Fast approximate minimum spanning tree based clustering algorithm

Abstract

Minimum Spanning Tree (MST) based clustering algorithms have been employed successfully to detect clusters of heterogeneous nature. Given a dataset of n random points, most of the MST-based clustering algorithms first generate a complete graph G of the dataset and then construct MST from G. The first step of the algorithm is the major bottleneck which takes O(n2) time. This paper proposes an algorithm namely MST-based clustering on partition-based nearest neighbor graph for reducing the computational overhead. By using a centroid based nearest neighbor rule, the proposed algorithm first generates a sparse Local Neighborhood Graph (LNG) and then the approximate MST is constructed from LNG. We prove that both size and computational time to construct the graph (LNG) is O(n3/2), which is a O(n) factor improvement over the traditional algorithms. The approximate MST is constructed from LNG in O(n3/2lgn) time, which is asymptotically faster than O(n2). Experimental analysis on both synthetic and real datasets demonstrates that the computational time has been reduced significantly by maintaining the quality of clusters obtained from the approximate MST.