On the order equivalence relation of binary association measures

Paradowski, Mariusz

doi:10.1515/amcs-2015-0047

Abstract

Over a century of research has resulted in a set of more than a hundred binary association measures. Many of them share similar properties. An overview of binary association measures is presented, focused on their order equivalences. Association measures are grouped according to their relations. Transformations between these measures are shown, both formally and visually. A generalization coefficient is proposed, based on joint probability and marginal probabilities. Combining association measures is one of recent trends in computer science. Measures are combined in linear and nonlinear discrimination models, automated feature selection or construction. Knowledge about their relations is particularly important to avoid problems of meaningless results, zeroed generalized variances, the curse of dimensionality, or simply to save time

References

Batagelj, V. and Bren, M. (1995). Comparing resemblance measures, Journal of Classification 12(1): 73-90.10.1007/BF01202268
Search in Google Scholar
Buczyński, A. (2004). Text Acquisition from the Internet for Linguistic Research, Master’s thesis, Warsaw University, Warsaw, (in Polish).
Search in Google Scholar
Chapelle, O. and Wu, M. (2010). Gradient descent optimization of smoothed information retrieval metrics, Information Retrieval 13(3): 216-235.10.1007/s10791-009-9110-3
Search in Google Scholar
Cheetham, A.H. and Hazel, J.E. (1969). Binary (presence-absence) similarity coefficients, Journal of Paleontology 43(5): 1130-1136.
Search in Google Scholar
Choi, S.-S., Cha, S.-H. and Tappert, C.C. (2010). A survey of binary similarity and distance measures., Journal of Systemics, Cybernetics & Informatics 8(1): 43-48.
Search in Google Scholar
Clarke, K.R., Somerfield, P.J. and Chapman, M.G. (2006). On resemblance measures for ecological studies, including taxonomic dissimilarities and a zero-adjusted Bray-Curtis coefficient for denuded assemblages, Journal of Experimental Marine Biology and Ecology 330(1): 55-80.10.1016/j.jembe.2005.12.017
Search in Google Scholar
Consonni, V. and Todeschini, R. (2012). New similarity coefficients for binary data, Match-Communications in Mathematical and Computer Chemistry 68(2): 581.
Search in Google Scholar
Dice, L.R. (1945). Measures of the amount of ecologic association between species, Ecology 26(3): 297-302.10.2307/1932409
Search in Google Scholar
Duarte, J.M., Santos, J.B.d. and Melo, L.C. (1999). Comparison of similarity coefficients based on RAPD markers in the common bean, Genetics and Molecular Biology 22(3): 427-432.10.1590/S1415-47571999000300024
Search in Google Scholar
Friedman, J.H. (1997). On bias, variance, 0/1-loss, and the curse-of-dimensionality, Data Mining and Knowledge Discovery 1(1): 55-77.10.1023/A:1009778005914
Search in Google Scholar
Gower, J.C. and Legendre, P. (1986). Metric and Euclidean properties of dissimilarity coefficients, Journal of Classification 3(1): 5-48.10.1007/BF01896809
Search in Google Scholar
Hoang, H.H., Kim, S.N. and Kan, M.-Y. (2009). A re-examination of lexical association measures, Proceedings of the Workshop on Multiword Expressions: Identification, Interpretation, Disambiguation and Applications, Singapore, pp. 31-39.
Search in Google Scholar
Hubalek, Z. (1982). Coefficients of association and similarity, based on binary (presence-absence) data: An evaluation, Biological Reviews 57(4): 669-689.10.1111/j.1469-185X.1982.tb00376.x
Search in Google Scholar
Jaccard, P. (1912). The distribution of the flora in the alpine zone 1, New Phytologist 11(2): 37-50.10.1111/j.1469-8137.1912.tb05611.x
Search in Google Scholar
Johnson, R.A. and Wichern, D.W. (2007). Applied Multivariate Statistical Analysis, 6th Edn., Pearson International Edition, Prentice Hall, Upper Saddle River, NJ.
Search in Google Scholar
Kazienko, P. (2009). Mining indirect association rules for web recommendation, International Journal of Applied Mathematics and Computer Science 19(1): 165-186, DOI: 10.2478/v10006-009-0015-5.10.2478/v10006-009-0015-5
Search in Google Scholar
Kekäläinen, J. (2005). Binary and graded relevance in IR evaluations-comparison of the effects on ranking of IR systems, Information Processing & Management 41(5): 1019-1033.10.1016/j.ipm.2005.01.004
Search in Google Scholar
Liu, T.-Y. (2009). Learning to rank for information retrieval, Foundations and Trends in Information Retrieval 3(3): 225-331.10.1561/1500000016
Search in Google Scholar
Nieddu, L. and Rizzi, A. (2007). Proximity measures in symbolic data analysis, Statistica 63(2): 195-211.
Search in Google Scholar
Pecina, P. (2005). An extensive empirical study of collocation extraction methods, Proceedings of the Association for Computational Linguistics Student Research Workshop, Ann Arbor, MI, USA, pp. 13-18.
Search in Google Scholar
Pecina, P. (2008). A machine learning approach to multiword expression extraction, Proceedings of the Language Resources and Evaluation Workshop Towards a Shared Task for Multiword Expressions, Marrakech, Morocco, pp. 54-61.
Search in Google Scholar
Pecina, P. (2010). Lexical association measures and collocation extraction, Language Resources and Evaluation 44(1-2): 137-158.10.1007/s10579-009-9101-4
Search in Google Scholar
Pecina, P. and Schlesinger, P. (2006). Combining association measures for collocation extraction, Proceedings of the COLING/Association for Computational Linguistics on Main Conference, Sydney, Australia, pp. 651-658.
Search in Google Scholar
Petrović, S., Šnajder, J. and Bašić, B.D. (2010). Extending lexical association measures for collocation extraction, Computer Speech & Language 24(2): 383-394.10.1016/j.csl.2009.06.001
Search in Google Scholar
Rifqi, M., Lesot, M.-J. and Detyniecki, M. (2008). Fuzzy order-equivalence for similarity measures, Annual Meeting of the North American Fuzzy Information Processing Society, NAFIPS 2008, New York, NY, USA, pp. 1-6.
Search in Google Scholar
Segond, M. and Borgelt, C. (2011). Item set mining based on cover similarity, in J.Z. Huang, L. Cao and J. Srivastava (Eds.), Advances in Knowledge Discovery and Data Mining, Springer, Berlin/Heidelberg, pp. 493-505.10.1007/978-3-642-20847-8_41
Search in Google Scholar
Tan, P.-N., Kumar, V. and Srivastava, J. (2004). Selecting the right objective measure for association analysis, Information Systems 29(4): 293-313.10.1016/S0306-4379(03)00072-3
Search in Google Scholar
Tversky, A. (1977). Features of similarity, Psychological Review 84(4): 327.10.1037/0033-295X.84.4.327
Search in Google Scholar
Washtell, J. and Markert, K. (2009). A comparison of windowless and window-based computational association measures as predictors of syntagmatic human associations, Proceedings of the 2009 Conference on Empirical Methods in Natural Language Processing, Singapore, Vol. 2, pp. 628-637.
Search in Google Scholar
Wolda, H. (1981). Similarity indices, sample size and diversity, Oecologia 50(3): 296-302. 10.1007/BF0034496628309044
Search in Google Scholar

On the order equivalence relation of binary association measures

Abstract

Paradigm

My account