Matrix Decomposition on Graphs: A Simplified Functional View

Abstract

We propose a simplified functional view of matrix decomposition problems on graphs such as geometric matrix completion. Our unifying framework is based on the key idea that using a reduced basis to represent functions on the product space is sufficient to recover a low rank matrix approximation even from a sparse signal. We validate our framework on several real and synthetic benchmarks where it either out-performs very competitive baselines or achieves competitive results at a fraction of the computational effort of prior work.