Matrix Decomposition on Graphs: A Functional View
This work provides a unifying framework for graph-based matrix decomposition, potentially benefiting researchers and practitioners working with sparse graph data by offering more efficient solutions.
This paper proposes a functional view for matrix decomposition problems on graphs, such as geometric matrix completion and graph regularized dimensionality reduction. The framework, which uses a reduced basis to represent functions on a product space, recovers low-rank matrix approximations from sparse signals and achieves competitive or superior results on benchmarks with reduced computational effort.
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. 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 (for both problems) where it either outperforms state of the art or achieves competitive results at a fraction of the computational effort of prior work.