Extending the Functionality of Behavioural Change-Point Analysis with k-Means Clustering: A Case Study with the Little Penguin (Eudyptula minor)

Abstract

We present a simple framework for classifying mutually exclusive behavioural states within the geospatial lifelines of animals. This method involves use of three sequentially applied statistical procedures: (1) behavioural change point analysis to partition movement trajectories into discrete bouts of same-state behaviours, based on abrupt changes in the spatio-temporal autocorrelation structure of movement parameters; (2) hierarchical multivariate cluster analysis to determine the number of different behavioural states; and (3) k-means clustering to classify inferred bouts of same-state location observations into behavioural modes. We demonstrate application of the method by analysing synthetic trajectories of known ‘artificial behaviours’ comprised of different correlated random walks, as well as real foraging trajectories of little penguins (Eudyptula minor) obtained by global-positioning-system telemetry. Our results show that the modelling procedure correctly classified 92.5% of all individual location observations in the synthetic trajectories, demonstrating reasonable ability to successfully discriminate behavioural modes. Most individual little penguins were found to exhibit three unique behavioural states (resting, commuting/active searching, area-restricted foraging), with variation in the timing and locations of observations apparently related to ambient light, bathymetry, and proximity to coastlines and river mouths. Addition of k-means clustering extends the utility of behavioural change point analysis, by providing a simple means through which the behaviours inferred for the location observations comprising individual movement trajectories can be objectively classified.

Deriving Animal Movement Behaviors Using Movement Parameters Extracted from Location Data

“…BCPA is acknowledged in the literature as a good method for segmenting movement paths efficiently, and it is relatively straightforward to implement. The method developed by Zhang et al [21] is directly comparable to our method, since it also applies BCPA. Zhang et al [21] used a three-step framework, including BCPA, hierarchical multivariate cluster analysis, and k-means clustering.…”

“…The method developed by Zhang et al [21] is directly comparable to our method, since it also applies BCPA. Zhang et al [21] used a three-step framework, including BCPA, hierarchical multivariate cluster analysis, and k-means clustering. Hierarchical multivariate cluster analysis is required to determine the number of clusters (k) before doing k-mean clustering.…”

“…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.…”

“…Unlike the approach in [21], for each segment we consider the overall distribution of the movement parameters (in our case, persistence velocity), rather than a specific parameter like central tendency. We use the Kolmogorov-Smirnov (ks) distance [52] to determine the distance between the segments' persistence velocity distributions.…”

“…Hierarchical multivariate cluster analysis is required to determine the number of clusters (k) before doing k-mean clustering. We wanted to consider the overall distribution of the movement parameter values in the clustering process, rather than a specific statistic like central tendency or median as used in [21]. With our approach, we also do not have to worry about seed selection, which k-means is sensitive to.…”