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An Unsupervised Approach for Periodic Source Detection in Time Series
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Proposes an unsupervised periodic source detector that minimizes spectral entropy of learned representations while keeping them relative-entropy-close to input spectra, avoiding augmentations and batch-variance constraints.
Problem
Detecting periodic components in noisy time series (heart rate, respiratory rate, step counting) without labels, clean signals, or task-specific augmentations; existing SSL methods need augmentations and collapse-prevention relies on batch statistics.
Approach
Two opposing spectral regularizers: minimizing spectral entropy of the representation (maximizing periodicity) plus a KL divergence between input and representation spectra in the band of interest (prevents collapse by tying outputs to their source samples), together with out-of-band power minimization.
Key results
- On Clemson regular step counting, the method reaches 5.95 MAPE versus 6.01 for the best self-supervised baseline TS-TCC and 6.15 for FCN.
- On IEEE SPC12 PPG heart rate, the method achieves MAE 9.30 versus 10.05 for the CNN supervised baseline and 9.75 for TS2Vec.
- On PTB-XL ECG heart rate, the method achieves MAE 3.75 versus 3.97 for SiNC, the previous unsupervised method.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use both spectral-entropy periodicity maximization and sample-spectrum information preservation instead of removing periodicity maximization (ablation) | Proposed method · IEEE SPC12 | MAE: 12.69 -> 9.30 | Helped |
| Use both spectral-entropy periodicity maximization and sample-spectrum information preservation instead of removing periodicity maximization (ablation) | Proposed method · IEEE SPC22 | MAE: 14.51 -> 10.27 | Helped |
| Use both spectral-entropy periodicity maximization and sample-spectrum information preservation instead of removing periodicity maximization (ablation) | Proposed method · DaLiA PPG | MAE: 18.71 -> 27.41 | Hurt |
| Add the sample-spectrum information-preservation term rather than training without collapse prevention (ablation) | Proposed method · IEEE SPC12 | MAE: 39.14 -> 9.30 | Helped |
| Add the sample-spectrum information-preservation term rather than training without collapse prevention (ablation) | Proposed method · IEEE SPC22 | MAE: 39.71 -> 10.27 | Helped |
| Add the sample-spectrum information-preservation term rather than training without collapse prevention (ablation) | Proposed method · DaLiA PPG | MAE: 35.26 -> 27.41 | Helped |
| Use both proposed regularizers instead of removing periodicity maximization (ablation) | Proposed method · PTB-XL | MAE: 14.29 -> 3.75 | Helped |
| Use both proposed regularizers instead of removing collapse prevention (ablation) | Proposed method · PTB-XL | MAE: 7.74 -> 3.75 | Helped |
| Use both proposed regularizers instead of removing periodicity maximization (ablation) | Proposed method · DaLiA ECG | MAE: 5.23 -> 1.29 | Helped |
| Use both proposed regularizers instead of removing collapse prevention (ablation) | Proposed method · DaLiA ECG | MAE: 2.93 -> 1.29 | Helped |
| Use both proposed regularizers instead of removing periodicity maximization (ablation) | Proposed method · WESAD | MAE: 5.09 -> 2.13 | Helped |
| Use both proposed regularizers instead of removing collapse prevention (ablation) | Proposed method · WESAD | MAE: 3.44 -> 2.13 | Helped |
Surprising findings
- Removing the collapse-prevention term (training only with spectral entropy) yields worse performance than Fourier-based periodicity detection, with a degenerate solution failing even on easy cases.
- The SimPer method, designed for periodicity learning, performs worse than generic SSL methods on noisy time series despite the same downstream task.
Limitations
- Underperforms supervised and self-supervised methods on noisy datasets such as DaLiA PPG and Clemson semi-regular, where the periodic pattern is largely hidden.
- Performance depends on the training set containing sufficient high-SNR examples; purely unsupervised training may learn noise when this is absent.
- Gains over traditional methods are reported on a limited set of tasks and datasets, and baseline tuning was limited (e.g., RobustPeriod search space).
Experimental setup
Datasets: PTB-XL WESAD DaLiA IEEE SPC12 IEEE SPC22 CapnoBase BIDMC Clemson
Benchmarks: PTB-XL DaLiA WESAD IEEE SPC12 IEEE SPC22 CapnoBase BIDMC Clemson
Metrics: MAE RMSE Pearson correlation MAPE
Baselines: Fourier transform autocorrelation RobustPeriod DCL CNN SimCLR NNCLR BYOL TS-TCC TS2Vec VICReg Barlow Twins
Builds on: SiNC SimPer VICReg Barlow Twins TS2Vec
Closest papers by meaning
- Peri-midFormer: Periodic Pyramid Transformer for Time Series Analysis (NeurIPS 2024 · similarity 0.86)
- MPTSNet: Integrating Multiscale Periodic Local Patterns and Global Dependencies for Multivariate Time Series Classification (AAAI 2025 · similarity 0.86)
- Learning under Temporal Label Noise (ICLR 2025 · similarity 0.85)
- Frequency-Masked Embedding Inference: A Non-Contrastive Approach for Time Series Representation Learning (AAAI 2025 · similarity 0.85)
- TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis (ICLR 2025 · similarity 0.84)
- T-Rep: Representation Learning for Time Series using Time-Embeddings (ICLR 2024 · similarity 0.84)
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