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TUTORIAL

Hierarchical Cluster Analysis

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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.

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For dissimilarities, larger values indicate items which are very different.

Smaller values indicate items which are very similar.

This relationship is reversed if a similarity measure is used.’

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Hierarchical Cluster Analysis Agglomeration Schedule

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

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

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At each stage, one case or cluster is joined with another case or cluster.

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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.

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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.

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For a good cluster solution, you will see a sudden jump in the distance coefficient (or a sudden drop in the similarity coefficient) as you read down the table.

The stage before the sudden change indicates the optimal stopping point for merging clusters.

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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.

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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...

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...and cluster 5 is the cluster formed in stage 8.

The last column shows the subsequent stage at which the newly merged cluster is combined with yet another cluster.

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

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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.

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If you've requested a range of solutions, you'll see a column for each solution.

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Hierarchical Cluster Analysis Icicle Plot

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

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Each white bar represents a boundary between clusters.

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At each stage, two clusters are joined, and so the white bar separating the joined clusters ends.

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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.

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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:

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Choose Edit->Options, and select the Scripts tab...

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Now make sure the Enable Autoscripting option is activated...

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And make sure the Cluster_Table_Icicle_Create autoscript is checked.

Future icicle plots will be generated in the new bar format (but previously generated plots will not be altered).

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Hierarchical Cluster Analysis Dendrogram

The dendrogram (or "tree diagram") shows relative similarities between cases.

Notice how the "branches" merge together as you look from left to right in the dendrogram.

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Cases or clusters that are joined by lines "further down" the tree (near the left side of the dendrogram) are very similar.

Cases or clusters that are joined by lines "further up" the tree (near the right side) are dissimilar.

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Cluster distances are rescaled so that they range from 0 to 25 in this plot.

It can help to see different cluster solutions by imagining a vertical line through the dendrogram.

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For instance, in this example, we might draw a line at about 3 rescaled distance units.

This would identify 4 clusters, one for each point where a branch intersects our line.

By considering different cut points for our line, we can get solutions with different numbers of cluster.

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A good cluster solution is one with small within-cluster distances, but large between-cluster distances.

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