  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.
