Analyzing Consumer-Product Graphs: Empirical Findings and Applications in Recommender Systems

Abstract

Random graph theory has become a major modeling tool to study complex systems. In this paper we apply random graph theory to analyze bipartite consumer-product graphs that represent sales transactions to better understand consumer purchase behavior in e-commerce settings. Based on two real-world e-commerce datasets we found that such graphs demonstrate topological features that significantly deviate from theoretical predictions based on standard random graph models. In particular we observed consistently larger-than-expected average path lengths and tendency to cluster. Such deviations suggest that the consumers' choices of products are not random and provide justification for a large family of collaborative filtering-based recommendation algorithms that make product recommendations based only on previously observed sales transactions. By analyzing the artificial consumer-product graphs generated by graph generation models that embed two representative recommendation algorithms, we found that these recommendation-algorithm-induced graphs generally provided a better match with the real-world consumer-product graphs than purely random graph models. However, consistent deviations in topological features remained. These findings have motivated the development of a new recommendation algorithm based on graph partitioning aiming to achieve high clustering coefficients as observed in the real-world graphs. We show empirically that this algorithm significantly outperforms representative collaborative filtering algorithms in situations where the clustering coefficients of the consumer-product graphs are sufficiently larger than what can be accounted for by these standard algorithms.

Keywords: Random graph theory, consumer purchase behavior, topological features, recommender systems, collaborative filtering