Fast hierarchical clustering algorithm using locality-sensitive hashing

A hierarchical clustering is a clustering method in which each point is regarded as a single cluster initially and then the clustering algorithm repeats connecting the nearest two clusters until only one cluster remains. Because the result is presented as a dendrogram, one can easily figure out the distance and the inclusion relation between clusters. One drawback of the agglomerative hierarchical clustering is its large time complexity of O(n(2)), which would make this method infeasible against large data, where n expresses the number of the points in the data. This paper proposes a fast approximation algorithm for the single linkage clustering algorithm that is a well-known agglomerative hierarchical clustering algorithm. Our algorithm reduces its time complexity to O(nB) by finding quickly the near clusters to be connected by use of Locality-Sensitive Hashing known as a fast algorithm for the approximated nearest neighbor search. Here B expresses the maximum number of points thrown into a single hash entry and practically grows a simple constant compared to n for sufficiently large hash tables. By experiment, we show that (1) the proposed algorithm obtains similar clustering results to the single linkage algorithm and that (2) it runs faster for large data than the single linkage algorithm.