Tackling Provably Hard Representative Selection via Graph Neural Networks

TL;DR

This paper introduces RS-GNN, a graph neural network-based method for representative selection in attributed graphs, overcoming theoretical hardness and demonstrating superior empirical performance on multiple benchmarks.

Contribution

It establishes the hardness of representative selection without graph structure and proposes RS-GNN to effectively leverage graph data for improved selection.

Findings

RS-GNN outperforms baseline methods on eight benchmarks.

Theoretical hardness results highlight challenges in RS without graph structure.

Graph structure can transform intractable RS problems into solvable ones.

Abstract

Representative Selection (RS) is the problem of finding a small subset of exemplars from a dataset that is representative of the dataset. In this paper, we study RS for attributed graphs, and focus on finding representative nodes that optimize the accuracy of a model trained on the selected representatives. Theoretically, we establish a new hardness result forRS (in the absence of a graph structure) by proving that a particular, highly practical variant of it (RS for Learning) is hard to approximate in polynomial time within any reasonable factor, which implies a significant potential gap between the optimum solution of widely-used surrogate functions and the actual accuracy of the model. We then study the setting where a (homophilous) graph structure is available, or can be constructed, between the data points.We show that with an appropriate modeling approach, the presence of such a structure can turn a hard RS (for learning) problem into one that can be effectively solved. To this end, we develop RS-GNN, a representation learning-based RS model based on Graph Neural Networks. Empirically, we demonstrate the effectiveness of RS-GNN on problems with predefined graph structures as well as problems with graphs induced from node feature similarities, by showing that RS-GNN achieves significant improvements over established baselines on a suite of eight benchmarks.