Spectral Geometric Matrix Completion
This work addresses matrix completion in applications like recommender systems and drug-target interaction by enabling DMF models to exploit geometric relations, though it is incremental as it builds on existing DMF frameworks.
The paper tackled matrix completion problems with underlying geometric or topological relations, such as in recommender systems, by incorporating explicit regularization into Deep Matrix Factorization (DMF) models through a spectral geometry lens, resulting in competitive performance on real benchmarks.
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.