Time-Frequency Filtering Meets Graph Clustering

2025-10-08

AI Summary

This paper addresses the problem of identifying and separating multicomponent signals in time-frequency (TF) representations. We propose a novel graph-clustering paradigm: the TF structure of a signal is modeled as a weighted graph, where nodes represent TF bins and edge weights encode local similarity; spectral clustering or graph partitioning algorithms are then applied to automatically detect well-connected subgraphs with minimal inter-cluster connections—each corresponding to an individual signal component. Our key contribution is the first rigorous establishment of an equivalence between TF signal decomposition and graph clustering, yielding an interpretable and scalable graph-theoretic framework for signal separation. Numerical experiments demonstrate that the method achieves robust separation under challenging conditions—including additive noise, nonstationarity, and severe TF overlap—outperforming conventional TF filtering approaches.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Equating time-frequency signal separation with graph clustering
• Identifying strongly connected subgraphs with sparse connections
• Developing new methods for signal component identification

Innovation

• Time-frequency filtering transforms into graph clustering
• Graph clustering identifies strongly connected subgraphs
• Numerical experiments validate new signal component methods