Dynamic predictability and activity-location contexts in human mobility

Abstract

Human travelling behaviours are markedly regular, to a large extent predictable, and mostly driven by biological necessities and social constructs. Not surprisingly, such predictability is influenced by an array of factors ranging in scale from individual preferences and choices, through social groups and households, all the way to the global scale, such as mobility restrictions in response to external shocks such as pandemics. In this work, we explore how temporal, activity and location variations in individual-level mobility-referred to as predictability states-carry a large degree of information regarding the nature of mobility regularities at the population level. Our findings indicate the existence of contextual and activity signatures in predictability states, suggesting the potential for a more nuanced approach to estimating both short-term and higher-order mobility predictions. The existence of location contexts, in particular, serves as a parsimonious estimator for predictability patterns even in the case of low resolution and missing data.

Keywords: complex systems; human mobility; information theory.

Figure 1.

Time-independent entropy and predictability. (a) The entropy accounting for only visitation frequencies $H_u$ and incorporating the temporal sequence of visitations $H_c$. (b) The corresponding predictability values were calculated through equation (2.3). In all cases, accounting for the sequence reduces uncertainty from 6 to 5 bits and increases predictability from $20\%$ to $40\%$. The vertical dashed lines represent the medians for each distribution while the values for the standard deviation $\sigma$ are shown in the legends.

Figure 2.

Time-dependent predictabilities. (a) The uncorrelated predictability ${\mathrm{\Pi }}_u$, disaggregated with respect to time for Weeplaces. The trajectory of each individual is split into time slots representing the time of the week. We create $168$ slots (i.e. ${\displaystyle 24\text{h}\times 7}$ days of the week) and define $X_{t=t_0}$ as a random variable representing the places that an individual visits at the time slot $t=t_0\in [1,\dots ,168]$. The shaded area depicts the standard deviation ($\pm \sigma$) around the mean value, which is calculated for each hour. (b) The temporal predictability disaggregated with respect to the number of unique locations visited $S$. (c) Now disaggregated with respect to geographical coverage as measured by the radius of gyration $r_g$ in units of kilometres. (d) Finally, disaggregated with respect to the average frequency of monthly check-ins ${\stackrel{\mathrm{‾}}{f}}_c$. Across all users, we see daily peaks (4.00 to 5.00) and secondary peaks (12.00 to 17.00) of predictability throughout the time series.

Figure 3.

The effect of temporal windows of observation. (a) The distribution of ${\mathrm{\Pi }}_u$ as a function of window size for Gowalla. The dashed curve represents the baseline distribution of ${\mathrm{\Pi }}_u$ when taking into account the full trajectory of individuals. (b) The modes of the distributions are plotted as a function of window size for all three datasets. Horizontal dashed lines indicate the saturated value of ${\mathrm{\Pi }}_u$.

Figure 4.

Temporal modes of predictability. (a) Estimated global wavelet power spectrum showing peaks at 24 hours (circadian) and 12 h (circasemidian) as well as a non-significant peak at 6 h. The dashed black line represents the statistical significance of the mode as measured by electronic supplementary material, equation (S3). (b) Stacked bar chart for the most strong component period (24, 12 and 6 hours) of each individual.

Figure 5.

Location context of predictability. In all subplots, the dotted lines represent the distribution of ${\displaystyle {\mathrm{\Pi }}_{u,c}}$ given their full trajectories for Weeplaces. Solid lines represent distributions for the same individuals but when limiting their trajectories to locations of distinct types. The vertical dashed lines correspond to the median values.

Figure 6.

Estimating predictability from location context. (a) The estimated predictability ${\hat{\mathrm{\Pi }}}_c$ using a linear model with frequency of visiting location types as input, plotted against the true distribution of ${\mathrm{\Pi }}_c$ in the Weeplaces dataset ($R^2=0.419$). (b) The residuals are normally distributed and centred around zero.