Enhancing Geometric Deep Learning via Graph Filter Deconvolution

TL;DR

This paper introduces a graph filter deconvolution step into geometric deep learning, improving classification accuracy by pre-processing signals with a sparse deconvolution before neural network analysis.

Contribution

It proposes a novel pre-processing step using group-sparse deconvolution based on a filter bank, enhancing geometric CNN performance.

Findings

Improved classification accuracy on synthetic data.

Enhanced performance on real-world graph datasets.

Efficient convex relaxation algorithms for deconvolution.

Abstract

In this paper, we incorporate a graph filter deconvolution step into the classical geometric convolutional neural network pipeline. More precisely, under the assumption that the graph domain plays a role in the generation of the observed graph signals, we pre-process every signal by passing it through a sparse deconvolution operation governed by a pre-specified filter bank. This deconvolution operation is formulated as a group-sparse recovery problem, and convex relaxations that can be solved efficiently are put forth. The deconvolved signals are then fed into the geometric convolutional neural network, yielding better classification performance than their unprocessed counterparts. Numerical experiments showcase the effectiveness of the deconvolution step on classification tasks on both synthetic and real-world settings.