Seminar: Matrix Completion on Graphs by Prof. Pierre Vandergheynst (EPFL)

Date: 28/11/2014 at 2PM
Room: lecture room of the CBP (in the LR6 building of Monod campus) about :

Title: Matrix Completion on Graphs

Abstract: The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem is NP-hard, Candès and Recht showed that it can be exactly relaxed if the matrix is low-rank and the number of observed entries is sufficiently large. In this work, we introduce a novel matrix completion model that makes use of proximity information about rows and columns by assuming they form communities. This assumption makes sense in several real-world problems like in recommender systems, where there are communities of people sharing preferences, while products form clusters that receive similar ratings. Our main goal is thus to find a low-rank solution that is structured by the proximities of rows and columns encoded by graphs. We borrow ideas from manifold learning and signal processing to constrain our solution to be smooth on these graphs, in order to implicitly force row and column proximities. Our matrix recovery model is formulated as a convex non-smooth optimization problem, for which a well-posed iterative scheme is provided. We study and evaluate the proposed matrix completion on synthetic and real data, showing that the proposed structured low-rank recovery model outperforms the standard matrix completion model in many situations.

This is joint work with Vassilis Kalofolias, Michael Bronstein and Xavier Bresson.