- The paper introduces SAFA, a novel framework that combines temporal masking with a frequency adaptation layer to address spectral shifts in source-free domain adaptation.
- The paper demonstrates significant performance gains on benchmarks like MFD and Boiler, with improvements up to +21% MF1 using explicit frequency-domain modulation.
- The paper presents a robust strategy by freezing the backbone and employing self-supervised objectives to maintain temporal-spectral consistency and prevent catastrophic forgetting.
Temporal-Spectral Alignment with Frequency Adaptation for Source-Free Time-Series Adaptation
The paper addresses source-free domain adaptation (SFDA) for time-series classification, where only a pre-trained source model and unlabeled target data are available due to privacy, security, or practical constraints. Classical UDA approaches rely on concurrent access to source and target data, but SFDA must overcome distribution shifts, feature shift, and temporal drift intrinsic to time-series signals without labeled source data. Prior SFDA methods focus predominantly on temporal adaptation via self-supervision, pseudo-labeling, and entropy minimization, but largely neglect spectral shifts critical in time-series—changes in frequency content, amplitude, and phase, caused by sensor variability and user behavior, lead to misalignment if only feature-space adaptation is performed.
Proposed Approach: SAFA Framework
The paper introduces Temporal-Spectral Alignment with Frequency Adaptation (SAFA), a two-stage framework:
1. Source Pre-training (Temporal Enhancement)
A feature extractor, classifier, and auxiliary imputer network are trained using labeled source data. Temporal masking is applied to source signals, and the imputer reconstructs masked features, enforcing temporal correlation learning and robust time-series representation. The objective combines supervised cross-entropy and self-supervised imputation loss, producing a model architecture that can reconstruct temporal dynamics from corrupted input.
2. Source-Free Frequency-domain Adaptation
During adaptation, all source model weights (feature extractor, classifier, imputer) are frozen to preserve source knowledge and prevent catastrophic forgetting. Adaptation proceeds at the input signal level. The Frequency Adaptation Layer (FAL) decomposes target signals into amplitude and phase via FFT, applies trainable MLPs (initialized to identity) to perturb amplitude and phase, and reconstructs the adapted signal with iFFT. This explicit frequency-domain modulation aligns spectral characteristics with the source domain without updating the backbone.
Self-supervised adaptation objectives include Information Maximization (entropy minimization and diversity maximization) to produce confident, non-collapsed predictions, and Temporal Output Verification (TOV) to ensure that adapted features respect temporal dependencies learned by the source imputer network.
Experimental Evaluation
Extensive experiments are conducted on three heterogeneous benchmarks: WISDM (activity recognition), Machinery Fault Database (MFD), and Boiler (industrial fault detection). Macro F1-score is used due to class imbalance. SAFA is compared against six SFDA baselines: SHOT, NRC, AaD, MAPU, TemSR, and CE-SFDA.
Quantitative Results
- MFD: SAFA achieves the highest average MF1 (86.12%), outperforming CE-SFDA by 3.1%. Consistent performance across challenging transfers, especially where frequency shift dominates.
- WISDM: SAFA yields the best MF1 average (65.40%), with marked gains in transfer tasks involving inter-subject variability. Frequency adaptation proves crucial for dealing with phase misalignment and intra-class variation.
- Boiler: SAFA leads with 64.67% MF1, over 7% higher than TemSR, the second-best method. Explicit frequency-domain modulation is essential in multi-sensor industrial scenarios.
Ablation and Robustness Analysis
Ablation studies on MFD demonstrate that FAL is the main driver of performance (+21% MF1 gain), while TOV stabilizes adaptation (+8% MF1 from inclusion). Freezing the backbone during adaptation prevents catastrophic forgetting.
Parameter sensitivity analysis shows high robustness to amplitude and phase scaling hyperparameters, with relatively flat MF1 curves across a wide range—this alleviates the necessity for exhaustive search in source-free settings.
Implications and Future Directions
SAFA establishes a strong paradigm for SFDA in time-series recognition, where adaptation must operate signal-level and respect the domain-specific spectral characteristics. The explicit frequency adaptation enables robust, stable alignment even under severe distribution shifts, such as those induced by sensor changes and operational variabilities.
From a practical standpoint, this approach is well-suited for industrial and medical domains where data privacy prohibits source access. Spectral adaptation could be extended to non-linear and cross-channel modulations, and combined with more complex self-supervised objectives. Theoretically, the preservation of temporal-spectral consistency without source data offers a promising direction for robust, privacy-preserving transfer learning in time-series analysis.
Conclusion
The paper introduces a source-free domain adaptation method for time-series classification that aligns amplitude and phase spectra via a trainable frequency adaptation layer, while preserving temporal correlations through auxiliary imputation. Extensive empirical results demonstrate superior performance and robustness compared to state-of-the-art SFDA methods. The approach provides a scalable, signal-level solution to frequency-domain shift in real-world time-series applications, and its backbone-freezing strategy effectively prevents catastrophic forgetting. These findings suggest fruitful future directions in self-supervised spectral adaptation and private federated learning for time-series domains.
