Nesting the earth mover's distance for effective cluster tracing

Cluster tracing algorithms are used to mine temporal evolutions of clusters. Generally, clusters represent groups of objects with similar values. In a temporal context like tracing, similar values correspond to similar behavior in one snapshot in time. Recently, tracing based on object-value-similarity was introduced. In this new paradigm, the decision whether two clusters are considered similar is based on the similarity of the clusters' object values. Existing approaches of this paradigm, however, have a severe limitation. The mapping of clusters between snapshots in time is performed pairwise, i.e. global connections between a temporal snapshot's clusters are ignored; thus, impacts of other clusters that may affect the mapping are not considered and incorrect cluster tracings may be obtained. In this vision paper, we present our ongoing work on a novel approach for cluster tracing that applies the object-value-similarity paradigm and is based on the well-known Earth Mover's Distance (EMD). The EMD enables a cluster tracing that uses global mapping: in the mapping process, all clusters of compared snapshots are considered simultaneously. A special property of our approach is that we nest the EMD: we use it as a ground distance for itself to achieve most effective value-based cluster tracing.