Matrix Completion on Graphs

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