000203064 001__ 203064
000203064 005__ 20180317092108.0
000203064 037__ $$aCONF
000203064 245__ $$aMatrix Completion on Graphs
000203064 269__ $$a2014
000203064 260__ $$c2014
000203064 336__ $$aConference Papers
000203064 520__ $$aThe 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. Al- though the problem under the standard low rank assumption is NP-hard, Cande`s and Recht showed that it can be exactly relaxed if 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 prob- lems 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 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 con- vex 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 outper- forms the standard matrix completion model in many situations.
000203064 6531_ $$aMatrix Completion
000203064 6531_ $$aGraphs
000203064 6531_ $$aRobustness
000203064 6531_ $$aInverse Problems
000203064 6531_ $$aRecommendation systems
000203064 6531_ $$aConvex Optimization
000203064 700__ $$aKalofolias, Vassilis
000203064 700__ $$0241065$$aBresson, Xavier$$g140163
000203064 700__ $$aBronstein, Michael
000203064 700__ $$0240428$$aVandergheynst, Pierre$$g120906
000203064 7112_ $$aNeural Information Processing Systems 2014, Workshop "Out of the Box: Robustness in High Dimension"$$cMontreal, Canada$$dDecember 8-13, 2014
000203064 8564_ $$s4478283$$uhttps://infoscience.epfl.ch/record/203064/files/kalofolias_2014.pdf$$yPreprint$$zPreprint
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000203064 980__ $$aCONF