Estimating Centrality Blindly from Low-pass Filtered Graph Signals

TL;DR

This paper introduces a robust method for estimating node centrality in graphs from signals filtered through unknown low-pass processes, addressing limitations of traditional PCA-based heuristics.

Contribution

It proposes a new blind centrality estimation technique that outperforms PCA heuristics, especially when the graph filter is not strongly low-pass.

Findings

PCA heuristics can fail with less low-pass filters

The proposed method improves centrality estimation accuracy

Numerical results validate the approach on synthetic and real data

Abstract

This paper considers blind methods for centrality estimation from graph signals. We model graph signals as the outcome of an unknown low-pass graph filter excited with influences governed by a sparse sub-graph. This model is compatible with a number of data generation process on graphs, including stock data and opinion dynamics. Based on the said graph signal model, we first prove that the folklore heuristics based on PCA of data covariance matrix may fail when the graph filter is not sufficiently low-pass. To remedy, we propose a robust blind centrality estimation method which substantially improves the centrality estimation performance. Numerical results on synthetic and real data support our findings.