Dendrogram

A dendrogram (from Greek

Greek language

Greek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical...

 dendron "tree", -gramma "drawing") is a tree

Tree (graph theory)

In mathematics, more specifically graph theory, a tree is a graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree...

 diagram frequently used to illustrate the arrangement of the clusters produced by hierarchical clustering

Hierarchical clustering

In statistics, hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types:...

. Dendrograms are often used in computational biology

Computational biology

Computational biology is an interdisciplinary field that applies the techniques of computer science, applied mathematics and statistics to address biological problems. The main focus lies on developing mathematical modeling and computational simulation techniques...

 to illustrate the clustering of gene

Gene

A gene is the basic unit of heredity in a living organism. All living things depend on genes. Genes hold the information to build and maintain their cells and pass genetic traits to offspring...

s.

A dendrogram (from Greek

Greek language

Greek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical...

 dendron "tree", -gramma "drawing") is a tree

Tree (graph theory)

In mathematics, more specifically graph theory, a tree is a graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree...

 diagram frequently used to illustrate the arrangement of the clusters produced by hierarchical clustering

Hierarchical clustering

In statistics, hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types:...

. Dendrograms are often used in computational biology

Computational biology

Computational biology is an interdisciplinary field that applies the techniques of computer science, applied mathematics and statistics to address biological problems. The main focus lies on developing mathematical modeling and computational simulation techniques...

 to illustrate the clustering of gene

Gene

A gene is the basic unit of heredity in a living organism. All living things depend on genes. Genes hold the information to build and maintain their cells and pass genetic traits to offspring...

s.

For a clustering example, suppose this data is to be clustered using Euclidean distance

Euclidean distance

In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" distance between two points that one would measure with a ruler, and is given by the Pythagorean formula. By using this formula as distance, Euclidean space becomes a metric space...

 as the distance metric

Metric (mathematics)

In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric...

.

The hierarchical clustering

Hierarchical clustering

In statistics, hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two types:...

dendrogram would be as such:

Here the top row of nodes represent data, and the remaining nodes represent the clusters to which the data belong, and the arrows represent the distance.