DeepAI AI Chat
Log In Sign Up

Matrix Completion on Graphs

by   Vassilis Kalofolias, et al.
USI Università della Svizzera italiana

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 under the standard low rank assumption is NP-hard, Candès 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 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 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.


Matrix Completion with Sparse Noisy Rows

Exact matrix completion and low rank matrix estimation problems has been...

Graph-Based Matrix Completion Applied to Weather Data

Low-rank matrix completion is the task of recovering unknown entries of ...

Mixture Matrix Completion

Completing a data matrix X has become an ubiquitous problem in modern da...

Parameterized Algorithms for the Matrix Completion Problem

We consider two matrix completion problems, in which we are given a matr...

Structured Matrix Completion with Applications to Genomic Data Integration

Matrix completion has attracted significant recent attention in many fie...

Deep Learning Approach for Matrix Completion Using Manifold Learning

Matrix completion has received vast amount of attention and research due...

Deep geometric matrix completion: Are we doing it right?

We address the problem of reconstructing a matrix from a subset of its e...