Reductive Clustering: An Efficient Linear-time Graph-based Divisive Cluster Analysis Approach

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.