Natural Hierarchical Cluster Analysis by Nearest Neighbors with Near-Linear Time Complexity

TL;DR

This paper introduces a universal hierarchical clustering algorithm based on nearest neighbors that naturally produces a hierarchy and operates with near-linear time complexity for specific datasets.

Contribution

The paper presents a novel nearest neighbor based clustering method that is independent of iterative procedures and can be implemented in both bottom-up and top-down manners with consistent results.

Findings

Achieves near-linear time complexity on certain datasets

Produces a natural hierarchy of clusters directly from data

Works as both bottom-up and top-down approach

Abstract

We propose a nearest neighbor based clustering algorithm that results in a naturally defined hierarchy of clusters. In contrast to the agglomerative and divisive hierarchical clustering algorithms, our approach is not dependent on the iterative working of the algorithm, in the sense that the partitions of the hierarchical clusters are purely defined in accordance with the input dataset. Our method is a universal hierarchical clustering approach since it can be implemented as bottom up or top down versions, both of which result in the same clustering. We show that for certain types of datasets, our algorithm has near-linear time and space complexity.