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. 2016 Sep 29;4:e2537. doi: 10.7717/peerj.2537

Table 1. Features used in this study and their definitions.

Features indicated with stars (∗) are replicated from our previous study (Saeb et al., 2015a).

Feature Definition
Location variance Combined variance of latitude and longitude values:
Locationvariance= logσlat2+σ long2,
where σlat2 and σlong2 are the variance of latitude and longitude, respectively.
Circadian movement First, we used the least-squares spectral analysis (Press, 2007) to obtain the spectrum of the GPS signals. Then, we calculated the amount of energy that fell into the frequency bins within a 24 ± 0.5 h period, in the following way:
E=1iuiLi=iLiupsdfi,
where psd(fi) denotes the power spectral density at frequency bin fi, and iL and iU represent the lower and the upper bounds of the frequency range of interest, corresponding to 24.5 and 23.5 h periods respectively. We calculated E separately for longitude and latitude, and obtained the total circadian movement as:
CM= logElat+Elong
Speed mean Mean of the instantaneous speed obtained at each GPS data point. The instantaneous speed (degrees/sec) was calculated as the change in latitude and longitude values over time in the following way:
Vi=latilati1titi12+longilongi1titi12,
where lati, longi, and ti are latitude, longitude, and time at sample i.
Speed variance Variance of the instantaneous speed.
Total distance Total geographic displacement, as:
Total distance=ilatilati12+longilongi12,
where lati and longi show latitude and longitude values at sample i.
Number of clusters Number of location clusters found by the adaptive k-means algorithm (Saeb et al., 2015a.).
Entropy Information theoretical entropy (Shannon, 1997), which measured how each participant’s time was distributed over different location clusters:
Entropy=i=1Npi logpi,
where pi is the percentage of time spent at location i, and N is the total number of location clusters.
Normalized entropy Entropy normalized by the number of location clusters (N):
Normalizedentropy=EntropylogN
Raw entropy Same as entropy, with pi representing the number of data points in each latitude or longitude bin before clustering. A total number of N = 10 bins were used. The total raw entropy was defined as the sum of latitude and longitude raw entropies.
Home stay Percentage of time spent at home.
Transition time Percentage of time spent in transit, such as in a car or on bike.