# A-Wardpbeta: Effective hierarchical clustering using the Minkowski metric and a fast k -means initialisation

arXiv: https://arxiv.org/abs/1611.01060 · HTML: https://mlsanity.com/paper/1611.01060/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2016.

## Built on by (most cited first, 1 of 1)

- [Agglomerative Hierarchical Clustering for Selecting Valid Instrumental Variables](https://mlsanity.com/paper/2101.05774/) (2021)

## Abstract (arXiv)

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 pbeta , 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 pbeta provides better cluster recovery than both Ward and Ward p.