[Paper Review] Sampling and Recovery of Graph Signals based on Graph Neural Networks

Siheng Chen, Maosen Li+1 more|arXiv (Cornell University)|Nov 3, 2020

Advanced Graph Neural Networks70 references4 citations

TL;DR

This paper proposes interpretable graph neural networks for graph signal sampling and recovery by learning informative vertex selection via mutual information estimation and unrolling recovery algorithms into neural layers. The method achieves state-of-the-art performance in semi-supervised learning and graph classification, improving accuracy by over 10% on Cora and 1.3% on average across graph classification benchmarks.

ABSTRACT

We propose interpretable graph neural networks for sampling and recovery of graph signals, respectively. To take informative measurements, we propose a new graph neural sampling module, which aims to select those vertices that maximally express their corresponding neighborhoods. Such expressiveness can be quantified by the mutual information between vertices' features and neighborhoods' features, which are estimated via a graph neural network. To reconstruct an original graph signal from the sampled measurements, we propose a graph neural recovery module based on the algorithm-unrolling technique. Compared to previous analytical sampling and recovery, the proposed methods are able to flexibly learn a variety of graph signal models from data by leveraging the learning ability of neural networks; compared to previous neural-network-based sampling and recovery, the proposed methods are designed through exploiting specific graph properties and provide interpretability. We further design a new multiscale graph neural network, which is a trainable multiscale graph filter bank and can handle various graph-related learning tasks. The multiscale network leverages the proposed graph neural sampling and recovery modules to achieve multiscale representations of a graph. In the experiments, we illustrate the effects of the proposed graph neural sampling and recovery modules and find that the modules can flexibly adapt to various graph structures and graph signals. In the task of active-sampling-based semi-supervised learning, the graph neural sampling module improves the classification accuracy over 10% in Cora dataset. We further validate the proposed multiscale graph neural network on several standard datasets for both vertex and graph classification. The results show that our method consistently improves the classification accuracies.

Motivation & Objective

• To address the limitation of analytical graph signal sampling and recovery methods that rely on predefined, often inaccurate, graph signal models.
• To develop a data-driven, flexible approach that learns graph signal models directly from data using neural networks.
• To ensure interpretability by leveraging graph-specific properties such as neighborhood structure and signal expressiveness.
• To design a multiscale graph neural network with feature-crossing layers for improved learning across multiple graph scales.
• To validate the proposed framework on active sampling in semi-supervised learning and standard graph classification tasks.

Proposed method

• Introduces a graph neural sampling module that selects vertices based on mutual information between vertex features and their neighborhood features, estimated via a GNN.
• Develops a graph neural recovery module using algorithm unrolling, where each iteration of an analytical recovery algorithm is transformed into a learnable network layer.
• Proposes a new multiscale graph neural network architecture—Graph Cross Network (GXN)—featuring trainable multiscale graph filters and a novel feature-crossing layer for cross-scale feature communication.
• Employs a trainable graph filter bank structure that enables multiscale representation learning while maintaining interpretability through graph-aware design.
• Uses mutual information estimation as a differentiable proxy to guide the sampling module toward selecting vertices that best represent their local neighborhoods.
• Applies the proposed modules within a unified framework for both vertex-level and graph-level classification tasks, with consistent performance gains.

Experimental results

Research questions

• RQ1 Can a data-driven sampling strategy based on mutual information estimation outperform traditional analytical sampling methods in graph signal recovery?
• RQ2 Can algorithm unrolling of recovery algorithms into learnable layers improve reconstruction accuracy while maintaining interpretability?
• RQ3 How does the integration of multiscale graph representation with feature-crossing layers affect performance in graph classification tasks?
• RQ4 To what extent does the proposed neural sampling module enhance active-sampling-based semi-supervised learning?
• RQ5 Does the proposed framework generalize across diverse graph structures and signal models without requiring prior assumptions about signal sparsity or bandlimitedness?

Key findings

• The proposed graph neural sampling module improves classification accuracy by over 10% in active-sampling-based semi-supervised learning on the Cora dataset.
• The Graph Cross Network (GXN) achieves an average accuracy improvement of 1.15% over baseline GNNs in vertex classification across multiple datasets.
• The feature-crossing layer contributes an average accuracy gain of 1.10% across vertex classification tasks, demonstrating the benefit of cross-scale feature interaction.
• GXN outperforms state-of-the-art methods on 5 out of 6 graph classification benchmarks, achieving a 1.30% average accuracy improvement.
• The proposed graph neural sampling module consistently yields better performance than other neural pooling methods (gPool, SAGPool, AttPool) when integrated into GXN.
• The multiscale architecture with feature-crossing layers shows consistent performance gains across both vertex and graph classification tasks, indicating robustness and generalization ability.