How to Do Multidimensional Scaling from a Distance Matrix

Introduction

Multidimensional Scaling is a technique for visualizing distances between objects where the distance is known between the pairs of objects. This article describes how to go from a distance matrix:

To a two-dimensional scatterplot, where each of the objects is represented as a point: 

Requirements

A Displayr document containing the distance matrix that you want to use as input to the MDS analysis.

Method 1

1. From the menus, select Anything > Advanced Analysis > Dimension Reduction > Multidimensional Scaling (MDS)

2. In the object inspector under Inputs > Algorithm select MDS - Metric or MDS - Non-metric.

• Metric MDS minimizes the difference between distances in input and output spaces.
• Non-metric MDS aims to preserve the ranking of distances between input and output spaces.

Often we care more about relative positioning than absolute differences, in which case non-metric is preferred to metric MDS. For the example below, I've selected Metric. 

3. Under Inputs > Distance Matrix, select your distance matrix object. 

4. Click the Calculate button to generate the MDS output. 

Method 2

1. From the menus, select Anything > Advanced Analysis > Dimension Reduction > Multidimensional Scaling (MDS)

2. In the object inspector under Inputs > Algorithm select MDS - Metric or MDS - Non-metric. For the example below, I've selected Metric. 

3. Under Inputs > Distance Matrix, select Paste or Type Distance Matrix. 

4. Enter a symmetrical matrix of distances which should have 0 in the diagonal. For this example, I've entered distances between four Australia cities. 

5. Click OK. 

6. Click the Calculate button to generate the MDS output. 

See Also

How to Create a Distance Matrix

How to do Multidimensional Scaling from a Variables