Inferring Graph Signal Translations as Invariant Transformations for Classification Tasks

TL;DR

This paper introduces a deep learning method to infer graph signal translations that are invariant for classification, leveraging both graph structure and labeled data, applicable to images and networks.

Contribution

It proposes a novel approach to infer graph translations as edge-constrained operations using supervised learning, addressing the ill-posed nature of translation definition in GSP.

Findings

Effective translation inference on 2D images

Successful application to hyperlink networks

Improved invariance in classification tasks

Abstract

The field of Graph Signal Processing (GSP) has proposed tools to generalize harmonic analysis to complex domains represented through graphs. Among these tools are translations, which are required to define many others. Most works propose to define translations using solely the graph structure (i.e. edges). Such a problem is ill-posed in general as a graph conveys information about neighborhood but not about directions. In this paper, we propose to infer translations as edge-constrained operations that make a supervised classification problem invariant using a deep learning framework. As such, our methodology uses both the graph structure and labeled signals to infer translations. We perform experiments with regular 2D images and abstract hyperlink networks to show the effectiveness of the proposed methodology in inferring meaningful translations for signals supported on graphs.