Modeling Collaborative Similarity with the Signed Resistance Distance Kernel

We extend the resistance distance kernel to the domain of signed dissimilarity values, and show how it can be applied to collaborative rating prediction. The resistance distance is a graph kernel inspired by electrical network models where edges of a graph are interpreted as electrical resistances. We model the similarity between users of a large collaborative rating database using this signed resistance distance, generalizing the previously known regular resistance distance kernel which is limited to nonnegative values. We show that the signed resistance distance kernel can be computed effectively using the Moore-Penrose pseudoinverse of the Laplacian matrix of the bipartite rating graph, leading to fast computation based on the eigenvalue decomposition of the Laplacian matrix. We apply this technique to collaborative rating prediction on the Netflix Prize corpus, and show how our new kernel can replace the traditional Pearson correlation for rating prediction.