Data Clustering Using Topological Features

Clustering is one of the most used data mining techniques, while computational topology is a very recent field bridging abstract mathematics with concrete computational techniques. In this paper, we explore the hypothesis that topologically-similar clusters may indicate meaningful relationships. Our approach has an efficient implementation based on computing Minimum Spanning Trees to obtain topological information of each cluster. We then compute a discreteness and a disconnectedness index, used to characterize each cluster, thus allowing the retrieval of equivalence classes. We show that for a real-world high-dimensional network intrusion data set, the topologically-similar clusters retrieved by our approach do indeed correspond to meaningful equivalence classes present in the data set.