Age-related health issues have been increasing with the rise of life expectancy all over the world. One of these problems is cognitive impairment, which causes elderly people to have problems performing their daily activities. Detection of cognitive impairment at an early stage would enable medical doctors to deepen diagnosis and follow-up on patient status. Recent studies show that daily activities can be used to assess the cognitive status of elderly people. Additionally, the intrinsic structure of activities and the relationships between their sub-activities are important clues for capturing the cognitive abilities of seniors. Existing methods perceive each activity as a stand-alone unit while ignoring their inner structural relationships. This study investigates such relationships by modelling activities hierarchically from their sub-activities, with the overall goal of detecting abnormal activities linked to cognitive impairment. For this purpose, recursive auto-encoders (RAE) and their linear vs. greedy and supervised vs. semi-supervised variants are adopted to model the activities. Then, abnormal activities are systematically detected using RAE’s reconstruction error. Moreover, to apply RAEs for this problem, we introduce a new sensor representation called raw sensor measurement (RSM) that captures the intrinsic structure of activities, such as the frequency and the order of sensor activations. As real-world data are not accessible, we generated data by simulating abnormal behaviour, which reflects on cognitive impairment. Extensive experiments show that RAEs can be used as a decision-supporting tool, especially when the training set is not labelled to detect early indicators of dementia.