Time-Frequency Filtering Meets Graph Clustering
Marcelo A. Colominas, Stefan Steinerberger, Hau-Tieng Wu
TL;DR
The paper reframes the problem of identifying signal components in a time-frequency representation as a graph clustering task by mapping TF-plane pixels to graph vertices and connecting nearby, energy-rich pairs. It introduces a flexible, nonparametric TF filtering pipeline where components are recovered from masks derived either by connected components or graph clustering, with noise-informed thresholds $\gamma$ and $\tau$ guiding edge formation via $|A_{ij}|\cdot|A_{k\ell}| \ge \tau$. The approach is demonstrated on simulated signals with varying SNR and on real data (bat calls and fetal ECG), showing robustness and the ability to extract multiple components simultaneously without the error accumulation of peeling. The framework generalizes beyond STFT to other TF representations and offers a pathway to improved, one-shot TF-domain extraction across diverse signal modalities.
Abstract
We show that the problem of identifying different signal components from a time-frequency representation can be equivalently phrased as a graph clustering problem: given a graph $G=(V,E)$ one aims to identify `clusters', subgraphs that are strongly connected and have relatively few connections between them. The graph clustering problem is well studied, we show how these ideas can suggest (many) new ways to identify signal components. Numerical experiments illustrate the ideas.