Spectral Geometric Matrix Completion

Amit Boyarski, Sanketh Vedula, Alex Bronstein

Research output: Contribution to journalConference articlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)172-196
Number of pages25
JournalProceedings of Machine Learning Research
Volume145
StatePublished - 2021
Externally publishedYes
Event2nd Mathematical and Scientific Machine Learning Conference, MSML 2021 - Virtual, Online
Duration: 16 Aug 202119 Aug 2021

Keywords

  • deep linear networks
  • deep matrix factorization
  • drug-target interaction
  • graph signal processing
  • matrix completion
  • recommendation system
  • spectral geometry

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

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