K-means for semantically enriched trajectories

Abstract

Clustering a set of given objects is a standard component of many data analysis tasks. The well-known k-means algorithm is a centroid-based clustering algorithm that optimizes the sum of distances between data objects and their assigned cluster centers. Each centroid then represents all objects assigned to a given cluster. In this paper, we study the special case of clustering semantically enriched spatio-temporal trajectories, i. e., trajectories where each trace point can be annotated with arbitrary, possibly categorical semantic data in addition to numerical spatio-temporal data. Such trajectories result from, e. g., tracking animals, humans, or weather phenomena and capture semantic contexts analysts may want to be aware of when interpreting the resulting clusters. Most current clustering algorithms for spatio-temporal categories take into account the numerical spatio-temporal coordinates only; thus, the resulting clusters do not necessarily reflect the characteristics of the additional semantic data. Building upon our earlier work on computing a representative trajectory for a given set of semantically enriched spatio-temporal trajectories, we describe how to implement the k-means algorithm to work with such data. In particular, we define a similarity measure called EFSMSim between a trajectory and a graph-based representation of a cluster centroid and show how to use this in the context of the k-means algorithm. We evaluate our EFSMClust approach by comparing it with state-of-the-art clustering algorithms taking into account either spatio-temporal information only or semantic attributes as well. Our experiments show that our algorithm is competitive even with respect to purely geometric performance measure and at the same time returns a representation of the centroids that can be used by domain experts to interpret both spatio-temporal and semantic information as well as to explore their possible relationships.