## 2 Materials and Methods
### Use Cases for Calculating Periodicity Intensity  
#### 2.2.1 Periodicity Intensity in Sensor Data from the Homes of Older Adults  
The NEX project [27] developed an integrated IoT system to offer unobtrusive health and wellness monitoring to support older adults living independently in their homes. This involved the use of ambient sensors non-intrusively placed around the home to detect various domestic, in-home activities. The resulting time series data gathered from each sensor can be combined and analysed to create a model of an individual's normal daily patterns of activity. During the first half of 2022, twenty-four healthy older adults aged 60 years or older and living independently at home participated in a trial of the NEX project. The gender profile was predominantly female (81% \(n\) = 21), with a total population mean age of 73.2 years. The majority of participants were independent and high functioning, with only 8% (\(n\) = 2) reporting difficulties in completing activities of daily living (ADLS) [28], such as dressing, etc., and only 4% (\(n\) = 1) reporting difficulties in completing more complex tasks defined as instrumental activities of daily living (IADLS) [29], such as shopping for groceries, etc.  
A range of in-home sensors was installed in each participant's home, including (1) contact sensors on the doors of cupboards or drawers, which were used for kitchen crockery, cutlery, debln, food staples and pots, (2) contact sensors on the fridge door and (3) electrical plug sensors on the kettle, microwave and toaster. There were also contact sensors on wardrobe door(s) and on the drawer(s) in the bedroom, a 6-in-1 environmental sensor for temperature, humidity, light and presence in the bathroom and contact sensors on the front door, the pati door or the back door. Collectively, data from these sensors capture the purposeful actions of the participants, i.e., they indicate a deliberate action, thus the opening or closing of doors, the movement of a person and the switching on or off of electrical devices. Sensor data were gathered from the in-home sensors from the 24 participants' homes over periods varying from 6 weeks to 6 months each [27].  
The importance of the 24 h circadian rhythm and the conformance that each of the NEX project participants has to that 24-h rhythm can be shown by computing the strength of 24-h periodicity over all data from multiple sensor devices in the home. The fusion of multiple data streams from multiple sensors capture the activities of daily living, including food preparation and eating, self-grooming, cleaning, relaxing and others. Periodicity intensity emphasises the regular recurrence of such activities in the home.  
Periodicity intensity visualisations were presented to participants in the NEX project as a visualisation of their long-term behaviour and changes and the regularity of those trends over time. A periodicity intensity graph is a continuous timeline where high values indicate periods of regular behaviour as detected by the in-home sensors, and low values indicate periods of irregular activities. Such irregular activities are indicators of changes in regular habits and can point to changes in their sleep patterns (sleep onset, duration, waking during the night, napping during the day), in their movement into and out of, as well as around, the home (awake at night, sleeping during the day, staying in the home longer or shorter than normal), in self-grooming (using the restroom at irregular times) and in eating (snacking during the day or during the night as opposed to having regular meals).  
For the NEX trial, we used fused the data gathered from sensors in the homes of participants and computed a single overall periodicity intensity timeline for each participant, and we present some of these in the Results section (Section 3) of this paper.