Source-Free Domain Adaptation (SFDA) aims to adapt a pre-trained model from a labeled source domain to an unlabeled target domain without accessing source domain data, thereby protecting source domain privacy. Although SFDA has recently been applied to time series data, the inherent complex distribution characteristics including temporal variability and distributional diversity of such data remain underexplored. Time series data exhibit significant dynamic variability influenced by collection environments, leading to discrepancies between sequences. Additionally, multidimensional time series data face distributional diversity across dimensions. These complex characteristics increase the learning difficulty for source models and widen the adaptation gap between the source and target domains. To address these challenges, this paper proposes a novel SFDA method for time series data, named Adaptive Latent Subdomain feature extraction and joint Prediction (ALSP). The method divides the source domain, which has a complex distribution, into multiple latent subdomains with relatively simple distributions, thereby effectively capturing the features of different subdistributions. It extracts latent domain-specific and domain-invariant features to identify subdomain-specific characteristics. Furthermore, it combines domain-specific classifiers and a domain-invariant classifier to enhance model performance through multi-classifier joint prediction. During target domain adaptation, ALSP reduces domain dependence by extracting invariant features, thereby narrowing the distributional gap between the source and target domains. Simultaneously, it leverages prior knowledge from the source domain distribution to support the hypothesis space and dynamically adapt to the target domain. Experiments on three real-world datasets demonstrate that ALSP achieves superior performance in cross-domain time series classification tasks, significantly outperforming existing methods.
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