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Wavelet Canonical Coherence for Nonstationary Signals
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Proposes scale-specific wavelet canonical coherence (WaveCanCoh), extending canonical coherence to nonstationary two-group multivariate series via the multivariate locally stationary wavelet model, and applies it to hippocampal LFP in correct vs incorrect memory decisions.
Problem
Classical canonical coherence between two groups of multivariate time series assumes stationarity and lacks time-localization, so it cannot capture transient, scale-specific cross-group interactions in nonstationary signals such as neural LFP.
Approach
Defines a time- and scale-localized canonical coherence from the local wavelet spectral matrix of the fused two-group process, estimated by smoothed periodogram eigen-decomposition, with per-channel canonical vectors giving channel contributions, plus a causal lagged variant and a window-based permutation test.
Key results
- On the MvLSW simulation, WaveCanCoh averaged over 1000 replicates tracks the time-varying true coherence at scale j=2 across both halves of the series.
- On the AR(2) mixture simulation, only WaveCanCoh captures the sharp drop in cross-group coherence in the second half, while LSP does not.
- On the LFP data at scale j=5 (15.63-31.25 Hz), the correct-minus-incorrect difference at t=0.5 s is 0.334 (p=0.002), whereas the LSP baseline finds no significant differences.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use WaveCanCoh instead of LSP for localized time-frequency coherence analysis | LFP correct vs incorrect trials · LFP, j=4–6 after stimulus onset | permutation-test sensitivity to trial-condition differences: WaveCanCoh: 0.023 (0.001**) vs LSP: 0.010 (0.056*) at j=4, t=0.5s; 0.334 (0.002**) vs 0.008 (0.999) at j=5, t=0.5s; 0.03 | Helped |
| Compare correct and incorrect trials before stimulus onset | WaveCanCoh · LFP, t=-1.0s and -0.5s across scales j=3–7 | significant condition differences: WaveCanCoh p-values: 0.786, 0.704, 0.180, 0.506, 0.977, 0.999, 0.239, 0.111, 0.999, 0.640 | No clear effect |
| Compare correct and incorrect trials after stimulus onset | WaveCanCoh · LFP, t=0.5s and 1.0s across scales j=3–7 | significant condition differences: j=4, t=0.5: 0.023 (0.001**); j=5, t=0.5: 0.334 (0.002**); j=6, t=0.5: 0.039 (0.001**); j=6, t=1.0: 0.002 (0.025**); othe | Mixed |
| Use WaveCanCoh rather than LSP on the nonstationary AR(2) mixture | Time-varying canonical coherence estimation · AR(2) mixture simulation, first and second halves | tracking transient coherence changes | Helped |
Surprising findings
- The Fourier-based LSP baseline showed no significant correct vs incorrect differences on the LFP data, while WaveCanCoh did at scales 4 to 7 after odor onset.
Limitations
- Real LFP dataset is not publicly available, limiting external validation.
- Estimation relies on asymptotic conditions (T, M to infinity with M/T to 0) and smoothing bandwidth choice.
- Computational cost of per-time, per-scale eigendecomposition is higher than standard CCA.
Experimental setup
Datasets: simulated MvLSW process (P=6, Q=4, T=1024) simulated mixture of AR(2) processes (500 replicates) rat hippocampal LFP sequence memory task (22-electrode CA1 recordings, subject Mitt, 40 correct and 32 incorrect trials)
Benchmarks: simulated MvLSW process coherence recovery simulated AR(2) mixture vs LSP LFP correct vs incorrect trial permutation test
Metrics: estimated coherence vs true coherence 95% Wald confidence intervals median difference in WaveCanCoh permutation p-values
Baselines: LSP (Fourier-based time-varying canonical coherence via STFT)
Builds on: multivariate locally stationary wavelet model canonical coherence (Brillinger) local wavelet spectrum estimation
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