Title: Wavelet Canonical Coherence for Nonstationary Signals
Venue: NeurIPS 2025
Accepted: yes
Keywords: Multivariate time series

Neural signal analysis

Nonstationarity

Wavelet canonical coherence
Abstract: Understanding the evolving dependence between two sets 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 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. Code for implementing WaveCanCoh is available at https://github.com/mhaibo/WaveCanCoh.git.


Peer reviews:
comments: SUMMARY:
This paper studies the dependence between two clusters of multivariate time series with canonical coherence in the spectral domain. The authors specifically focus on brain activity signals which are nonstationary. Authors provide experiments and analysis to demonstrate the effectiveness of the proposed work.

STRENGTHS AND WEAKNESSES:
Strengths:
- The topic of studying dependency between multivariate signals is of great interest.
- Authors provide simulation study as supportive evidence for the proposed work.
- The paper is well-organized and easy to follow. 

Weaknesses:
- The proposed methodology is not quite innovative in my own opinion. Would be great if author can further emphasize the differences between the proposed method and existing techniques, and highlight the original work. 
- The experiment section lacks supportive evidence from more large-scale experiments. It is suggested to do validations on more datasets especially on real data.

QUESTIONS:
Please see above

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 2
ORIGINALITY: 3
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces scale-specific wavelet canonical coherence (WaveCanCoh), a new framework to measure time-varying coherence between two clusters of multivariate time series. The authors target the problem of analyzing dynamic dependencies between groups of signals in a nonstationary setting. The main contributions of this paper include defining this new measure of coherence, developing a theoretically grounded algorithm for its estimation, and demonstrating its utility on simulated data. Overall, this paper will have broad potential in certain specific time series applications, especially in non-stationary time series data such as EEG. Since the Fourier transform is widely used on some time series, the wavelet-based approach proposed by the author is interesting.\n\nSTRENGTHS AND WEAKNESSES:\nStrength\n\n1/ The paper is generally well-written and organized. The paper thoughtfully provides a detailed introduction to the technical background used, making this paper highly readable. \n\n2/ The use of wavelet models to calculate the correlation of time series is relatively rare in ML research. Therefore, this work may provide new insights and vitality to time series researchers in the ML community.\n\n3/ WaveCanCoh has strong innovation, extending Canonical Coherence to both time and frequency domains for the first time. This enables the model to extract non-stationary dependencies from some EEG signals.\n\n4/ The paper’s technical quality is excellent. It provides a rigorous theoretical development and backs it up with thorough experiments.\n\nWeakness\n\n1/ I personally is not entirely sure how relevant this topic is to the NeurIPS audience. But I am open to be convinced otherwise.\n\n2/ The manuscript includes a large amount of notation in the paper, which may not be friendly for the researchers to follow.\n\n3/ Please add a citation where LSP first appears in the paper, or at least let readers know that the Fourier-based approach you mentioned above is LSP.\n\nQUESTIONS:\nDoes the effect of WaveCanCoh depend on frequency band design? For example, does the high-frequency part lead to low correlation?\n\nLIMITATIONS:\nThe authors have addressed potential limitations.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIn this work, the authors describe a new framework which uses wavelets to measure canonical coherence between sets of multivariate time series. Their approach, called wavelet canonical coherence (WaveCanCoh) builds from the local wavelet spectral (LWS) matrix along with eigenvector analysis typically seen in canonical correlation analysis (CCA) in order to quantify associations given in terms of spectral associations, rather than standard temporal associations.  The authors demonstrate their method on simulated time series and real local field potential (LFP) data.\n\nSTRENGTHS AND WEAKNESSES:\n# Quality\nOverall, the quality of this work is good. The work is technically sound, rigorous, and correct as far as I have found. Limitations are not provided, which lowers this to a good for me, but I am willing to change this if I missed them or they are included in a revision. \n## Strengths\nTo the best of my knowledge, the theoretical framework and its associated proofs are all technically sound. The provided experiments are rigorous and demonstrate the benefits of the proposed method.\n## Weaknesses\nAlthough the authors claim to discuss limitations, I could not find the referenced material anywhere in the text or appendix. \n\nAdditionally, the related work section is limited in its discussion of actual related literature. Although the authors are right and I know of no exactly analogous methods which do CCA as such with Wavelets, there are plenty of techniques that use the frequency domain or wavelet-based transformations to study associations between time-series, especially in neuroimaging e.g. [1,2,3,4]. These methods (and others) are indeed related—at least in spirit—and ought to be mentioned. I think using the related work section to introduce the theoretical background is an unconventional choice. \n\n[1] Skidmore, F., et al. \"Connectivity brain networks based on wavelet correlation analysis in Parkinson fMRI data.\" Neuroscience letters 499.1 (2011): 47-51.\n\n[2] Ghuman, Avniel Singh, Jonathan R. McDaniel, and Alex Martin. \"A wavelet-based method for measuring the oscillatory dynamics of resting-state functional connectivity in MEG.\" Neuroimage 56.1 (2011): 69-77.\n\n[3] Sato, Joao Ricardo, et al. \"A method to produce evolving functional connectivity maps during the course of an fMRI experiment using wavelet-based time-varying Granger causality.\" Neuroimage 31.1 (2006): 187-196.\n\n[4] Tan, Qitao, et al. \"Frequency‐specific functional connectivity revealed by wavelet‐based coherence analysis in elderly subjects with cerebral infarction using NIRS method.