Correlation Analysis

The Correlation analysis is performed on log normalised spot expression levels. Spots can then be clustered according to how closely correlated they are. Spots with a high correlation value (i.e. close to 1) show similar expression profiles while spots which a high negative correlation value (i.e. close to -1) show opposing expression profiles.

What can we do with this information?

Draw a dendrogram showing clusters of spots according to how strongly correlated the spots are. This correlation can be seen in the expression profiles of spots from the same cluster.

What is a Dendrogram?

The dendrogram is a visual representation of the spot correlation data. The individual spots are arranged along the bottom of the dendrogram and referred to as leaf nodes. Spot clusters are formed by joining individual spots or existing spot clusters with the join point referred to as a node. This can be seen in the diagram above. At each dendrogram node we have a right and left sub-branch of clustered spots. In the following discussion, spot clusters can refer to a single spot of a group of spots. The vertical axis is labelled distance and refers to a distance measure between spots or spot clusters. The height of the node can be thought of as the distance value between the right and left sub-branch clusters. The distance measure between two clusters is calculated as follows:

D=1-C

where D = Distance and C = correlation between spot clusters.

If spots are highly correlated, they will have a correlation value close to 1 and so D=1-C will have a value close to zero. Therefore, highly correlated clusters are nearer the bottom of the dendrogram. Spot clusters that are not correlated have a correlation value of zero and a corresponding distance value of 1. Spots that are negatively correlated, i.e. showing opposite expression behaviour, will have a correlation value of -1 and D = 1 - -1 = 2.

As we move up the dendrogram, the spot clusters get bigger and the distance between spot clusters increases in value. It becomes difficult to interpret distance between spot clusters when spot clusters increase in size. A possible way to think about the expression profile behaviour of two spots would be to see how far up the dendrogram you need to go so you can move between the two spots. In the dendrogram above, you see that to get from the spot on the left to the spot in the middle, you need to move up a distance of 0.6 (just follow the branches).

Therefore, you would expect the same general behaviour for these spots. This can be seen in the following expression profile graph

Now, compare the following spot clusters. Cluster 1 (left side and in red), cluster 2 (middle left and in brown) and cluster 3 (middle right and in blue). This illustrates the degree to which you can comment on the distance between spot clusters.

The expression profiles for spots in those clusters are show below.

Finally, looking at all the expression profiles on the main right hand branch, we see that while expression profiles are generally quite similar, there is certainly a variety in individual expression behaviour. In other words, as clusters increase in size, their expression profiles become more general.