Leveraging Semi-Markov Models to Identify Anomalies of Activities of Daily Living in Smart Homes Processes

Stochastic Process Mining, in particular, Markov processes, is used to represent uncertainty and variability in Activities of Daily Living (ADLs). However, the Markov models inherently assume that the time spent in each state must follow an exponential distribution. This presents a significant challenge to model real-life complexities in ADLs. Therefore, this paper employs semi-Markov models on publicly available ADL event logs to model state durations, where results are validated via goodness-of-fit tests (Kullback–Leibler, Kolmogorov–Smirnov, Cramér–von Mises). Synthetic durations are generated using the inverse transform sampling technique. To simulate dementia-based behaviours, the weights of the mixture model are altered to reflect prolonged duration in napping, toileting, meal, and drink preparation. These anomalies are then detected through the employment of log-likelihood ratio and chi-square tests. Experimental results demonstrate that the proposed approach can be used to reliably identify abnormal ADL durations, offering a proven framework to track early detection of behavioural shifts, and showcasing the effectiveness of detecting duration-based anomalies in ADL. By identifying such anomalies, our work aims to detect deterioration in the smart home resident’s condition, focusing in particular on their ability to execute different ADLs.