A Standardized Treatment of Binary Similarity Measures with an Introduction to k-Vector Percentage Normalized Similarity

Stacey, Brian (2016): A Standardized Treatment of Binary Similarity Measures with an Introduction to k-Vector Percentage Normalized Similarity.

Abstract

This paper attempts to codify a standard nomenclature for similarity measures based on recent literature and to advance the field of similarity measures through the introduction of non-binary similarity between more than two attribute vectors.

• Item Type: MPRA Paper
• Language: English
• Keywords: Binary Similarity Nonbinary Similarity Nonparametric Similarity Testing Multivector Similarity
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools

References

Choi, S. S., Cha, S. H., & Tappert, C. C. (2010). A survey of binary similarity and distance measures. Journal of Systemics, Cybernetics and Informatics, 8(1), 43-48.

Clarke, K. R. (1993). Non‐parametric multivariate analyses of changes in community structure. Australian journal of ecology, 18(1), 117-143.

Consonni, V., & Todeschini, R. (2012). New similarity coefficients for binary data. Match-Communications in Mathematical and Computer Chemistry, 68(2), 581.

De Benedictis, L., & Tajoli, L. (2007). Economic integration and similarity in trade structures. Empirica, 34(2), 117-137.

DeSarbo, W. S., De Soete, G., & Eliashberg, J. (1987). A new stochastic multidimensional unfolding model for the investigation of paired comparison consumer preference/choice data. Journal of Economic Psychology, 8(3), 357-384.

Egghe, L. (2010). Good properties of similarity measures and their complementarity. Journal of the American Society for Information Science and Technology, 61(10), 2151-2160.

Eric, O. N., Gilbert, J. F., Marshall, K. G., & Oladi, R. (2015). A New Measure of Economic Distance (No. 5362). CESifo Group Munich.

Jones, D. L., PhD. (2016). Analysis of Similarity (ANOSIM). Retrieved June 03, 2016, from http://www.marine.usf.edu/user/djones/anosim/anosim.html

Kim, J., & Billard, L. (2013). Dissimilarity measures for histogram-valued observations. Communications in Statistics-Theory and Methods, 42(2), 283-303.

Lourenço, F., Lobo, V., & Bação, F. (2006) Binary-based similarity measures for categorical data and their application in Self-Organizing Maps. Retrieved June 08, 2016, from http://www.ai.rug.nl/nl/vakinformatie/sr/articles/categorical-distances.pdf

Marks, R. E. (2013). Validation and model selection: Three similarity measures compared. Complexity Economics, 2(1), 41-61.

Novak, Z., & Pap, Z. (2012). Exploiting interest-based proximity for content recommendation in peer-to-peer networks. Communications, IET, 6(12), 1595-1601.

Shirkhorshidi, A. S., Aghabozorgi, S., & Wah, T. Y. (2015). A Comparison Study on Similarity and Dissimilarity Measures in Clustering Continuous Data. PloS one, 10(12), e0144059.

Stein, B., Niggemann, O., & Husemeyer, U. (2000). Learning Complex Similarity Measures. In Classification and Information Processing at the Turn of the Millennium (pp. 254-263). Springer Berlin Heidelberg.

Stein, B., & Niggemann, O. (2001). Generation of similarity measures from different sources. In Engineering of Intelligent Systems (pp. 197-206). Springer Berlin Heidelberg.

Warrens, M. J. (2008). Similarity coefficients for binary data: properties of coefficients, coefficient matrices, multi-way metrics and multivariate coefficients. Psychometrics and Research Methodology Group, Leiden University Institute for Psychological Research, Faculty of Social Sciences, Leiden University.

Wilson, D. R., & Martinez, T. R. (1997). Improved heterogeneous distance functions. Journal of artificial intelligence research, 1-34.

Zhang, B., & Srihari, S. N. (2003). Properties of binary vector dissimilarity measures. In Proc. JCIS Int’l Conf. Computer Vision, Pattern Recognition, and Image Processing (Vol. 1).