Fast Graph Subset Selection Based on G-optimal Design

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.