cophenet (Statistics Toolbox)

Cophenetic correlation coefficient

Syntax

```
c = cophenet(Z,Y)
```

Description

c = cophenet(Z,Y) computes the cophenetic correlation coefficient which compares the distance information in Z, generated by linkage, and the distance information in Y, generated by pdist. Z is a matrix of size (m-1)-by-3, with distance information in the third column. Y is a vector of size .

For example, given a group of objects {1, 2, ..., m} with distances Y, the function linkage produces a hierarchical cluster tree. The cophenet function measures the distortion of this classification, indicating how readily the data fits into the structure suggested by the classification.

The output value, c, is the cophenetic correlation coefficient. The magnitude of this value should be very close to 1 for a high-quality solution. This measure can be used to compare alternative cluster solutions obtained using different algorithms.

The cophenetic correlation between Z(:,3) and Y is defined as

where:

Y_ij is the distance between objects i and j in Y.
Z_ij is the distance between objects i and j in Z(:,3).
y and z are the average of Y and Z(:,3), respectively.

Example

rand('seed',12); 
X = [rand(10,3);rand(10,3)+1;rand(10,3)+2];
Y = pdist(X);
Z = linkage(Y,'centroid');
c = cophenet(Z,Y)
c =
    0.6985

See Also

cluster, dendrogram, inconsistent, linkage, pdist, squareform

combnk cordexch