On Sparse Graph Fourier Transform

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.