Expectation-Maximization Binary Clustering for Behavioural Annotation

Abstract

The growing capacity to process and store animal tracks has spurred the development of new methods to segment animal trajectories into elementary units of movement. Key challenges for movement trajectory segmentation are to (i) minimize the need of supervision, (ii) reduce computational costs, (iii) minimize the need of prior assumptions (e.g. simple parametrizations), and (iv) capture biologically meaningful semantics, useful across a broad range of species. We introduce the Expectation-Maximization binary Clustering (EMbC), a general purpose, unsupervised approach to multivariate data clustering. The EMbC is a variant of the Expectation-Maximization Clustering (EMC), a clustering algorithm based on the maximum likelihood estimation of a Gaussian mixture model. This is an iterative algorithm with a closed form step solution and hence a reasonable computational cost. The method looks for a good compromise between statistical soundness and ease and generality of use (by minimizing prior assumptions and favouring the semantic interpretation of the final clustering). Here we focus on the suitability of the EMbC algorithm for behavioural annotation of movement data. We show and discuss the EMbC outputs in both simulated trajectories and empirical movement trajectories including different species and different tracking methodologies. We use synthetic trajectories to assess the performance of EMbC compared to classic EMC and Hidden Markov Models. Empirical trajectories allow us to explore the robustness of the EMbC to data loss and data inaccuracies, and assess the relationship between EMbC output and expert label assignments. Additionally, we suggest a smoothing procedure to account for temporal correlations among labels, and a proper visualization of the output for movement trajectories. Our algorithm is available as an R-package with a set of complementary functions to ease the analysis.

Geographical variation in the foraging behaviour of the pantropical red-footed booby

“…Values of the dependent variables are given as mean ± standard deviation. The Marascuilo (1966) procedure was used to compare the pairwise proportions of the behaviours defined according to the EMbC algorithm (Garriga et al 2016) among breeding colonies. …”

“…To determine the different behaviours of individuals during their foraging trips, we used the Expectation Maxi misation binary Clustering (EMbC) algorithm (Garriga et al 2016), a variant of the maximum likelihood estimation of Gaussian mixture models (Redner & Walker 1984). The EMbC algorithm is a robust, non-supervised multi-variate clustering algorithm that considers correlation and un certainty of variables, giving a meaningful local labelling easily linked to biological interpretations.…”

“…A smoothing procedure in clu ded in the package was applied to better account for the temporal associations among behaviours. All trips from all breeding colonies were treated simultaneously in the analysis which was conducted with the R package EMbC (Garriga et al 2016). Proportions of each behaviour along tracks were compared between sites and during daytime or night-time, i.e.…”

Path segmentation for beginners: an overview of current methods for detecting changes in animal movement patterns

“…Different methods for answering the three type of broad research questions (study aims) are listed together with the analytical category they stem from, a short description of each method as well as the considered categories of input path-signals and important referencesStudy aimMethodAnalytical categoryDescriptionInput signalReferencesMovement pattern descriptionThresholdingTopology-basedApplies thresholding schemes (cut-off values) to separate relocations into different groups based on single or multiple path parameters (e.g., short- vs. Long-range movements)Primary and secondary signals[45, 80, 84, 127]Supervised ClassificationTopology-basedRelocations (steps) of a trajectory are assigned to certain classes of movement behavior based on a classification scheme fitted with a training datasetPrimary and secondary signals, additional information like activity data[129–131]ClusteringTopology-basedUnsupervised classification for identifying distinctive groups within a multivariate set of path-signalsPrimary and secondary signals, additional information like activity data[21, 132]Bayesian Partitioning of Markov Models (BPMM)Topology- and time- series basedClassification algorithm for determining the number and sequence of homogenous classes within a sequential path-signal (time series)Primary and secondary signals[35, 91, 92]Change-point detectionLine SimplificationTopology- or time-series basedTests whether reducing the number of vertices in a trajecotry significantly impacts path topology to determine change points (can also be applied with graphs of sequential path-signals)Primitive signals (spatial position)[12, 133]Change Point TestTopology-basedDetects significant changes in the observed movement direction (orientation) between the starting point and an attraction point of a trajectoryPrimitive signals (spatial position)[86, 134]Spatio-Temporal Criteria SegmentationTopology-basedSpecial type of thresholding seeking optimal segmentation of a trajectory based on monotone criteria: relocations are included in a segment as long as they fullfill certain predefined requirementsPrimitive, primary and secondary signals[32, 87]Piecewise RegressionTime-series analysis…”

Deriving Animal Movement Behaviors Using Movement Parameters Extracted from Location Data

“…From the animal movement behavior perspective, clustering analysis can be applied as either a main analysis [46][47][48] or a subsequent analysis [7,21] to infer movement behavior components from bio-logged movement data, including location data and activity sensor data.…”