Human Activity Recognition (HAR) plays a crucial role in various applications such as human-computer interaction and healthcare monitoring. However, challenges persist in HAR models due to the data distribution differences between training and real-world data distributions, particularly evident in cross-user scenarios. This paper introduces a novel framework, termed Diffusion-based Noise-centered Adversarial Learning Domain Adaptation (Diff-Noise-Adv-DA), designed to address these challenges by leveraging generative diffusion modeling and adversarial learning techniques. Traditional HAR models often struggle with the diversity of user behaviors and sensor data distributions. Diff-Noise-Adv-DA innovatively integrates the inherent noise within diffusion models, harnessing its latent information to enhance domain adaptation. Specifically, the framework transforms noise into a critical carrier of activity and domain class information, facilitating robust classification across different user domains. Experimental evaluations demonstrate the effectiveness of Diff-Noise-Adv-DA in improving HAR model performance across different users, surpassing traditional domain adaptation methods. The framework not only mitigates distribution mismatches but also enhances data quality through noise-based denoising techniques.

Current research on human activity recognition (HAR) mainly assumes that training and testing data are drawn from the same distribution to achieve a generalised model, which means all the data are considered to be independent and identically distributed $\displaystyle (i.i.d.) $. In many real-world applications, this assumption does not hold, and collected training and target testing datasets have non-uniform distribution, such as in the case of cross-user HAR. Domain adaptation is a promising approach for cross-user HAR tasks. Existing domain adaptation works based on the assumption that samples in each domain are $\displaystyle i.i.d. $ and do not consider the knowledge of temporal relation hidden in time series data for aligning data distribution. This strong assumption of $\displaystyle i.i.d. $ may not be suitable for time series-related domain adaptation methods because the samples formed by time series segmentation and feature extraction techniques are only coarse approximations to $\displaystyle i.i.d. $ assumption in each domain. In this paper, we propose the temporal relation optimal transport (TROT) method to utilise temporal relation and relax the $\displaystyle i.i.d. $ assumption for the samples in each domain for accurate and efficient knowledge transfer. We obtain the temporal relation representation and implement temporal relation alignment of activities via the Hidden Markov model (HMM) and optimal transport (OT) techniques. Besides, a new regularisation term that preserves temporal relation order information for an improved optimal transport mapping is proposed to enhance the domain adaptation performance. Comprehensive experiments are conducted on three public activity recognition datasets (i.e. OPPT, PAMAP2 and DSADS), demonstrating that TROT outperforms other state-of-the-art methods.