Tensor-based Hidden Semi-Markov Model for CPSS user activity analysis and services

Cyber-Physical-Social Systems (CPSSs) represent a transformative paradigm that integrates human, machine, and environmental interactions to support intelligent services in smart spaces. However, providing accurate and efficient user activity analysis in such environments remains challenging due to the complex, high-dimensional, and noisy nature of sensory data. Although existing tensor-based models have shown promising accuracy in user activity analysis, they often suffer from low efficiency and reduced robustness to data noise, limiting their practicality in real-time applications. To address these challenges, this study proposes a Tensor-based Hidden Semi-Markov Model (T-HSMM) designed to efficiently analyze user activity durations and their dependencies using probabilistic distributions in tensor space. The main objective is to reduce redundant tensor computations while enhancing both the accuracy and robustness of activity analysis. Moreover, to effectively address the three basic micro-services in CPSSs - evaluation, learning, and prediction - we develop tensor-based algorithms, including the Forward-Backward, Baum-Welch, and Viterbi algorithms, for the proposed T-HSMM. These algorithms facilitate three computational subtasks of activity sequence probabilities, model parameter learning, and activity prediction. We evaluated the performance of the proposed model on three widely used open datasets. The results show that T-HSMM surpasses other models in terms of accuracy, precision, recall, and F1-score while maintaining acceptable time consumption. Additionally, we discuss the impact of varying parameters on the model's performance across different daily activities.

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