Using semi-Markov models to identify long holding times of activities of daily living in smart homes

Monitoring the activities of daily living (ADL) in smart homes is crucial, especially for older people and patients, to maintain or enhance their functioning, independence, and overall well-being. Additionally, by detecting unusual or abnormal inhabitant behaviour, it provides an opportunity for facilitating reminders, customised assistance for ADL completion, or alarms to notify carers or medical services. This study utilizes semi-Markov models integrated with gamma mixture models for modelling ADLs, as well as identifying anomalies, especially long holding times. The method is evaluated on a publicly available sensorised smart home dataset, with 2, 12 and 2 anomalies detected in activities, sensors and locations respectively, demonstrating its effectiveness in ADL modelling and anomaly detection.