Mixing Individual and Collective Behaviours to Predict Out-of-Routine Mobility

TL;DR

The study targets next-location prediction, focusing on out-of-routine mobility, by dynamically integrating individual mobility patterns with collective movement information. It formalizes the mixture as $M_i^{(u)} = (1 - S^{(u)}_i) I^{(u)}_i + S^{(u)}_i C_i$, where $S^{(u)}_i$ is the normalised Shannon entropy of the individual's transitions, and uses softmax normalization for the resulting probabilities. The model is trained and evaluated on privacy-preserving GPS trajectories from Boston, NYC, and Seattle (Jan–Aug 2020), with LCST-based stratification of train–test overlap to gauge generalisation. Results show that $M$ significantly outperforms $I$ and $C$ (up to +15% relative to $I$ and +35% relative to $C$) and is competitive with RNNs, while offering robustness to disruptive events such as the COVID-19 pandemic where individual-only models degrade substantially. Spatial analysis reveals that collective signals are most predictive near POI-dense urban zones, with a strong negative correlation between collective entropy $S^{(C)}_i$ and ACC@5$_i$, suggesting localized predictability driven by urban structure; the approach remains interpretable and resilient, indicating practical value for urban mobility analytics.

Abstract

Predicting human displacements is crucial for addressing various societal challenges, including urban design, traffic congestion, epidemic management, and migration dynamics. While predictive models like deep learning and Markov models offer insights into individual mobility, they often struggle with out-of-routine behaviours. Our study introduces an approach that dynamically integrates individual and collective mobility behaviours, leveraging collective intelligence to enhance prediction accuracy. Evaluating the model on millions of privacy-preserving trajectories across three US cities, we demonstrate its superior performance in predicting out-of-routine mobility, surpassing even advanced deep learning methods. Spatial analysis highlights the model's effectiveness near urban areas with a high density of points of interest, where collective behaviours strongly influence mobility. During disruptive events like the COVID-19 pandemic, our model retains predictive capabilities, unlike individual-based models. By bridging the gap between individual and collective behaviours, our approach offers transparent and accurate predictions, crucial for addressing contemporary mobility challenges.

Figures (4)

• Figure 1: Dynamic interplay of individual and collective mobility.(A) An individual origin-destination matrix for a synthetic individual $u$. (B) The collective origin-destination (OD) matrix computed for Boston using GPS trajectories. (C) An individual trajectory for a user $u$ starting from location $i$. Next location prediction consists of predicting $u$'s next visited location. (D) The set of $u$'s historical trajectories (panel A) is used to define the transition probabilities $I^{(u)}_{i}$ from location $i$. $C_i$ represents the probability distribution of all transitions made by any user starting from location $i$, generated from the OD matrix (panel B). Destinations' locations $j$ are coloured based on their visitation probability, $T_{ij}$, from origin $i$. (E)$M_i^{(u)}$'s prediction of individual $u$'s next location is performed by dynamically combining $I^{(u)}_{i}$ and $C_i$, based on the normalised Shannon entropy $S^{(u)}_i$ computed from the mobility trajectories of $u$. Maps: Stamen Maps. Icons: Fontawesome.
• Figure 2: Accuracy of the models. Top-5 accuracy (ACC@5) for Boston, New York City (NYC) and Seattle using models $I$, $C$, and $M$. (A) ACC@5 on the full test set. $M$ shows a performance better than $I$ and $C$ and comparable to Recurrent Neural Networks (RNNs). (B) Models are tested against different train-test overlap scenarios, with 0-20% describing out-of-routine mobility and 80-100% routinary mobility behaviour. $M$ shows improvements in accuracy over $I$ in smaller overlaps, where test trajectories mostly consist of novel transitions never observed during training. (C) Distributions of $M$'s confidence, represented by $1 - S^{(u)}_i$, in relying on individual information $I$. In the case of out-of-routine behaviours (low overlaps), the lower median value of $1 - S^{(u)}_i$ indicates less reliance of $M$ on individual information $I$. In this scenario, collective behaviours $C$ enhance the predictive capabilities of $M$. The peaks observed around $1-S^{(u)}_{i} = 0$ result from instances of transitions from a location $i$ that is not represented in the training trajectories of user $u$. In such a case, we set $S^{(u)}_i = 1$, forcing $M$ to rely only on $C$.
• Figure 3: Spatial distributions of accuracies.(A) Distribution of accuracies for $I$, $C$ and $M$ in predicting movements from a location $i$ (ACC@5$_{i}$). As the test set includes more out-of-routine movements (e.g., 0-40% overlap), model $M$ aided by collective information $C$ performs better. Conversely, the individual model $I$ provides better predictions when tested on routinary trajectories (high overlaps). (B) Spatial autocorrelation of the models' accuracies in corresponding overlaps quantified via the Moran's index. For low overlaps, such as 0-40%, model $C$ exhibits clustered accuracy (large Moran's index). (C) Spatial distribution of ACC@5$_{i}$ in Boston for $I$, $C$ and $M$ in the 0-40% overlap. Notably, for $C$ and $M$, areas with higher accuracies are concentrated in proximity to downtown (upper centre) and Boston Logan International Airport (upper right). Maps: Stamen Maps.
• Figure 4: Statistical properties of collective mobility in Boston.(A) Accuracy of $C$ (ACC@5$_{i}$) from a location $i$ versus its entropy $S_{i}^{(C)}$. We find a negative correlation (Pearson $\rho = -0.86$). (B) Spatial distribution of the number of Points of Interest (POIs) per location, $W_{i}$ (extracted from OpenStreetMap). (Inset) In orange, locations within a distance $D = 2$ km from the location $i^*$ with the largest number of POIs ($W_{i}^*$). In green, locations farther away from $i^*$ by a distance greater than $D$. (C) Distribution of travel distances, $P(r)$, distinguishing between origins within the two aforementioned areas and fitted with a power-law function barbosa2018human in the interval of 0 to 10 km. The exponent of $\gamma = -1.45 \pm 0.04$ underscores the prevalence of localised mobility when individuals are in proximity to $i^*$, while in other areas we have an exponent of $\gamma = -0.92 \pm 0.04$. This result indicates that mobility near POIs tends to be more concentrated and less spatially dispersed towards specific destinations. This behaviour is further corroborated by the entropy $S_{i}^{(C)}$ distribution, which skews towards lower values and indicates mobility directed towards specific tiles. Maps: Stamen Maps.