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[Loet Leydesdorff]

The relation between  <http://www.leydesdorff.net/CosineVsPearson/index.htm>
Pearson's correlation coefficient r and Salton's cosine measure

Journal of the American Society for Information Science & Technology
(forthcoming)

 

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 -norm and the -norm of a vector. These different values yield a sheaf
of increasingly straight lines which form together 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 which
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.

 

 <http://www.leydesdorff.net/CosineVsPearson/CosineVsPearson.pdf> <click
here for pdf>

Leo Egghe and Loet Leydesdorff 

 
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