DBA and K-means clustering : Explainability problems for research on behaviors and strategies

Overview & Synopsis

Studying creative problem solving (CPS) activities can enrich our understanding of human learning by facilitating the observation of behaviors related to realistic situations of complex open-ended problem solving . Actions taken by an individual in such activities are situated in time, thus allowing the creation of time sequences of observations. These observations are not purely numerical, and thus can be represented by symbolic time sequences. In particular, the formal analysis of such time sequences leads to a better understanding of the role of temporality in the adoption of CPS strategies. For this, we propose to apply clustering algorithms in order to group sequences in categories that could be associated with emergent behavioral patterns, either at the whole activity level or at the level of subsequences of actions. Clustering requires the definition of a distance between symbolic data structures representing observations, used to determine the distance (more precisely dissimilarity), and the capacity to interpret such clusters. Our ongoing research uses Dynamic Time Warping (DTW) as an algorithm to compute dissimilarity between sequences. This technical report addresses the issue of computing a K-means clustering algorithm and centroids with DTW for symbolic sequences, using an approximation algorithm named DTW Barycenter Averaging (DBA). It appears that DBA for symbolic sequences is not relevant as it produces non-explainable sequences for the pattern analysis, but this negative result is of interest and allows us to propose an alternative. Clustering algorithms using medoids will be preferred in future research, and we explain why in this report.