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Abstract

Co-occurrence matrices, such as cocitation, coword, and colink matrices, have been used widely in the information sciences. However, confusion and controversy have hindered the proper statistical analysis of these data. The underlying problem, in our opinion, involved understanding the nature of various types of matrices. This article discusses the difference between a symmetrical cocitation matrix and an asymmetrical citation matrix as well as the appropriate statistical techniques that can be applied to each of these matrices, respectively. Similarity measures (such as the Pearson correlation coefficient or the cosine) should not be applied to the symmetrical cocitation matrix but can be applied to the asymmetrical citation matrix to derive the proximity matrix. The argument is illustrated with examples. The study then extends the application of co-occurrence matrices to the Web environment, in which the nature of the available data and thus data collection methods are different from those of traditional databases such as the Science Citation Index. A set of data collected with the Google Scholar search engine is analyzed by using both the traditional methods of multivariate analysis and the new visualization software Pajek, which is based on social network analysis and graph theory.

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Abstract

The debate about which similarity measure one should use for the normalization in the case of Author Co-citation Analysis (ACA) is further complicated when one distinguishes between the symmetrical co-citation - or, more generally, co-occurrence - matrix and the underlying asymmetrical citation - occurrence - matrix. In the Web environment, the approach of retrieving original citation data is often not feasible. In that case, one should use the Jaccard index, but preferentially after adding the number of total citations (i.e., occurrences) on the main diagonal. Unlike Salton's cosine and the Pearson correlation, the Jaccard index abstracts from the shape of the distributions and focuses only on the intersection and the sum of the two sets. Since the correlations in the co-occurrence matrix may be spurious, this property of the Jaccard index can be considered as an advantage in this case.

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Date

6.11.2005 19:02:22

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Date

22. 3.2009 19:07:20