\" Medical physics 42.9 (2015): 5391-5403.\n\n# Clarity\nOverall, the clarity of the work is good. I am willing to raise this score if my concerns are addressed.\n## Strengths\nOverall, this work is well-structured and well-written. I have no issues with the structure of the paper or the writing quality.\n## Weaknesses\nMany of the figures have been scaled down to fit the space. While this is fine, much of the text in the figures (especially in the legends) is quite small and difficult to read when printed. For example: \n* The text of the legend in figures 2 and 3 is especially hard to read. \n* Figure 4 is clearer, but larger text or scaling up the figure would be an improvement.  \n* Figure 10 in the appendix also has quite small text, especially “Odor presentation”.\n# Significance\nOverall, the significance of this work is excellent. Good work!\n## Strengths\nI believe this method holds great promise for applications in M/EEG and other neuroimaging analyses. Upon reading this paper, I immediately want to try to compare this method to other metrics for studying associations in EEG/MEG, such as wPLI. I am especially excited to see if this approach could be used for multi-modal fusion of time-series from different acquisitions.\n## Weaknesses\nI have no weaknesses to discuss in terms of significance.\n# Originality\nOverall, I would call the originality of this work fair to good (I am going to put fair on my score, but I am leaning toward good). I am willing to improve this score if the authors ground their work in the literature and provide a convincing argument for why this method stands out from other wavelet-based connectivity approaches.\n## Strengths\nAs far as I have found, this work is original in terms of performing CCA to find multivariate time-series associations via wavelets.\n## Weaknesses\nDespite the apparent originality, the authors have neglected to ground the approach in other wavelet-based measures for brain connectivity. This work would be significantly improved by a more thorough grounding in the literature.\n\nQUESTIONS:\n1. CCA has seen quite a few applications in fusion across imaging modalities (e.g. fMRI+EEG). Could the proposed method be used for multi-modal fusion of time-series data with different sampling rates? I fear the scale-specifity of the method might limit this potential?\n2. How does the provided estimation procedure scale in terms of time and memory complexity?  How does that compare to standard CCA? Eigenvalue decompositions in particular are notoriously intensive both in time and memory. \n3. How do the asymptotic guarantees given for the WaveCanCoh estimator apply in practice? Time time points and smoothing needing to approach infinity doesn’t provide a good idea of the practical upshot of longer sequences or increased smoothing.\n\nLIMITATIONS:\nAs stated earlier, I cannot find any discussion of the limitations in this work except for one sentence in the appendix. My questions regarding computational complexity and scale-specificity hint at some possible limitations that may arise, but a more thorough discussion of limitations in the main body of the text is required.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors present a method for quantifying multi-channel correlations at different time scales. The method produces scale-specific components for each channel via wavelet decomposition and then applies CCA to the resulting components (with some additional pre-processing). The method is presented in the context of canonical coherence for stationary processes and outlines both the model and estimation procedure. The model is then validated with simulated data using both wavelet-based and non-wavelet based nonstationary generative models and is then used on LFP data from mice performing a 2AF task at a pre-selected number of scales, and lags.\n\nSTRENGTHS AND WEAKNESSES:\nThe paper is organized clearly and logically developed and is mostly well-written, with a few omissions that could be corrected rather easily. I would imagine the method being useful to some researchers but could require some considerable guidance on how to choose wavelets, scales, and averaging window sizes M. Using specific windows of analysis to deal with nonstationary data is a pretty intuitive step for many neuroscientists but developing an approach explicitly in a wavelet setting is certainly more rigorous. However, it is not entirely clear from the text what impact it could have, however. First, the analysis was not compared against the most obvious benchmark, which would have been to apply canonical coherence on a moving window and evaluate the SNR against their method. Second, the analysis of LFP data was extremely limited with ambiguous ROI. Specifically, the results were not independently validated or interpreted either physiologically or algorithmically.\n\nQUESTIONS:\n- I would recommend changing the word “clusters” used throughout the manuscript to refer to distinct sets of channels since “clustering” is unrelated to the present paper.\n- The a and b elements in the inline text under equation (8) are bolded but the authors previously used the convention of non-bold symbols for scalars earlier in th paper. The authors should maintain a single convention throughout the paper.\n- Please explain A_{jl} in equation (14). It is not mentioned anywhere in the text\n- What kind of wavelet was used for the analysis in section 6?\n- Could the authors include the benchmark I mentioned in S&W?\n- Could the authors independently validate the results with another approach and/or give a deeper explanation for what the results mean and why they demonstrate the validity or value of their method? Alternatively, could the authors demonstrate that another method could not be used? This is perhaps the most important point to address for me to increase my score.\n- It is not stated if the authors controlled for multiple comparisons in their LFP data analysis. They should control for multiple comparisons in this case.\n\nLIMITATIONS:\nThe authors didn’t list any limitations. They could provide ways of further improving on their method and suggest scenarios where their method would not work. They could also comment on the scalability of their method and the suitability of their method for exploratory or discovery-based analysis.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-03"}