On the Properties of α-Unchaining Single Linkage Hierarchical Clustering

Abstract

In the election of a hierarchical clustering method, theoretic properties may give some insight to determine which method is the most suitable to treat a clustering problem. Herein, we study some basic properties of two hierarchical clustering methods: α-unchaining single linkage or SL(α) and a modified version of this one, SL * (α). We compare the results with the properties satisfied by the classical linkage-based hierarchical clustering methods.

Accelerated Hierarchical Density Based Clustering

“…Hartigan's results while impressive, only apply to one dimensional data. The commonly cited drawback of single linkage clustering is that it is not robust to noise and suffers from chaining effects (spurious points merging clusters prematurely) [38], [61]. Wishart proposed a heuristic algorithm as a potential solution to this in [61].…”

“…Unfortunately this approach, much like the Čech complex, is too computationally expensive to construct for all but trivial cases. Other alternative, but similar, approaches are proposed in [37] and [38], however we will follow Lesnick and Wright [31] for a computationally tractable density-sensitive simplicial complex construction.…”

Editorial

“…In the fifth paper, Alvaro Martinez-Perez introduces a densitysensitive hierarchical clustering method. This work is an extension of his prior work α-unchaining single-linkage clustering (Martinez-Perez, 2016). This paper focuses on the single-linkage clustering algorithm that is famously known to have the "best" mathematical properties (Jardine and Sibson, 1971) and performs quite poorly when attempting to recover cluster structure that is known a-priori (see Milligan, 1980, for example).…”