Many biological systems exhibit collective behaviors that strengthen their adaptability to their environment, compared to more solitary species. Describing these behaviors is challenging yet necessary in order to understand these biological systems. We propose a probabilistic model that enables us to uncover the collective behaviors observed in a colony of ants. This model is based on the assumption that the behavior of an individual ant is a time-dependent mixture of latent behaviors that are specific to the whole colony. We apply this model to a large-scale dataset obtained by observing the mobility of nearly 1000 Camponotus fellah ants from six different colonies. Our results indicate that a colony typically exhibits three classes of behaviors, each characterized by a specific spatial distribution and a level of activity. Moreover, these spatial distributions, which are uncovered automatically by our model, match well with the ground truth as manually annotated by domain experts. We further explore the evolution of the behavior of individual ants and show that it is well captured by a second order Markov chain that encodes the fact that the future behavior of an ant depends not only on its current behavior but also on its preceding one.

We are interested in inferring the set of waypoints (or intermediate destinations) of a mobility trajectory in the absence of timing information. We find that, by mining a dataset of real mobility traces, computing the entropy of conditional Markov trajectory enables us to uncover waypoints, even though no timing information nor absolute geographic location is provided. We build on this observation and design an efficient algorithm for trajectory segmentation. Our empirical evaluation demonstrates that the entropy-based heuristic used by our segmentation algorithm outperforms alternative approaches as it is 43% more accurate than a geometric approach and 20% more accurate than path-stretch based approach. We further explore the link between trajectory entropy, mobility predictability and the nature of intermediate locations using a route choice model on real city maps.

Geotagged data can be used to describe regions in the world and discover local themes. However, not all data produced within a region is necessarily specifically descriptive of that area. To surface the content that is characteristic for a region, we present the geographical hierarchy model (GHM), a probabilistic model based on the assumption that data observed in a region is a random mixture of content that pertains to different levels of a hierarchy. We apply the GHM to a dataset of 8 million Flickr photos in order to discriminate between content (i.e. tags) that specifically characterizes a region (e.g. neighborhood) and content that characterizes surrounding areas or more general themes. Knowledge of the discriminative and non-discriminative terms used throughout the hierarchy enables us to quantify the uniqueness of a given region and to compare similar but distant regions. Our evaluation demonstrates that our model improves upon traditional Naive Bayes classification by 47% and hierarchical TF-IDF by 27%. We further highlight the differences and commonalities with human reasoning about what is locally characteristic for a neighborhood, distilled from ten interviews and a survey that covered themes such as time, events, and prior regional knowledge.

To quantify the randomness of Markov trajectories with fixed initial and final states, Ekroot and Cover proposed a closed-form expression for the entropy of trajectories of an irreducible finite state Markov chain. Numerous applications, including the study of random walks on graphs, require the computation of the entropy of Markov trajectories conditional on a set of intermediate states. However, the expression of Ekroot and Cover does not allow for computing this quantity. In this paper, we propose a method to compute the entropy of conditional Markov trajectories through a transformation of the original Markov chain into a Markov chain that exhibits the desired conditional distribution of trajectories. Moreover, we express the entropy of Markov trajectories-a global quantity-as a linear combination of local entropies associated with the Markov chain states.