dendrogrammi

A dendrogram, or dendrogrammi in some languages, is a tree-like diagram used to illustrate the arrangement of clusters produced by hierarchical clustering or to show relationships among items based on a measure of similarity or distance. It is widely used in statistics, bioinformatics, data mining, and related fields to visualize how data group together at different levels of similarity.

In construction, a data set of items is first transformed into a distance or dissimilarity matrix. A hierarchical clustering algorithm—commonly agglomerative (bottom-up) or divisive (top-down)—then merges or splits clusters step by step. The resulting diagram has leaves that correspond to the original items and internal nodes representing clusters formed at successive steps. The vertical axis (height) typically reflects the distance or dissimilarity at which merges occur. By “cutting” the dendrogram at a chosen height, one can define a set of clusters corresponding to a desired level of similarity.

Variants of dendrograms arise from different linkage criteria and distance metrics. Linkage methods such as single, complete, average, and Ward’s criterion influence where branches join, while distance measures (Euclidean, Manhattan, correlation-based, etc.) shape the overall tree. Some clustering methods yield ultrametric trees, as in UPGMA, where all leaves lie at the same distance from the root.

Limitations include sensitivity to scaling, metric choice, and linkage method; different analyses can produce substantially different trees. Dendrograms are descriptive tools that summarize hierarchical relationships but do not in themselves prove evolutionary ancestry or causation. They are commonly employed in gene expression analysis, taxonomy, ecology, and market research to explore structure in complex data.