Wavelet Canonical Coherence for Nonstationary Signals

2025-05-20

AI Summary

Modeling cross-cluster dynamic dependencies in nonstationary multivariate signals remains challenging due to limitations in time–frequency resolution. Method: This paper proposes WaveCanCoh—a scale-specific wavelet graph canonical coherence framework—that extends canonical coherence analysis to nonstationary settings by integrating multivariate locally stationary wavelet (LSW) models with wavelet time–frequency decomposition. Contribution/Results: WaveCanCoh enables interpretable, time-varying, and frequency-localized analysis of inter-cluster dynamic coherence without assuming signal stationarity, achieving both high temporal resolution and scale specificity. On synthetic data, it accurately recovers ground-truth coherence structures. Applied to hippocampal local field potential (LFP) recordings, it uncovers dynamic neural coordination patterns associated with memory decision accuracy—providing a novel analytical tool for investigating interactions among neural subnetworks.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Multi-instance/Multi-view Learning
• Humans and AI: Brain-Sensing and Analysis

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Mining multimedia, multimodal, multilingual, cross-lingual Web data
• Security and Privacy: Large-scale security measurements

Abstract

Understanding the evolving dependence between two clusters of multivariate signals is fundamental in neuroscience and other domains where sub-networks in a system interact dynamically over time. Despite the growing interest in multivariate time series analysis, existing methods for between-clusters dependence typically rely on the assumption of stationarity and lack the temporal resolution to capture transient, frequency-specific interactions. To overcome this limitation, we propose scale-specific wavelet canonical coherence (WaveCanCoh), a novel framework that extends canonical coherence analysis to the nonstationary setting by leveraging the multivariate locally stationary wavelet model. The proposed WaveCanCoh enables the estimation of time-varying canonical coherence between clusters, providing interpretable insight into scale-specific time-varying interactions between clusters. Through extensive simulation studies, we demonstrate that WaveCanCoh accurately recovers true coherence structures under both locally stationary and general nonstationary conditions. Application to local field potential (LFP) activity data recorded from the hippocampus reveals distinct dynamic coherence patterns between correct and incorrect memory-guided decisions, illustrating the capacity of the method to detect behaviorally relevant neural coordination. These results highlight WaveCanCoh as a flexible and principled tool for modeling complex cross-group dependencies in nonstationary multivariate systems. The code for WaveCanCoh is available at: https://github.com/mhaibo/WaveCanCoh.git.

Problem

• Analyzing dynamic dependence between multivariate signal clusters
• Overcoming stationarity assumptions in coherence analysis
• Detecting frequency-specific transient interactions in nonstationary systems

Innovation

• Extends canonical coherence via wavelet model
• Estimates time-varying scale-specific coherence
• Detects dynamic neural coordination patterns