Efficient Coxian duration modelling for activity recognition in smart environments with the hidden semi-Markov model

In this paper, we exploit the discrete Coxian distribution and propose a novel form of stochastic model, termed as the Coxian hidden semi-Makov model (Cox-HSMM), and apply it to the task of recognising activities of daily living (ADLs) in a smart house environment. The use of the Coxian has several advantages over traditional parameterization (e.g. multinomial or continuous distributions) including the low number of free parameters needed, its computational efficiency, and the existing of closed-form solution. To further enrich the model in real-world applications, we also address the problem of handling missing observation for the proposed Cox-HSMM. In the domain of ADLs, we emphasize the importance of the duration information and model it via the Cox-HSMM. Our experimental results have shown the superiority of the Cox-HSMM in all cases when compared with the standard HMM. Our results have further shown that outstanding recognition accuracy can be achieved with relatively low number of phases required in the Coxian, thus making the Cox-HSMM particularly suitable in recognizing ADLs whose movement trajectories are typically very long in nature.