Dimensionality reduction & clustering / Hierarchical clustering
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Hierarchical clustering merges the most similar objects step by step into a tree: the lower two branches join, the more similar the objects. The dashed line marks the cut, and branches of the same colour form one cluster.
The distance and linkage determine the result: expression profiles commonly use “1 − correlation” or Euclidean distance (after z-scoring) with average linkage; Ward’s method (R ward.D2) needs Euclidean distance and tends to give compact clusters of similar size.
The cophenetic correlation measures how faithfully the tree reflects the original distances; values above about 0.75 indicate a good representation.
The heatmap orders rows by the dendrogram leaves and shows z-scores of each variable (limited to ±2.5), which helps to see the variables that characterise each cluster.
Clustering always produces clusters; whether they are stable and biologically meaningful needs other evidence.
Müllner D. (2011) arXiv:1109.2378; Murtagh & Legendre (2014) J Classif 31:274–295 (Ward ward.D2); Sokal & Rohlf (1962) Taxon 11:33–40 (cophenetic correlation). Linkage matrix, tree cutting and cophenetic distances match scipy.cluster.hierarchy (linkage, fcluster, cophenet).
Up to 3,000 objects; the heatmap is drawn for up to 400 objects and 200 variables.
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