Weighted one mode projection of a bipartite graph as a local similarity measure

Abstract

Bipartite graphs are a common structure to model relationships between two populations. Many times a compression of the graph to one population, namely a one mode projection (OMP), is needed in order to gain insight into one of the populations. Since this compression leads to loss of information, several works in the past attempted to quantify the connection quality between the items from the population that is being projected, but have ignored the edge weights in the bipartite graph. This paper presents a novel method to create a weighted OMP (WOMP) by taking edge weights of the bipartite graph into account. The usefulness of the method is then displayed in a case-based reasoning (CBR) environment as a local similarity measure between unordered symbols, in an attempt to solve the long-tail problem of infrequently used but significant symbols of textual CBR. It is shown that our method is superior to other similarity options.