The tree structure is generated by
- letting each sampe be a cluster
- calculating pairwise distances between all clusters
- joining the two closest clusters into one new cluster
- iterating 2-3 until there is only one cluster left (which will contain all samples).
(See [Eisen et al., 1998] for a classical example of application of a hierarchical clustering algorithm in microarray analysis. The example is on features rather than samples).
To start the clustering:
Toolbox | Transcriptomics Analysis ()| Quality Control | Hierarchical Clustering of Samples ()
Select a number of samples ( () or ()) or an experiment () and click Next.
This will display a dialog as shown in figure 28.74. The hierarchical clustering algorithm requires that you specify a distance measure and a cluster linkage. The similarity measure is used to specify how distances between two samples should be calculated. The cluster distance metric specifies how you want the distance between two clusters, each consisting of a number of samples, to be calculated.
- Euclidean distance. The ordinary distance between two points - the length of the segment connecting them. If
then the Euclidean distance between and is
- 1 - Pearson correlation. The Pearson correlation coefficient between two elements
is defined as
- Manhattan distance. The Manhattan distance between two points is the distance measured along axes at right angles. If
then the Manhattan distance between and is
- Single linkage. The distance between two clusters is computed as the distance between the two closest elements in the two clusters.
- Average linkage. The distance between two clusters is computed as the average distance between objects from the first cluster and objects from the second cluster. The averaging is performed over all pairs , where is an object from the first cluster and is an object from the second cluster.
- Complete linkage. The distance between two clusters is computed as the maximal object-to-object distance , where comes from the first cluster, and comes from the second cluster. In other words, the distance between two clusters is computed as the distance between the two farthest objects in the two clusters.
At the bottom, you can select which values to cluster (see Selecting transformed and normalized values for analysis).
Click Next if you wish to adjust how to handle the results. If not, click Finish.