# Hierarchical Clustering Distance Matrix

## Contents

## Introduction

Distance matrix is a matrix (two-dimensional array) containing the distances, taken pairwise, of a set of points. This matrix will have a size of NxN where N is the number of points, nodes or vertices.

The output of this is a graph which shows how similar each of the different areas are when taking into account a range of variables. Closeness to each other on the distance matrix suggests greater and greater similarity

## Inputs

To illustrate the use of theHierarchical Clustering Distance Matrix 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 GCCSA*as your area**Select***SA2 OECD Indicators: Income, Inequality and Financial Stress 2011*as your dataset

Once you have done this, open the Hierarchical Clustering Distance Matrix tool (*Tools → Charts→ Hierarchical Clusting Distance Matrix*) and enter the parameters as shown in the image below (they are also explained under the image in more detail

*Cluster Analysis Hierarchical Dataset Input:*Select a dataset that contains the variables of interest. Here we select*SA2 OECD Indicators: Income, Inequality and Financial Stress 2011**Cluster Analysis Variable List:*A set of independent variables. Here we select*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”. Here we select*Euclidean**Cluster Analysis Cluster Metric:**Complete*-
*Chart Title:*A title for your Hierarchical Clustering Distance Matrix -
*Grid:* -
*Greyscale:*Specify whether you would like your graph to be grey-scale (checked) or colour (unchecked)

Note : Please see the documentation of Hierarchical Cluster Analysis for further details

Once you have selected your parameters, click the **Add and Run** button.

## Outputs

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

## References

(2) Aldenderfer, M. S. and R. K. Blashfiled (1984) Cluster Analysis, SAGE Publications, Inc, Newbury Park.

(3) CaliŃski, T. (2005) Dendrogram, Encyclopedia of Biostatistics, Vol. 2, pp. 1415 – 1417, Wiley, New York.

(4) http://www.mathworks.com.au/help/stats/hierarchical-clustering.html