Matrix Completion As Graph Bandlimited Reconstruction

This paper develops new designs for recommender systems inspired by recent advances in graph signal processing. Recommender systems aim to predict unknown ratings by exploiting the information revealed in a subset of user-item observed ratings. Leveraging the notions of graph frequency and graph filters, we demonstrate that linear latent factor models, such as low-rank matrix completion, can be viewed as bandlimited interpolation algorithms that operate in a frequency domain given by the spectrum of a joint user and item network. This new interpretation paves the way to new methods for enhanced rating prediction. We propose a low complexity method by exploiting the eigen-vector of correlation matrices constructed from known ratings. In the MovieLens 100k dataset, our designs reduce the root mean squared error compared to the ones in benchmark matrix completion by 0.6% and benchmark nearest neighbor methods by 4.2%.