R, Walther G, Botstein D, Brown P (2001) Cluster validation by prediction strength. Technical report, Statistics Department, Stanford University, Stanford, CA"},{"key":"99_CR22","unstructured":"Dudoit S, Fridlyand JA (2002) Prediction-based resampling method for estimating the number of clusters in a data set. Genome Biol 3(7). Available online: http:\/\/genomebiology.com\/2002\/317\/research\/0036"},{"key":"99_CR23","first-page":"617","volume":"15","author":"T Lange","year":"2002","unstructured":"Lange T, Braun M, Roth V, Buhmann JM (2002) Stability-based model selection. Adv Neural Inf Process Syst 15:617\u2013624","journal-title":"Adv Neural Inf Process Syst"},{"key":"99_CR24","doi-asserted-by":"crossref","unstructured":"Salem SA, Nandi AK (2005) New assessment criteria for clustering algorithms. In: Proceedings of the IEEE international workshop on machine learning for signal processing, Mystic, CT, USA, pp 285\u2013290","DOI":"10.1109\/MLSP.2005.1532915"},{"key":"99_CR25","volume-title":"Digital communications","author":"JG Proakis","year":"2001","unstructured":"Proakis JG (2001) Digital communications. McGraw-Hill, Boston"},{"key":"99_CR26","unstructured":"UCI Machine Learning. http:\/\/www.ics.uci.edu\/\u223cmlearn\/MLRepository.html"},{"key":"99_CR27","unstructured":"Ng AY, Jordan MI, Weiss Y (2002) On spectral clustering: analysis and an algorithm. In: Advances in neural information processing systems, vol 14. MIT Press, Cambridge"},{"key":"99_CR28","unstructured":"Cormen TH, Leiserson CE, Rivest LR, Stein C (2001) Introduction to algorithms. ISBN 10:0-262-03293-7. The MIT Press, London"},{"key":"99_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TPAMI.2003.1159942","volume":"25","author":"B Fischer","year":"2003","unstructured":"Fischer B, Buhmann JM (2003) Path based clustering for grouping smooth curves and texture segmentation. IEEE Trans Pattern Anal Mach Intell 25:1\u20136","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"99_CR30","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316801","volume-title":"Finding groups in data: an introduction to cluster analysis","author":"L Kaufman","year":"1990","unstructured":"Kaufman L, Rousseeuw P (1990) Finding groups in data: an introduction to cluster analysis. Wiley, New York"},{"key":"99_CR31","doi-asserted-by":"crossref","first-page":"155","DOI":"10.3233\/IDA-2007-11204","volume":"11","author":"JRS Fonseca","year":"2007","unstructured":"Fonseca JRS, Cardoso MGMS (2007) Mixture-model cluster analysis using information theoretical criteria. Intell Data Anal 11:155\u2013173","journal-title":"Intell Data Anal"},{"key":"99_CR32","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/s10044-004-0206-5","volume":"7","author":"B Kverh","year":"2004","unstructured":"Kverh B, Leonardis A (2004) A generalisation of model selection criteria. Pattern Anal Appl 7:51\u201365","journal-title":"Pattern Anal Appl"},{"key":"99_CR33","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s10044-005-0251-8","volume":"8","author":"T Hu","year":"2005","unstructured":"Hu T, Sung Y (2005) Clustering spatial data with a hybrid EM approach. Pattern Anal Appl 8:139\u2013148","journal-title":"Pattern Anal Appl"},{"key":"99_CR34","first-page":"1","volume":"4","author":"X Hu","year":"2004","unstructured":"Hu X, Xu L (2004) Investigation on several model selection criteria for determining the number of clusters. Neural Inf Process Lett Rev 4:1\u201310","journal-title":"Neural Inf Process Lett Rev"},{"issue":"3","key":"99_CR35","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1145\/331499.331504","volume":"31","author":"AK Jain","year":"1999","unstructured":"Jain AK, Murty MN, Flyn PJ (1999) Data clustering: a review. ACM Comput Surv 31(3):264\u2013323","journal-title":"ACM Comput Surv"},{"key":"99_CR36","unstructured":"Han J, Kamber M (2001) Data mining: concepts and techniques. Morgan Kaufmann, San Francisco"},{"key":"99_CR37","doi-asserted-by":"crossref","unstructured":"Kohonen T (1997) Self-organizing maps. Springer, Heidelberg","DOI":"10.1007\/978-3-642-97966-8"},{"issue":"2","key":"99_CR38","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1007\/s100440050025","volume":"2","author":"T Chen","year":"1999","unstructured":"Chen T, Chen L-K, MA K-K (1999) Colour image