Different linking methods used in hierarchical clustering

Hierarchical clustering is an unsupervised learning technique that groups similar observations based on distance or similarity measures. The linking method determines how distances between clusters are calculated.

This article will introduce the link methods used in hierarchical clustering, including single link, complete link, average link and sum of squares of deviation method.

Single linkage (Single linkage) is also called the nearest neighbor link, which defines the distance between two clusters as the shortest distance between any two points in the two clusters. In other words, the distance between two clusters is determined by the distance between their closest points. However, this approach often results in long chains of clusters and is very sensitive to outliers and noise in the data.

Complete linkage (Ccomplete linkage), also known as the farthest neighbor link, uses the longest distance between any two points in two clusters to determine the distance between two clusters. This means that the distance between two clusters is defined by the distance between their farthest points. Full linkage methods tend to produce compact spherical clusters that are less sensitive to outliers and noise in the data.

The average linkage method calculates the distance between two clusters as the average distance between all pairs of points in the two clusters. This approach tends to produce cluster morphologies intermediate between the long chain-like clusters generated by single links and the compact spherical clusters generated by complete links.

The Ward linkage method, also known as the minimum variance linkage, is used to determine the distance between two clusters by minimizing the increase in variance when the two clusters are merged. This method tends to generate clusters with similar variance and size.

The choice of linking method used in hierarchical clustering has an important impact on the clustering results. Different linking methods lead to different clustering outputs. Single linkage methods tend to form long chains of clusters, full linkage methods produce compact spherical clusters, and average linkage methods produce clusters in between. Additionally, the sum-of-squares rule of deviations produces clusters with similar variances and sizes. Before choosing a specific linking method, we need to carefully consider the characteristics of the data as well as the current task goals, as this will have an important impact on the clustering results.

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