The Normalization of Occurrence and Co-occurrence Matrices in Bibliometrics using Cosine Similarities and Ochiai Coefficients; preprint

[Loet Leydesdorff]

Qiuju Zhou and Loet Leydesdorff, "The Normalization of Occurrence and
Co-occurrence Matrices in Bibliometrics using Cosine Similarities and Ochiai
Coefficients <http://arxiv.org/abs/1503.08944> "; preprint is now available
at http://arxiv.org/abs/1503.08944

 

Abstract:

We prove that Ochiai similarity of the co-occurrence matrix is equal to
cosine similarity in the underlying occurrence matrix. Neither the cosine
nor the Pearson correlation should be used for the normalization of
co-occurrence matrices because the similarity is then normalized twice, and
therefore over-estimated; the Ochiai coefficient can be used instead.
Results are shown using a small matrix (5 cases, 4 variables) for didactic
reasons, and also Ahlgren et al.'s (2003) co-occurrence matrix of 24 authors
in library and information sciences. The over-estimation is shown
numerically and will be illustrated using multidimensional scaling and
cluster dendograms. If the occurrence matrix is not available (such as in
internet research or author co-citation analysis) using Ochiai for the
normalization is preferable to using the cosine.

 

  _____  

Loet Leydesdorff 

Emeritus University of Amsterdam
Amsterdam School of Communications Research (ASCoR)

 <mailto:loet at leydesdorff.net> loet at leydesdorff.net ;
<http://www.leydesdorff.net/> http://www.leydesdorff.net/ 
Honorary Professor,  <http://www.sussex.ac.uk/spru/> SPRU, University of
Sussex; 

Guest Professor  <http://www.zju.edu.cn/english/> Zhejiang Univ., Hangzhou;
Visiting Professor,  <http://www.istic.ac.cn/Eng/brief_en.html> ISTIC,
Beijing;

Visiting Professor,  <http://www.bbk.ac.uk/> Birkbeck, University of London;


 <http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en>
http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en

 

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