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This paper presents an on-device semi-supervised human activity detection system that can learn and predict human activity patterns in real time. The clinical objective is to monitor and detect the unhealthy sedentary lifestyle of a user. The proposed semi-supervised learning (SSL) framework uses sparsely labelled user activity events acquired from Inertial Measurement Unit sensors installed as wearable devices. The proposed cluster-based learning model in this approach is trained with data from the same target user, thus preserving data privacy while providing personalized activity detection services. Two different cluster labelling strategies, namely, population-based and distance-based strategies, are employed to achieve the desired classification performance. The proposed system is shown to be highly accurate and computationally efficient for different algorithmic parameters, which is relevant in the context of limited computing resources on typical wearable devices. Extensive experimentation and simulation study have been conducted on multi-user human activity data from the public domain in order to analyze the trade-off between classification accuracy and computation complexity of the proposed learning paradigm with different algorithmic hyper-parameters. With 4.17 h of training time for 8000 activity episodes, the proposed SSL approach consumes at most 20 KB of CPU memory space, while providing a maximum accuracy of 90% and 100% classification rates. [ABSTRACT FROM AUTHOR]