Bipartite Graphs and Recommendation Systems

Bipartite graphs are used to model many real-world relationships with applications in several domains, such as: medicine, social networks and marketing. Examples of such relationships include drugs-adverse reactions associations, links between genes and various pathologies, actors and the movies they play in, researchers and the papers they author. We explore several properties of bipartite graphs and propose several notions including the measure of biclique similarity of a set of vertices, the measure of biclique connectivity of a set of vertices, and the notion of chains in bipartite graphs. We introduce the Biclique Similarity Ordering Recommendation (BISOR) algorithm, an application of maximal bicliques of bipartite graphs to recommendation systems that makes use of the notion of biclique similarity of a set of vertices in order to recommend items to users in a certain order of preference. We justify our approach by presenting experimental results that use real-world datasets: Sushi, MovieLens 100k and MovieLens 1Million.