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Hierarchical clustering is a powerful unsupervised learning technique used to group similar observations together based on their distance or similarity measures. The linkage method used in hierarchical clustering determines how the distance between clusters is calculated. There are several linkage methods used in hierarchical clustering, including single linkage, complete linkage, average linkage, and ward linkage.
Single linkage, also known as nearest neighbor linkage, determines 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 defined by the distance between their closest points. This method tends to produce long, chain-like clusters that are sensitive to outliers and noise in the data.
Complete linkage, also known as farthest neighbor linkage, determines the distance between two clusters as the longest distance between any two points in the two clusters. In other words, the distance between two clusters is defined by the distance between their farthest points. This method tends to produce compact, spherical clusters that are less sensitive to outliers and noise in the data.
Average linkage determines the distance between two clusters as the average distance between all pairs of points in the two clusters. This method tends to produce clusters that are somewhere between the long, chain-like clusters produced by single linkage and the compact, spherical clusters produced by complete linkage.
Ward linkage, also known as minimum variance linkage, determines the distance between two clusters by minimising the increase in variance when the two clusters are merged. This method tends to produce clusters that have similar variances and sizes.
Therefore, the choice of linkage method used in hierarchical clustering can greatly affect the clustering output. Single linkage tends to produce long, chain-like clusters, complete linkage produces compact, spherical clusters, average linkage produces clusters that are somewhere between the two, and ward linkage produces clusters with similar variances and sizes. It is important to carefully consider the characteristics of the data and the research question at hand before selecting a particular linkage method.
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