A-Ward_p\b{eta}: Effective hierarchical clustering using the Minkowski metric and a fast k -means initialisation

TL;DR

This paper introduces A-Ward and A-Ward pta, novel hierarchical clustering methods that improve convergence speed and clustering flexibility by using an anomalous pattern initialisation and extending Ward algorithms with Minkowski metric variations.

Contribution

The paper presents a new initialisation technique for hierarchical clustering and extends Ward algorithms to allow different feature weight and distance exponents, enhancing clustering performance.

Findings

A-Ward reduces clustering convergence time significantly.

A-Ward pta achieves better cluster recovery than Ward and Ward p.

Parameters can be effectively estimated using a cluster validity index.

Abstract

In this paper we make two novel contributions to hierarchical clustering. First, we introduce an anomalous pattern initialisation method for hierarchical clustering algorithms, called A-Ward, capable of substantially reducing the time they take to converge. This method generates an initial partition with a sufficiently large number of clusters. This allows the cluster merging process to start from this partition rather than from a trivial partition composed solely of singletons. Our second contribution is an extension of the Ward and Ward p algorithms to the situation where the feature weight exponent can differ from the exponent of the Minkowski distance. This new method, called A-Ward p\b{eta} , is able to generate a much wider variety of clustering solutions. We also demonstrate that its parameters can be estimated reasonably well by using a cluster validity index. We perform numerous experiments using data sets with two types of noise, insertion of noise features and blurring within-cluster values of some features. These experiments allow us to conclude: (i) our anomalous pattern initialisation method does indeed reduce the time a hierarchical clustering algorithm takes to complete, without negatively impacting its cluster recovery ability; (ii) A-Ward p\b{eta} provides better cluster recovery than both Ward and Ward p.