Quantifying daily rhythms with non-negative matrix factorization applied to mobile phone data

Human activities follow daily, weekly, and seasonal rhythms. The emergence of these rhythms is related to physiology and natural cycles as well as social constructs. The human body and its biological functions undergo near 24-h rhythms (circadian rhythms). While their frequencies are similar across people, their phases differ. In the chronobiology literature, people are categorized into morning-type, evening-type, and intermediate-type groups called chronotypes based on their tendency to sleep at different times of day. Typically, this typology builds on carefully designed questionnaires or manually crafted features of time series data on people's activity. Here, we introduce a method where time-stamped data from smartphones are decomposed into components using non-negative matrix factorization. The method does not require any predetermined assumptions about the typical times of sleep or activity: the results are fully context-dependent and determined by the most prominent features of the activity data. We demonstrate our method by applying it to a dataset of mobile phone screen usage logs of 400 university students, collected over a year. We find four emergent temporal components: morning activity, night activity, evening activity and activity at noon. Individual behavior can be reduced to weights on these four components. We do not observe any clear categories of people based on the weights, but individuals are rather placed on a continuous spectrum according to the timings of their phone activities. High weights for the morning and night components strongly correlate with sleep and wake-up times. Our work points towards a data-driven way of characterizing people based on their full daily and weekly rhythms of activity and behavior, instead of only focusing on the timing of their sleeping periods.