## 4 Discussion  
This paper presents three applications of calculating periodicity intensity throughout a time series on three very different real-world use cases. In each case, we gain deeper insights into the data than would have been revealed without periodicity analysis. These powerful insights into the underlying time series data can be obtained from any data source that has underlying periodicity as an inherent feature. The value of this form of data analysis is that it is unsupervised, requires no training data, and thus, it is generalisable. This makes the value of the technique in terms of economic impact quite attractive as it can be applied to any use case where there is longitudinal time series data to be analysed in order to detect gradual shifts or changes over time. In terms of implementation, the choice of values for the three parameters is not difficult to determine. The frequency of the recurring pattern to be investigated, _Fo_, is often 24 h but not always so and the use case usually already knows what this should be. The size of the window in which the periodicity is calculated \(m\) is also usually known in advance. For example, if _Fo_ is 24 h, then setting \(m\) to 7 days nullifies any effects of weekend/weekday behaviour transitions in the underlying data. The overlap between windows or stride length \(l\) is influenced by the demands of the use case and the amount of computation resources available and not any algorithmic limitation. The technique is agile in terms of the number and even the type of time series data used, and it is fast to compute. Because we use the Lomb-Scargle algorithm [13] to calculate periodicity in windows, it handles irregularly sampled data, such as our students' access to their VLE, as well as moderate amounts of missing data, though not completely missing data as in those calves whom's collars fell off but were replaced quickly in our third use case. Finally, the algorithm for calculating periodicity intensity is mathematically deterministic, producing the same output from the same input repeatedly. Periodicity intensity is a complex metric to fully comprehend because it is novel and non-conventional. In the two of our use cases which involved human participants--in-home sensors in the homes of older adults and students accessing their VLE--we needed the support of an animated helper video to describe what the periodicity intensity was because our users were healthcare professionals and older adults. For future work, we will concentrate on ways to make the metric more intuitively understandable by mapping changes in a periodicity intensity graph back to the underlying data, thus showing exactly what data has caused changes in periodicity intensity, and this would be useful in those use cases involving human subjects. We will also explore the robustness of the algorithm as a function of data quality by introducing noise to see how a decrease in data quality impacts the generated output. Finally, we will focus on the implementation of the Lomb-Scargle algorithm to determine periodicity at the 24 h frequency only, as our experience has been that this frequency setting is the one that most use cases are interested in. Conceptualization, A.F.S. and F.H. ; methodology, A.F.S. and F.H. ; software, F.H. ; validation, A.F.S. and F.H. ; formal analysis, A.F.S. and F.H. ; investigation, A.F.S. and F.H. ; data curation, A.F.S. ; writing--original draft preparation, A.F.S. ; writing--review and editing, A.F.S. and F.H. All authors have read and agreed to the published version of the manuscript. This research was funded by Science Foundation Ireland grant number SFI/12/RC/2289_P2, cofunded by the European Regional Development Fund and by the Disruptive Technologies Innovation Fund administered by Enterprise Ireland, project grant number DT-2018-0258 and by a UCD Wellcome Institutional Strategic Support Fund, which was financed jointly by University College Dublin and the SFI-HRB-Wellcome Biomedical Research Partnership (ref 204844/Z/16/Z).