NON-BINARY COSINE vs BINARY COSINE SIMILARITY FOR CO-AUTHOR COCITATION
This page shows crossplots of non-binary cosine similarities against binary cosine similarities from 27 collections of papers covering various subjects. For each collection of papers the 200 most cited reference authors were used. A paper to reference author matrix, O(p,ra) was constructed. Element o(i,j), the (i,j)th element of O(p,ra) is equal to the number of times paper i cites reference author j.
Assume the general formula s(i,j)= A(i,j)/sqrt[B(i)*B(j)] defines the similarity between author i and author j.
For binary cosine similarity A(i,j) is the number of papers citing both authors i and author j. B(i) and B(j) is the number of papers citing author i and author j respecively.
For non-binary cosine similarity A(i,j)=sum[o(k,i)*o(j,k)], with k summed over all papers. Thus A(i,j) is the sum over all papers of the product of the number of citations to author i and author j within each paper. B(i) and B(k) is the sum over all papers of the number of times in each paper that author i and author j were cited respectively.
The non-binary cosine and binary cosine s values are crossplotted below. Non-binary cosine is on the x axis and binary cosine s is on the y axis.
These papers were collected from ISI's Web of Science product in the period from January 2002 to December 2003 by using queries and seed references.
