Discovering the Signal Subgraph: An Iterative Screening Approach on Graphs

TL;DR

This paper introduces an iterative vertex screening method to identify a signal subgraph in high-dimensional graph data, improving classification accuracy by reducing dimensionality while leveraging structural information.

Contribution

The paper presents a novel iterative screening approach for signal subgraph discovery that is theoretically grounded and demonstrates superior performance on real and simulated datasets.

Findings

Accurately estimates the true signal subgraph with high probability.

Achieves asymptotically optimal classification performance under high-dimensional conditions.

Outperforms full graph analysis in classification tasks.

Abstract

Supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. Existing conventional methods are designed for standard Euclidean data and do not account for the structural information inherent in graphs. In this paper, we propose an iterative vertex screening method to achieve dimension reduction across multiple graph datasets with matched vertex sets and associated graph attributes. Our method aims to identify a signal subgraph to provide a more concise representation of the full graphs, potentially benefiting subsequent vertex classification tasks. The method screens the rows and columns of the adjacency matrix concurrently and stops when the resulting distance correlation is maximized. We establish the theoretical foundation of our method by proving that it estimates the true signal subgraph with high probability. Additionally, we establish the convergence rate of classification error under the Erdos-Renyi random graph model and prove that the subsequent classification can be asymptotically optimal, outperforming the entire graph under high-dimensional conditions. Our method is evaluated on various simulated datasets and real-world human and murine graphs derived from functional and structural magnetic resonance images. The results demonstrate its excellent performance in estimating the ground-truth signal subgraph and achieving superior classification accuracy.