Spectral Geometric Matrix Completion
Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix. In this work we interpret the DMF model through the lens of spectral geometry. This allows us to incorporate explicit regularization without breaking the DMF structure, thus enjoying the best of both worlds. In particular, we focus on matrix completion problems with underlying geometric or topological relations between the rows and/or columns. Such relations are prevalent in matrix completion problems that arise in many applications, such as recommender systems and drug-target interaction. Our contributions enable DMF models to exploit these relations, and make them competitive on real benchmarks, while exhibiting one of the first successful applications of deep linear networks.
Code (1)
Tasks
Matrix CompletionRecommendation SystemsSimilar Papers 제목 키워드 기반
Deep geometric matrix completion: Are we doing it right?
We address the problem of reconstructing a matrix from a subset of its entries. Current methods, branded as geometric matrix completion, augment classical rank regularization techniques by incorporating geometric informa…
Matrix CompletionRecommendation SystemsBayesian Matrix Completion via Adaptive Relaxed Spectral Regularization
Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral …
Bayesian InferenceCollaborative FilteringMatrix CompletionGeometric Matrix Completion: A Functional View
We propose a totally functional view of geometric matrix completion problem. Differently from existing work, we propose a novel regularization inspired from the functional map literature that is more interpretable and th…
Matrix CompletionMissing Entries Matrix Approximation and Completion
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For…
Electrical EngineeringMatrix CompletionConvolutional Geometric Matrix Completion
Geometric matrix completion (GMC) has been proposed for recommendation by integrating the relationship (link) graphs among users/items into matrix completion (MC). Traditional GMC methods typically adopt graph regulariza…
Matrix Completion