Deep geometric matrix completion: Are we doing it right?

Amit Boyarski, Sanketh Vedula, Alex Bronstein

TL;DR: A simple spectral geometric approach for matrix completion, based on the framework of functional maps.

Abstract:

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 information into the solution. This information is usually provided as graphs encoding relations between rows/columns.
In this work we propose a simple spectral approach for solving the matrix completion problem, via the framework of functional maps. We introduce the zoomout loss, a multiresolution spectral geometric loss inspired by recent advances in shape correspondence, whose minimization leads to state-of-the-art results on various recommender systems datasets. Surprisingly, for some datasets we were able to achieve comparable results even without incorporating geometric information. This puts into question both the quality of such information and current methods' ability to use it in a meaningful and efficient way.

Keywords: Geometric Matrix Completion, Spectral Graph Theory, Functional Maps, Deep Linear Networks

Code: https://colab.research.google.com/drive/1OkNEiTHok14gcVf3NxFIbAFutDN6-Tx6