Generative Adversarial Networks For Graph Data Imputation From Signed Observations

TL;DR

This paper introduces a GAN-based method for imputing missing graph signals from signed, one-bit observations at a subset of nodes, leveraging graph-aware losses to improve estimation accuracy.

Contribution

It proposes a novel GAN framework incorporating graph-aware losses for signal imputation from signed observations, addressing a new problem setting.

Findings

Effective in reconstructing true signals from signed, partial observations.

Outperforms baseline methods in numerical experiments on MNIST data.

Demonstrates the potential of GANs for graph signal processing tasks.

Abstract

We study the problem of missing data imputation for graph signals from signed one-bit quantized observations. More precisely, we consider that the true graph data is drawn from a distribution of signals that are smooth or bandlimited on a known graph. However, instead of observing these signals, we observe a signed version of them and only at a subset of the nodes on the graph. Our goal is to estimate the true underlying graph signals from our observations. To achieve this, we propose a generative adversarial network (GAN) where the key is to incorporate graph-aware losses in the associated minimax optimization problem. We illustrate the benefits of the proposed method via numerical experiments on hand-written digits from the MNIST dataset