A dendrogram (from Greek dendro "tree" and gramma "drawing") is a tree diagram widely used to illustrate the arrangement of the clusters produced by hierarchical clustering. The hierarchical clustering algorithms begin with each object in individual clusters. At every step, the two clusters that are most similar are joined into a single new cluster. Once fused, objects are never separated. Dendrograms are often used in computational biology to illustrate the clustering of genes, proteins, metabolites or samples.
Distance Method of hierarchical clustering specifies with Euclidean or Manhattan distance is used. Euclidean distance is used more widely. Euclidean distance may be considered as straight-line distance. Manhattan distance is often referred to as city-block distance since it is analogous to walking along an imaginary sidewalk to get from point A to B.
The followings are the most commonly used methods that represent eight methods of defining the similarity between clusters:
- Simple Average (Weighted Pair-Group)
- Group Average (Unweighted Pair-Group)
- Single Linkage (Nearest Neighbor)
- Complete Linkage (Furthest Neighbor)
- Flexible Strategy Requires the Distance Method to be Euclidean
- Ward’s Minimum Variance Requires the Distance Method to be Euclidean
- Median (Weighted Pair-Group Centroid) Requires the Distance Method to be Euclidean
- Centroid (Unweighted Pair-Group Centroid) Requires the Distance Method to be Euclidean
The horizontal axis of the above dendrogram represents the distance or dissimilarity between different clusters. The vertical axis represents the clusters and objects. The main interest of researchers is in similarity and clustering. Each joining of two clusters is represented on this graph by splitting a horizontal line into two horizontal lines. The horizontal position of the split that was shown by the short vertical bar gives the distance (dissimilarity) between the two clusters.
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