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

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.

Merging Knockout and Round-Robin Tournaments: A Flexible Linear Elimination Tournament Design

“…Such a loss function will probably have a very convoluted structure and potentially non-convex (hard to solve) [70], [71]. Since it has a very convoluted structure, nonparametric analysis [72], [73] is desirable. Because of these complexities, tournament design is a relatively hard problem.…”