Efficient construction of an approximate similarity graph for minimum spanning tree based clustering

Abstract

Minimum spanning tree (MST) based unsupervised learning techniques are popular due to their ability to identify intrinsic clusters of heterogeneous structures. One of the important factors which affects their effectiveness is how to construct a sparse similarity graph which can effectively capture the local neighborhood information in sub quadratic time. In this paper, we propose a technique which efficiently uses the local nearest neighbors of data points to construct a similarity graph. The proposed approach consists of two steps. In the first step, the dataset is divided into groups using the dispersion level of data points and then all pair intra-partition edges are computed. In the second step, the boundary data points across the neighboring partitions are considered to produce inter-partition edges for increasing the accuracy. The resulting graph is generated by considering all intra- and inter-partition edges. Approximate MST of the similarity graph is constructed to show its efficacy. Experimental analyses demonstrate that the similarity graph captures shorter edges and discards the longest edges, based on graph diameter, all pair shortest path and weight error of MST. Moreover, the quality of the approximate MST is also validated by applying clustering technique on various synthetic and real data sets of different characteristics and cluster quality analyses demonstrate that it has a satisfying performance over other competing approximate MST construction techniques.