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Good properties of similarity measures and their complementarity

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  • Leo Egghe

Abstract

Similarity measures, such as the ones of Jaccard, Dice, or Cosine, measure the similarity between two vectors. A good property for similarity measures would be that, if we add a constant vector to both vectors, then the similarity must increase. We show that Dice and Jaccard satisfy this property while Cosine and both overlap measures do not. Adding a constant vector is called, in Lorenz concentration theory, “nominal increase” and we show that the stronger “transfer principle” is not a required good property for similarity measures. Another good property is that, when we have two vectors and if we add one of these vectors to both vectors, then the similarity must increase. Now Dice, Jaccard, Cosine, and one of the overlap measures satisfy this property, while the other overlap measure does not. Also a variant of this latter property is studied.

Suggested Citation

  • Leo Egghe, 2010. "Good properties of similarity measures and their complementarity," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 61(10), pages 2151-2160, October.
    • Handle: RePEc:bla:jamist:v:61:y:2010:i:10:p:2151-2160
    DOI: 10.1002/asi.21380
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    Cited by:

    1. Yongming Song & Jun Hu, 2017. "Vector similarity measures of hesitant fuzzy linguistic term sets and their applications," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-13, December.
    2. Sabeena Begam S & Vimala J & Ganeshsree Selvachandran & Tran Thi Ngan & Rohit Sharma, 2020. "Similarity Measure of Lattice Ordered Multi-Fuzzy Soft Sets Based on Set Theoretic Approach and Its Application in Decision Making," Mathematics, MDPI, vol. 8(8), pages 1-15, July.
    3. Lukun Zheng, 2019. "Using mutual information as a cocitation similarity measure," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(3), pages 1695-1713, June.
    4. Brian Stacey, 2017. "A Standardized Treatment of Binary Similarity Measures with an Introduction to k-Vector Percentage Normalized Similarity," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(1), pages 1-3.
    5. Yueyang Zhao & Lei Cui, 2023. "Fusion Matrix–Based Text Similarity Measures for Clustering of Retrieval Results," Scientometrics, Springer;Akadémiai Kiadó, vol. 128(2), pages 1163-1186, February.
    6. Kraker, Peter & Schlögl, Christian & Jack, Kris & Lindstaedt, Stefanie, 2015. "Visualization of co-readership patterns from an online reference management system," Journal of Informetrics, Elsevier, vol. 9(1), pages 169-182.

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