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

arXiv: https://arxiv.org/abs/1503.08944 · HTML: https://mlsanity.com/paper/1503.08944/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2015.

## Built on by (most cited first, 2 of 2)

- [Graph-Based Similarity of Neural Network Representations](https://mlsanity.com/paper/2111.11165/) (2021)
- [Applications of Binary Similarity and Distance Measures](https://mlsanity.com/paper/2307.00411/) (2023)

## Abstract (arXiv)

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.