Fast Graph Subset Selection Based on G-optimal Design

TL;DR

This paper introduces a fast graph subset selection method based on G-optimal design that avoids eigen-decomposition, significantly improving computational efficiency while maintaining competitive accuracy, especially at low sampling rates.

Contribution

It proposes a novel eigen-decomposition-free subset selection method using an $\alpha$-supermodular objective function based on G-optimal design.

Findings

The method achieves high computational efficiency.

It performs competitively with state-of-the-art methods.

It is especially effective at low sampling rates.

Abstract

Graph sampling theory extends the traditional sampling theory to graphs with topological structures. As a key part of the graph sampling theory, subset selection chooses nodes on graphs as samples to reconstruct the original signal. Due to the eigen-decomposition operation for Laplacian matrices of graphs, however, existing subset selection methods usually require high-complexity calculations. In this paper, with an aim of enhancing the computational efficiency of subset selection on graphs, we propose a novel objective function based on the optimal experimental design. Theoretical analysis shows that this function enjoys an $\alpha$-supermodular property with a provable lower bound on $\alpha$. The objective function, together with an approximate of the low-pass filter on graphs, suggests a fast subset selection method that does not require any eigen-decomposition operation. Experimental results show that the proposed method exhibits high computational efficiency, while having competitive results compared to the state-of-the-art ones, especially when the sampling rate is low.