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The relation between Pearson's correlation coefficient r and Salton's cosine measure

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  • Leo Egghe
  • Loet Leydesdorff

Abstract

The relation between Pearson's correlation coefficient and Salton's cosine measure is revealed based on the different possible values of the division of the L1‐norm and the L2‐norm of a vector. These different values yield a sheaf of increasingly straight lines which together form a cloud of points, being the investigated relation. The theoretical results are tested against the author co‐citation relations among 24 informetricians for whom two matrices can be constructed, based on co‐citations: the asymmetric occurrence matrix and the symmetric co‐citation matrix. Both examples completely confirm the theoretical results. The results enable us to specify an algorithm that provides a threshold value for the cosine above which none of the corresponding Pearson correlations would be negative. Using this threshold value can be expected to optimize the visualization of the vector space.

Suggested Citation

  • Leo Egghe & Loet Leydesdorff, 2009. "The relation between Pearson's correlation coefficient r and Salton's cosine measure," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 60(5), pages 1027-1036, May.
    • Handle: RePEc:bla:jamist:v:60:y:2009:i:5:p:1027-1036
    DOI: 10.1002/asi.21009
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    6. Viergutz, Tim & Schulze-Ehlers, Birgit, 2018. "The use of hybrid scientometric clustering for systematic literature reviews in business and economics," DARE Discussion Papers 1804, Georg-August University of Göttingen, Department of Agricultural Economics and Rural Development (DARE).
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    8. Brian L. Egleston & Tian Bai & Richard J. Bleicher & Stanford J. Taylor & Michael H. Lutz & Slobodan Vucetic, 2021. "Statistical inference for natural language processing algorithms with a demonstration using type 2 diabetes prediction from electronic health record notes," Biometrics, The International Biometric Society, vol. 77(3), pages 1089-1100, September.
    9. Jun-Ping Qiu & Ke Dong & Hou-Qiang Yu, 2014. "Comparative study on structure and correlation among author co-occurrence networks in bibliometrics," Scientometrics, Springer;Akadémiai Kiadó, vol. 101(2), pages 1345-1360, November.
    10. Georg Groh & Christoph Fuchs, 2011. "Multi-modal social networks for modeling scientific fields," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(2), pages 569-590, November.
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    15. Th I Götz & G Lahmer & V Strnad & Ch Bert & B Hensel & A M Tomé & E W Lang, 2017. "A tool to automatically analyze electromagnetic tracking data from high dose rate brachytherapy of breast cancer patients," PLOS ONE, Public Library of Science, vol. 12(9), pages 1-31, September.
    16. Cristian Colliander & Per Ahlgren, 2012. "Experimental comparison of first and second-order similarities in a scientometric context," Scientometrics, Springer;Akadémiai Kiadó, vol. 90(2), pages 675-685, February.
    17. Shuqing Li & Ying Sun & Dagobert Soergel, 2015. "A new method for automatically constructing domain-oriented term taxonomy based on weighted word co-occurrence analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 103(3), pages 1023-1042, June.
    18. Dong, Keqiang & Long, Linan & Zhang, Hong & Gao, You, 2018. "The mutual information based minimum spanning tree to detect and evaluate dependencies between aero-engine gas path system variables," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 248-253.
    19. Chen, Lixin, 2017. "Do patent citations indicate knowledge linkage? The evidence from text similarities between patents and their citations," Journal of Informetrics, Elsevier, vol. 11(1), pages 63-79.
    20. Masih Hosseinzadeh & Hossein Mashhadimoslem & Farid Maleki & Ali Elkamel, 2022. "Prediction of Solid Conversion Process in Direct Reduction Iron Oxide Using Machine Learning," Energies, MDPI, vol. 15(24), pages 1-25, December.
    21. Bu, Yi & Ni, Shaokang & Huang, Win-bin, 2017. "Combining multiple scholarly relationships with author cocitation analysis: A preliminary exploration on improving knowledge domain mappings," Journal of Informetrics, Elsevier, vol. 11(3), pages 810-822.
    22. Jorge Martinez-Gil & José F. Aldana-Montes, 2013. "Semantic similarity measurement using historical google search patterns," Information Systems Frontiers, Springer, vol. 15(3), pages 399-410, July.
    23. Wolfram, Dietmar & Zhao, Yuehua, 2014. "A comparison of journal similarity across six disciplines using citing discipline analysis," Journal of Informetrics, Elsevier, vol. 8(4), pages 840-853.

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