indexing using SOM for region-of-interest retrieval. Pattern Anal Appl 2(2):164\u2013171","journal-title":"Pattern Anal Appl"},{"issue":"5","key":"99_CR39","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1006\/mssp.1996.0036","volume":"10","author":"S Zhang","year":"1996","unstructured":"Zhang S, Ganesan R, Xistris GD (1996) Self-organizing neural networks for automated machinery monitoring systems. Mech Syst Signal Process 10(5):517\u2013532","journal-title":"Mech Syst Signal Process"},{"issue":"12","key":"99_CR40","doi-asserted-by":"crossref","first-page":"1673","DOI":"10.1109\/83.730379","volume":"7","author":"GW Chen","year":"1998","unstructured":"Chen GW, Luo JB, Parker KJ (1998) Image segmentation via adaptive k means clustering and knowledge-based morphological operations with biomedical operations. IEEE Trans Image Process 7(12):1673\u20131683","journal-title":"IEEE Trans Image Process"},{"key":"99_CR41","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/s10044-005-0240-y","volume":"8","author":"H Frigui","year":"2005","unstructured":"Frigui H (2005) Unsupervised learning of arbitrarily shaped clusters using ensembles of Gaussian models. Pattern Anal Appl 8:32\u201349","journal-title":"Pattern Anal Appl"},{"key":"99_CR42","unstructured":"Pelleg D, Moore AW (2000) X-means: extending K-means with efficient estimation of the number of clusters. In: Seventeenth international conference on machine learning. Morgan Kaufmann, San Francisco, pp 727\u2013734"},{"key":"99_CR43","doi-asserted-by":"crossref","unstructured":"Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithm. Plenum Press, New York","DOI":"10.1007\/978-1-4757-0450-1"},{"key":"99_CR44","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0895-7177(93)90202-A","volume":"18","author":"MS Yang","year":"1993","unstructured":"Yang MS (1993) A survey of fuzzy clustering. Math Comput Modell 18:1\u201316","journal-title":"Math Comput Modell"},{"issue":"6","key":"99_CR45","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1109\/3477.809032","volume":"29","author":"A Baraldi","year":"1999","unstructured":"Baraldi A, Blonda P (1999) A survey of fuzzy clustering algorithms for pattern recognition. IEEE Trans Syst Man Cybern Part B 29(6):778\u2013801","journal-title":"IEEE Trans Syst Man Cybern Part B"},{"issue":"5","key":"99_CR46","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1049\/ip-vis:20030752","volume":"150","author":"W Xu","year":"2003","unstructured":"Xu W, Nandi AK, Zhang J (2003) Novel fuzzy reinforcement learning vector quantization algorithm and its application in image compression. IEEE Proc Vis Image Signal Process 150(5):292\u2013298","journal-title":"IEEE Proc Vis Image Signal Process"},{"key":"99_CR47","unstructured":"Ester M, Kriegel H, Sander J, Xu X (1996) 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). Portland,OR, USA, pp 226\u2013231"},{"key":"99_CR48","unstructured":"Ankerst M, Breuing M, Kriegel H, Sander J (1996) OPTICS: ordering points to identify the clustering structure. In: Proceedings of the international conference on management of data, (SIGMOD). ACM Press, Philadelphia 28(2):49\u201360"},{"key":"99_CR49","unstructured":"Jack LB, Nandi AK (2004) Microarray data using the self organising oscillator network. In: Proceedings of EUSIPCO 2004, Vienna, Austria, pp 2183\u20132186"},{"key":"99_CR50","unstructured":"Von Luxburg U (2006) A tutorial on spectral clustering. Max Planck Institute for Biological Cybernetics. Technical report no. TR-149"}],"container-title":["Pattern Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-007-0099-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10044-007-0099-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10044-007-0099-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T08:02:27Z","timestamp":1559116947000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10044-007-0099-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,26]]},"references-count":50,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,2]]}},"alternative-id":["99"],"URL":"https:\/\/doi.org\/10.1007\/s10044-007-0099-1","relation":{},"ISSN":["1433-7541","1433-755X"],"issn-type":[{"value":"1433-7541","type":"print"},{"value":"1433-755X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1,26]]}}}