Correcting Jaccard and other similarity indices for chance agreement in cluster analysis

Advances in Data Analysis and Classification

Volumn 5, Issue 3, 2011, Pages 179-200

  Albatineh, Ahmed N ^a   Niewiadomska Bugaj, Magdalena ^b  

^a FLORIDA INTERNATIONAL UNIVERSITY   (United States)

^b WESTERN MICHIGAN UNIVERSITY   (United States)

Author keywords

Cluster analysis; Comparing partitions; Correction for chance agreement; Jaccard index; Matching counts matrix; Similarity indices

Indexed keywords

CLUSTER ANALYSIS; NORMAL DISTRIBUTION; TAYLOR SERIES;

BIVARIATE NORMAL DISTRIBUTIONS; COMPARING PARTITIONS; JACCARD INDEX; LEGENDRE; MATRIX; SIMILARITY INDICES; SIMULATION STUDIES; TAYLOR SERIES EXPANSIONS; UNSTRUCTURED DATA;

CLUSTER COMPUTING;

EID: 80052039988     PISSN: 18625347     EISSN: 18625355     Source Type: Journal    
DOI: 10.1007/s11634-011-0090-y     Document Type: Article

References (38)

1. Albatineh AN, Niewiadomska-Bugaj M, Mihalko DP (2006) On similarity indices and correction for chance agreement. J Classif 23: 301-313.
2. Albatineh AN, Niewiadomska-Bugaj M (2011) MCS: a method for finding the number of clusters. J Classif 28. doi: 10. 1007/s00357-010-9069-1.
3. Albatineh AN (2010) Means and variances for a family of similarity indices used in cluster analysis. J Stat Plan Inference 140: 2828-2838.
4. Czekanowski J (1932) "Coefficient of racial likeness" und "durchschnittliche Differenz". Anthropologischer Anzeiger 14: 227-249.
5. Dice LR (1945) Measures of the amount of ecological association between species. Ecology 26: 297-302.
6. Fligner MA, Verducci JS, Blower PE (2002) A modification of the Jaccard-Tanimoto similarity index for diverse selection of chemical compounds using binary strings. Technometrics 44: 110-119.
7. Fowlkes EB, Mallows CL (1983) A method for comparing two hierarchical clusterings. J Am Stat Assoc 78: 553-569.
8. Gower JC, Legendre P (1986) Metric and Euclidean properties of dissimilarity coefficients. J Classif 3: 5-48.
9. Hamann U (1961) Merkmalsbestand und Verwandtschaftsbeziehungen der Farinosae. Willdenowia 2: 639-768.
10. Hubálek Z (1982) Coefficients of association and similarity based on binary (presence-absence) data: an evaluation. Biol Rev 57: 669-689.
11. Hubert L, Arabie P (1985) Comparing partitions. J Classif 2: 193-218.
12. Jaccard P (1908) Nouvelles recherches sur la distribution florale. Bull Soc Vaudoise Sci Nat 44: 223-270.
13. Jaccard P (1912) The distribution of the flora of the alpine zone. New Phytol 11: 37-50.
14. Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice Hall, New Jersey.
15. Janson S, Vegelius J (1981) Measures of ecological association. Oecologia 49: 371-376.
16. Johnson SC (1967) Hierarchical clustering schemes. Psychometrika 32: 241-254.
17. Kulczynski S (1927) Die Pflanzenassoziationen der Pinien, Bulletin International de L'Académie Polonaise des Sciences et des Lettres, Classe des Sciences Mathématiques et Naturelles. Series B, Supplément II 2: 57-203.
18. Lamont BB, Grant KJ (1979) A comparison of twenty-one measures of site dissimilarity. In: Orlóci L, Rao CR, Stiteler WM (eds) Multivariate methods in ecological work. International Cooperation Publishing House, Fairland, pp 101-126.
19. Lancaster HO (1969) The Chi-squared distribution. John Wiley, New York.
20. Lehmann EL (1959) Testing statistical hypothesis. Wiley, New York.
21. Legendre P, Legendre L (1998) Numerical ecology. Elsevier, Amsterdam.
22. Mcconnaughey BH (1964) The determination and analysis of plankton communities. Marine Research, Special No, Indonesia, pp 1-40.
23. Milligan G, Cooper M (1986) A study of the comparability of external criteria for hierarchical cluster analysis. Multivar Behav Res 21: 441-458.
24. Milligan G, Soon S, Sokol L (1983) The effect of cluster size, dimensionality, and the number of clusters on recovery of true cluster structure. IEEE Trans Patt Anal Mach Intell PAMI-5: 40-47.
25. Morey L, Agresti A (1984) The measurement of classification agreement: an adjustment to the Rand statistic for chance agreement. Educ Psychol Meas 44: 33-37.
26. Rand W (1971) Objective criteria for the evaluation of clustering methods. J Am Stat Assoc 66: 846-850.
27. Rogers DJ, Tanimoto TT (1960) A computer program for classifying plants. Science 132: 1115-1118.
28. Russell PF, Rao TR (1940) On habitat and association of species of anopheline larvae in South-Eastern Madras. J Malar Inst India 3: 153-178.
29. Saxena PC, Navaneerham K (1991) The effect of cluster size, dimensionality, and number of clusters on recovery of true cluster structure through Chernoff-type faces. Statistician 40: 415-425.
30. Saxena PC, Navaneerham K (1993) Comparison of Chernoff-type face and non-graphical methods for clustering multivariate observations. Comput Stat Data Anal 15: 63-79.
31. Snijders TAB, Dormaar M, van Schuur WH, Dijkman-Caes C, Driessen G (1990) Distribution of some similarity coefficients for dyadic binary data in the case of associated attributes. J Classif 7: 5-31.
32. Sokal RR, Michener CD (1958) A statistical method for evaluating systematic relationships. Univ Kansas Sci Bull 38: 1409-1438.
33. Sokal RR, Sneath PHA (1963) Principles of numerical taxonomy. WH Freeman, San Francisco.
34. Sørensen T (1948) A Method of establishing groups of equal amplitude in plant sociology based on similarity of species content. Biologiske Skrifter 5: 1-34.
35. Southwood TS (1978) Ecological methods. Chapman and Hall, London.
36. Steinley D (2004) Properties of the Hubert-Arabie adjusted Rand index. Psychol Methods 9: 386-396.
37. van Der Maarel E (1969) On the use of ordination models in phytosociology. Vegetatio 19: 21-46.
38. Wallace DL (1983) A method for comparing two hierarchical clusterings: comment. J Am Stat Assoc 78: 569-576.