On Sparse Graph Fourier Transform

TL;DR

This paper introduces a regression-based Sparse Graph Fourier Transform method that incorporates regularizations like lasso to produce sparse components, enabling localized frequency analysis and improved anomaly detection in network traffic data.

Contribution

It presents a novel sparse GFT framework with regularization flexibility, particularly using lasso, to enhance signal source identification and local frequency analysis.

Findings

Sparse GFT identifies correlated signal sources in sub-graphs

It performs effective local frequency analysis within sub-graphs

Achieves superior anomaly detection performance on real network data

Abstract

In this paper, we propose a new regression-based algorithm to compute Graph Fourier Transform (GFT). Our algorithm allows different regularizations to be included when computing the GFT analysis components, so that the resulting components can be tuned for a specific task. We propose using the lasso penalty in our proposed framework to obtain analysis components with sparse loadings. We show that the components from this proposed {\em sparse GFT} can identify and select correlated signal sources into sub-graphs, and perform frequency analysis {\em locally} within these sub-graphs of correlated sources. Using real network traffic datasets, we demonstrate that sparse GFT can achieve outstanding performance in an anomaly detection task.