  We propose an efficient linear-time graph-based divisive cluster analysis
approach called Reductive Clustering. The approach tries to reveal the
hierarchical structural information through reducing the graph into a more
concise one repeatedly. With the reductions, the original graph can be divided
into subgraphs recursively, and a lite informative dendrogram is constructed
based on the divisions. The reduction consists of three steps: selection,
connection, and partition. First a subset of vertices of the graph are selected
as representatives to build a concise graph. The representatives are
re-connected to maintain a consistent structure with the previous graph. If
possible, the concise graph is divided into subgraphs, and each subgraph is
further reduced recursively until the termination condition is met. We discuss
the approach, along with several selection and connection methods, in detail
both theoretically and experimentally in this paper. Our implementations run in
linear time and achieve outstanding performance on various types of datasets.
Experimental results show that they outperform state-of-the-art clustering
algorithms with significantly less computing resource requirements.
