linkagemetoder

Linkage methods (linkagemetoder in Swedish) are techniques used in hierarchical clustering to determine the distance between clusters during the agglomerative process. At each step, two clusters are merged based on a chosen linkage criterion, which specifies how the distance between clusters should be computed from the pairwise distances of their members. The method chosen influences the shape and composition of the resulting clusters and affects the interpretation of the dendrogram.

Common linkage methods include single linkage, where the distance between two clusters is the minimum distance between any pair of observations from the clusters; this method tends to produce long, chain-like clusters and is sensitive to outliers. Complete linkage uses the maximum pairwise distance and tends to yield more compact clusters, but can fragment larger clusters. Average linkage (UPGMA) uses the average of all cross-cluster distances, providing a balance between chaining and compactness. Ward's method minimizes the increase in within-cluster sum of squares at each merge, often producing compact, spherical clusters. Centroid and median linkages compute distances between cluster centroids or medoids and can lead to inversions in the dendrogram or non-monotone merges in some datasets.

The choice of linkage method depends on data characteristics and analysis goals. Single linkage emphasizes connectivity and can reveal irregular shapes but is sensitive to noise; Ward's method emphasizes compactness and tends to yield well-separated clusters. Practitioners often standardize or scale data and select a distance metric consistent across methods. These linkage criteria are widely implemented in statistical software and are central to exploratory data analysis in unsupervised learning.