Hierarchical Cluster Analysis: A Comprehensive Tutorial, Study notes of Computational and Statistical Data Analysis

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TUTORIAL

Hierarchical Cluster Analysis

Hierarchical Cluster Analysis Proximity Matrix

This table shows the matrix of proximities between cases or variables.

These values represent the similarity or dissimilarity between each pair of items.

In this example, we use Squared Euclidean Distance, which is a measure of dissimilarity.

Hierarchical Cluster Analysis Agglomeration Schedule

This table shows how the cases are clustered together at each stage of the cluster analysis.

Clusters are formed by merging cases and clusters a step at a time, until all cases are joined in one big cluster.

For instance, in this example, cases 4 and 11 are joined at stage 3. This is shown in the Clusters Combined columns.

When clusters or cases are joined, they are subsequently labeled with the smaller of the two cluster numbers.

The Coefficients column indicates the distance between the two clusters (or cases) joined at each stage.

The values here depend on the proximity measure and linkage method used in the analysis.

For this example, we should consider using a 4-cluster solution.

The next part of the table shows the stage at which each cluster first appears.

Single cases existed before we started the analysis, so they are indicated by zeroes here.

In stage 9, cluster 1 is the cluster that was formed in stage 6...

For example, the cluster formed in stage 2 next appears in stage 10, where it is merged with cluster 1.

Hierarchical Cluster Analysis Cluster Membership

This table shows cluster membership for each case, according to the number of clusters you requested.

You can attempt to interpret the clusters by observing which cases are grouped together.

Hierarchical Cluster Analysis Icicle Plot

This plot gives a graphic representation of how the cases are joined at each stage of the analysis.

Each white bar represents a boundary between clusters.

Within a row, each contiguous black band indicates cases grouped as a cluster.

Formatting Icicle Plots

The default output for icicle plots displays columns of X's instead of bars.

If you find it easier to see the pattern in the plot with bars, you can set your options to automatically reformat future icicle plots as follows: