Cluster Analysis (Hierarchical)

Cluster Analysis (Hierarchical) is performed using a set of dissimilarities for all objects being clustered. Initially, each object is assigned to its own cluster and then the algorithm proceeds iteratively, at each stage joining the two most similar clusters, continuing until there is only one cluster. Hierarchical cluster analysis can be used to discover structures in a data set without providing an explanation.

The following algorithm is used in the implementation of this tool:

  • Compute the distance matrix
  • Each object is assigned to its own cluster
  • Repeat
    • Merge the two most similar clusters
    • Update the distance matrix until there is only one cluster


To illustrate the use of the Cluster Analysis (Hierarchical) tool, we will use a dataset with a number of variables in it that can be related to each other: Income, Inequality and Financial Stress across the Greater Hobart area. To do this:

  • Select Greater Hobart as your area
  • Select SA2 OECD Indicators: Income, Inequality and Financial Stress 2011 as your dataset, selecting all variables.


Once you have done this, open the Cluster Analysis (Hierarchical) tool (Tools → Statistical Analysis→ Cluster Analysis (Hierarchical)) and enter the parameters as listed below:

  • Dataset Input: The dataset that contains the variables of interest. Select SA2 OECD Indicators: Income, Inequality and Financial Stress 2011.
  • Variable: A set of independent variables. Select the following five attributes:
    • Median Disposable Income (Synthetic Data)
    • Gini Coefficient (Synthetic Data)
    • Poverty Rate (Synthetic Data)
    • % with no access to emergency money (Synthetic Data)
    • % Can’t afford a night out (Synthetic Data)
  • Cluster Analysis Distance Metric: The distance measure to be used. This must be one of euclidean, maximum, manhattan, Canberra, binary or minkowski. Select euclidean.
  • Cluster Analysis Cluster Metric: The agglomeration method (linkage rule) to be used. This should be one of ward, single, complete, average, mcquitty, median or centroid. Select complete.


Once you have selected your parameters, click the Run Tool button.


Once you have run the tool, click the Display Output button which appears in the pop-up dialogue box. This should open up a textual output looking like the one shown below.

  • The output can be interpreted with the following:
  • Merge: An n-1 by 2 matrix. Row i of merge describes the merging of clusters at step i of the clustering. If an element j in the row is negative, then observation -j was merged at this stage. If j is positive then the merge was with the cluster formed at the (earlier) stage j of the algorithm. Thus negative entries in merge indicate agglomerations of singletons, and positive entries indicate agglomerations of non-singletons.
  • Height: A set of n-1 real values (non-decreasing for ultrametric trees). The clustering height: that is, the value of the criterion associated with the clustering method for the particular agglomeration.
  • Order: A vector giving the permutation of the original observations suitable for plotting, in the sense that a cluster plot using this ordering and matrix merge will not have crossings of the branches.
  • Labels: Labels for each of the objects being clustered.
  • Method: The agglomeration method that has been used.
  • Distance Method: The distance measure that has been used to create a dissimilarity structure.

The results of cluster analysis can be displayed on the AURIN portal using Hierarchical Clustering (Tree Chart), Hierarchical Clustering (Heat Map), Hierarchical Clustering (Dendrogram) or Hierarchical Clustering (Distance Matrix).

Aldenderfer, M. S., & Blashfield, R. K. (1984). Cluster analysis. In Quantitative applications in the social sciences (Vol. 2). Sage Publications Beverly Hills.
Venables, W. N., Smith, D. M., & Team, R. C. (1999). An introduction to R: Notes on R: A programming environment for data analysis and graphics Version 3.1. 0 (2014-04-10). R Core Team.

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