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 language | English |
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Pages (from-to) | 172-196 |
Number of pages | 25 |
Journal | Proceedings of Machine Learning Research |
Volume | 145 |
State | Published - 2021 |
Externally published | Yes |
Event | 2nd Mathematical and Scientific Machine Learning Conference, MSML 2021 - Virtual, Online Duration: 16 Aug 2021 → 19 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