Identifying prototypical components in behaviour using clustering algorithms

Abstract

Quantitative analysis of animal behaviour is a requirement to understand the task solving strategies of animals and the underlying control mechanisms. The identification of repeatedly occurring behavioural components is thereby a key element of a structured quantitative description. However, the complexity of most behaviours makes the identification of such behavioural components a challenging problem. We propose an automatic and objective approach for determining and evaluating prototypical behavioural components. Behavioural prototypes are identified using clustering algorithms and finally evaluated with respect to their ability to represent the whole behavioural data set. The prototypes allow for a meaningful segmentation of behavioural sequences. We applied our clustering approach to identify prototypical movements of the head of blowflies during cruising flight. The results confirm the previously established saccadic gaze strategy by the set of prototypes being divided into either predominantly translational or rotational movements, respectively. The prototypes reveal additional details about the saccadic and intersaccadic flight sections that could not be unravelled so far. Successful application of the proposed approach to behavioural data shows its ability to automatically identify prototypical behavioural components within a large and noisy database and to evaluate these with respect to their quality and stability. Hence, this approach might be applied to a broad range of behavioural and neural data obtained from different animals and in different contexts.

Figure 1. Hierarchical clustering approach.

A) Artificial data of a two dimensional feature set. B) Dendrogram of applying agglomerative hierarchical clustering using Ward's criterion on the data shown in A. The x-axis indicates individual data points from A. C) Joining costs plotted against the number of clusters. D) Differential joining costs for the interesting range of number of clusters. Costs increase significantly if the algorithm groups the data in less than five clusters.

Figure 2. K-means clustering approach.

A) Two dimensional artificial feature vectors to be clustered. B) Solid lines divide the feature space into Voronoi cells for the random centroid starting positions. Each of the cell's centroids is denoted by an individual marker. C) Voronoi plots of the nine steps needed by a k-means algorithm to find five stable clusters. The greyness of lines and markers indicates to which step of clustering they belong. D) The final clustering is shown in black above the data in grey. E,F) Results of clustering assuming an improper numbers of clusters.

Figure 3. Evaluations for k-means clustering the artificial data of Figures 1 and 2.

The number of clusters and the data sets are varied. A) Instability values. B) Mean quality values. C) Mean quality of mean set for each number of clusters, respectively.

Figure 4. Quality values and centroid visualisation for individual clusters within the complete artificial data set.

Clusters result from determining the mean set of four and five centroids, respectively. Visualisation of the five centroids as modified star plots, see text for explanation.

Figure 5. Calculating fly head velocity features.

A) The fly head fixed coordinate system used for calculating three translational and three rotational velocities. B) PCA analysis of the two different sets of Calliphora head velocity data. Part of the covered data variance in dependence on the number of principal components taken into account. C) Visualisation of the principal components sorted in decreasing order of variance content, each.

Figure 6. Hierarchical clustering of normalised Calliphora head velocity data.

Three different data segments containing 5000 data points each were clustered using Ward's joining criterion. A) Joining costs in dependence on the remaining number of clusters. B) The deviation of the cost function for the most interesting range of fewer than 100 clusters.

Figure 7. Criteria for validating the k-means clustering results for the normalised Calliphora head velocity data.

Instability A) within and B) between data set configurations and C) quality of clustering results in dependence on the number of clusters for varying data sets. D) Individual quality values for mean nine centroids of the complete data set.

Figure 8. Mean set of nine centroids calculated based on the normalised complete data set for Calliphora free flight head velocity data.

The part of the data in percent assigned to the individual centroid is given with each centroid.

Figure 9. Mean set of nine velocity prototypes for Calliphora head data.

Feature values are accomplished with physical units: m/s for translational, deg/ms for rotational velocities. Note the different scales for the rotationally and translationally dominated prototypes.

Figure 10. Segmentation of behavioural sequences into prototypical movements.

A) Overall occurring lengths of prototypical movements for the individual prototypes. B) Velocity data and individually assigned velocity prototypes (prototype numbers as in Figure 9) for an exemplary part of a fly head trajectory. C) Segmentation of the example trajectory into prototypical movements. For better visualisation the trajectory is projected into two dimensions, just yaw rotation is shown, and the four saccadic prototypes are summarized resulting in six remaining differently coloured prototypes.