Statistics Toolbox

Finding the Natural Divisions in the Data Set

In the hierarchical cluster tree, the data set may naturally align itself into clusters. This can be particularly evident in a dendrogram diagram where groups of objects are densely packed in certain areas and not in others. The inconsistency coefficient of the links in the cluster tree can identify these points where the similarities between objects change. (See Evaluating Cluster Formation for more information about the inconsistency coefficient.) You can use this value to determine where the cluster function draws cluster boundaries.

For example, if you use the cluster function to group the sample data set into clusters, specifying an inconsistency coefficient threshold of 0.9 as the value of the cutoff argument, the cluster function groups all the objects in the sample data set into one cluster. In this case, none of the links in the cluster hierarchy had an inconsistency coefficient greater than 0.9.

T = cluster(Z,0.9)
T =
     1
     1
     1
     1
     1

The cluster function outputs a vector, T, that is the same size as the original data set. Each element in this vector contains the number of the cluster into which the corresponding object from the original data set was placed.

If you lower the inconsistency coefficient threshold to 0.8, the cluster function divides the sample data set into three separate clusters.

T = cluster(Z,0.8)
T =
    1
    3
    1
    2
    2

This output indicates that objects 1 and 3 were placed in cluster 1, objects 4 and 5 were placed in cluster 2, and object 2 was placed in cluster 3.

Creating Clusters

Specifying Arbitrary Clusters