Interpretable hierarchical clustering by constructing an unsupervised decision tree

We propose a method for hierarchical clustering based on the decision tree approach. As in the case of supervised decision tree, the unsupervised decision tree is interpretable in terms of rules, i.e., each leaf node represents a cluster, and the path from the root node to a leaf node represents a rule. The branching decision at each node of the tree is made based on the clustering tendency of the data available at the node. We present four different measures for selecting the most appropriate attribute to be used for splitting the data at every branching node (or decision node), and two different algorithms for splitting the data at each decision node. We provide a theoretical basis for the approach and demonstrate the capability of the unsupervised decision tree for segmenting various data sets. We also compare the performance of the unsupervised decision tree with that of the supervised one.