Figure 1.
Average distribution (relative frequency) of locations in the timeslots. The data is averaged over all the different users in the set. A power-law fit to the statistics is also indicated, with an exponent −1.69. We also show two different random users with the “personal” statistics plus the cut-offs (see text) for the analysis of patterns.
Figure 2.
Patterns of life: Joe Random and Jane Regular.
Upper panel: Clustering result for the dayvectors of user Joe. Lower panel: Clustering result for the dayvectors of user Jane. In both panels, in the first row are the results obtained with the extremal optimization algorithm and in the second row the corresponding result with the k-means clustering. Each color is one location – the clusters are separated by white lines. The first column shows the unclustered days. The second and third column show the clustered days and the corresponding average days of each cluster. The last column shows the deviations from the average day, where the color of the location is only shown if it deviates from the location of the average day of the cluster – otherwise the color is black.
Figure 3.
Statistics of patterns, and life entropy.
a) The clustering results for 58 accepted users with the first place definition (off-line clustering) and a time slot of 1 hour. The clustering was done with the EO algorithm and . b) The cumulative distributions of the entropies for the three cases - bare entropy, reference model, and after clustering.
Figure 4.
a) The prediction accuracy of the first, location based method in the case of with clustering and without as a function of time during the day. The clustering is from the EO algorithm with . b) The predictions by the transfer matrix method for various
and
up to 12 hours. The dashed line is a logarithmic fit to the
case. c) The correlation of the personal entropy and the resulting predictability for both the prediction methods (
). The entropy values are either the “bare” ones or those after clustering if that is used to aid prediction.
Figure 5.
Length-of-working-day distribution in scaled units and the model fit. The parameters for the leaving early and late -processes are 0.045 and 0.046, respectively (in inverse -slot lengths).