Phase-driven Generalizable Representation Learning for Nonstationary Time Series Classification

TMLR Paper3968 Authors

Abstract: Pattern recognition is a fundamental task in continuous sensing applications, but real-world scenarios often experience distribution shifts that necessitate learning generalizable representations for such tasks. This challenge is exacerbated with time-series data, which also exhibit inherent \emph{nonstationarity}—variations in statistical and spectral properties over time. In this work, we offer a fresh perspective on learning generalizable representations for time-series classification by considering the phase information of a signal as an approximate proxy for nonstationarity and propose a phase-driven generalizable representation learning framework for time-series classification, \method{}. It consists of three key elements: 1) \emph{Hilbert transform-based augmentation}, which diversifies nonstationarity while preserving task-specific discriminatory semantics, 2) \emph{separate magnitude-phase encoding}, viewing time-varying magnitude and phase as independent modalities, and 3) \emph{phase-residual feature broadcasting}, integrating 2D phase features with a residual connection to the 1D signal representation, providing inherent regularization to improve distribution-invariant learning. Extensive evaluations on five datasets from sleep-stage classification, human activity recognition, and gesture recognition against 13 state-of-the-art baseline methods demonstrate that \method{} consistently outperforms the best baselines by an average of 5\% and up to 11\% in some cases. Additionally, the principles of \method{} can be broadly applied to enhance the generalizability of existing time-series representation learning models.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

# Summary of Key changes made to the paper

Dear Reviewers,

We are extremely grateful for your insightful comments and concrete suggestions. We have revised our submission accordingly to address them.

In this short note, we summarize the main changes in the latest revision of our submission (the key updates are on pages 3, 4, 5, 7, 8, and 12, including improved method description and additional experiments in Tables 1, 2 and Figures 4, 5). We have also included an updated Appendix with further results and details.

- **Reviewers VAfw, pFjB:** Following your suggestion, we have added a new experiment in Table 2 to demonstrate that the proposed augmentation preserves task-specific semantics.

- **Reviewers VAfw, MkRX:** To provide more intuition on how phase shifts using the Hilbert Transform can diversify nonstationarity, we have:
1. Added a new example study in Section 2.2 with Figure 4.
2. Included Table 1 reporting domain discrepancy accuracy to illustrate meaningful diversification.

- **Reviewer MkRX:** We have added an additional intuitive example in Section 2.2 with Figure 4 to demonstrate that phase encodes information related to signal nonstationarity.

- **Reviewers VAfw, pFjB:** Following your suggestion, we have conducted a controlled study to empirically illustrate the generalization improvement from phase-residual broadcasting in Section 2.4, Figure 5. We have also included a clarifying explanation of the implications of our theoretical support for PhASER's design in Section 2.5.

- **Reviewer A8Mk:**
- We have included additional prior works in the Related Works section (Section 4).
- As requested, we have conducted additional analyses using wavelet transform and empirical mode decomposition as alternative tools for time-frequency representation of nonstationary time series. We have presented a comparative illustration and these results in Section B (Table 9 and Figure 10) of the Appendix.
- Additionally, as requested, we have conducted further analyses on the UEA dataset, albeit it is not well-suited for domain generalization evaluation since domain discrepancy is not guaranteed.

All updates in the revised manuscript are highlighted in blue. In our responses, we use W to denote mentioned weaknesses and RQ to denote requested changes, followed by our responses.

Assigned Action Editor: ~Min_Wu2

Submission Number: 3968