Graph Signal Denoising Via Unrolling Networks

Abstract

We propose an interpretable graph neural network framework to denoise single or multiple noisy graph signals. The proposed graph unrolling networks expand algorithm unrolling to the graph domain and provide an interpretation of the architecture design from a signal processing perspective. We unroll an iterative denoising algorithm by mapping each iteration into a single network layer where the feed-forward process is equivalent to iteratively denoising graph signals. We train the graph unrolling networks through unsupervised learning, where the input noisy graph signals are used to supervise the networks. By leveraging the learning ability of neural networks, we adaptively capture appropriate priors from input noisy graph signals, instead of manually choosing signal priors. To validate the proposed methods, we conduct extensive experiments on both real-world datasets and simulated datasets, and demonstrate that our methods have smaller denoising errors than conventional denoising algorithms and state-of-the-art graph neural networks. For denoising a single smooth graph signal, the normalized mean square error of the proposed networks is around 40% and 60% lower than that of graph Laplacian denoising and graph wavelets, respectively.

T-HyperGNNs: Hypergraph Neural Networks Via Tensor Representations

“…A variety of recent work has demonstrated that robust GNN architectures can be formed via graph propagation layers that mirror the unfolded descent iterations of a graph-regularized energy function (Chen & Eldar, 2021;Liu et al, 2021;Ma et al, 2020;Pan et al, 2021;Yang et al, 2021;Zhang et al, 2020;Zhu et al, 2021;Ahn et al, 2022). In doing so, the node embeddings at each layer can be viewed as increasingly refined approximations of an interpretable energy minimizer, that may be designed, for example, to mitigate GNN oversmooth-ing or perhaps inject robustness to spurious edges.…”

Transformers from an Optimization Perspective

“…Optimization Induced Graph Neural Networks A variety of graph neural network architectures have also been developed from a similar optimization perspective [7,29,31,34,48,49,52,54]. For example, graph attention mechanisms were derived using the iterative reweighted least squares (IRLS) algorithm in [49]; this result is related to self-attention, which can be viewed as graph attention on fully connected graphs [5]; however, it fails to produce the Transformer softmax term or the combined self-attention/feedforward Transformer stack.…”