Hierarchical clustering of samples
A hierarchical clustering of samples is a tree representation of their relative similarity. The tree structure is generated by
- letting each feature 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).
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 28.81. 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.
Figure 28.80: Parameters for hierarchical clustering of samples.
At the top, you can choose three kinds of Distance measures:
- Euclidean distance. The ordinary distance between two points - the length of the segment connecting them. If
and
, then the Euclidean distance between
and
is
- 1 - Pearson correlation. The Pearson correlation coefficient between two elements
and
is defined as
is the average of values in
and
is the sample standard deviation of these values. It takes a value
. Highly correlated elements have a high absolute value of the Pearson correlation, and elements whose values are un-informative about each other have Pearson correlation 0. Using
as distance measure means that elements that are highly correlated will have a short distance between them, and elements that have low correlation will be more distant from each other.
- Manhattan distance. The Manhattan distance between two points is the distance measured along axes at right angles. If
and
, then the Manhattan distance between
and
is
Next, you can select the cluster linkage to be used:
- 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.
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