How can I perform 'Hierarchical Clustering' by Absolute value of correlation?

I'm trying to do hierarchical clustering in MATLAB using 'linkage' and 'pdist' functions. I'm familiar with the functions, but I'm attempting to cluster by the absolute value of the correlation values.

The default for the 'pdist' function, 'correlation', would include both the positive and negatives, but I'm interested in grouping inverse relationships as well.

Does anyone know how I can achieve this?

Answer 1

[MathWorks Support Team]

There are two ways in which this can be done:

First, notice that 'pdist' computes one minus the correlations among rows:

>> x
x =
     1     2     3     4
     2     3     2     3
     1     2     3     4
     4     3     2     1

>> pdist(x,'cor')
ans =
    0.5528         0    2.0000    0.5528    1.4472    2.0000

>> 1-corr(x')
ans =
         0    0.5528         0    2.0000
    0.5528         0    0.5528    1.4472
         0    0.5528         0    2.0000
    2.0000    1.4472    2.0000         0

1) The first way is to compute the distance as one minus the absolute correlation, and compute linkage based on that.

>> D = pdist(x,'cor');

>> linkage(D,'single')
ans =
    1.0000    3.0000         0
    2.0000    5.0000    0.5528
    4.0000    6.0000    1.4472

>> C = 1-D % get correlation
C =
    0.4472    1.0000   -1.0000    0.4472   -0.4472   -1.0000

>> D = 1-abs(C) % get 1-abs(correlation)
D =
    0.5528         0         0    0.5528    0.5528         0

>> linkage(D,'single') % cluster using that
ans =
    3.0000    4.0000         0
    1.0000    5.0000         0
    2.0000    6.0000    0.5528

Notice that points 1,3,4 are clustered with zero distance, even though the correlation with the point 4 is '-1'.

2) The second way is to write the distance into the 'linkage' command:

>> linkage(x,'single',@(xrow,ymat) 1-abs(corr(xrow',ymat')))
ans =
    3.0000    4.0000         0
    1.0000    5.0000         0
    2.0000    6.0000    0.5528