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Multidimensional Scaling: Definition & Use

Instructor: David Gloag
In this lesson, we will define scaling and, in particular, multidimensional scaling. We will examine what multidimensional scaling is used for. At the end, you should have a good understanding of this useful technique.

Perspective

We want to make sense of the plethora of information available to us. Newspapers and online news sites keep us up-to-date on local and world happenings, social media keeps us informed on what our friends are up to, and websites keep us abreast of things like the weather. But, by the time it reaches us, most information has been manipulated in some fashion. It has to be. It would be difficult to comprehend otherwise. Can you imagine stock market prices without a graph? Or weekly precipitation values without some context? So, we use a variety of techniques to put things into perspective. And one of the most useful is scaling.

What is Scaling?

Scaling is the process of adjusting a set of values so that they fit in a known framework. The adjustment is uniform and preserves the relative proportions of the items with respect to each other. The purpose is to allow the observer to compare the unfamiliar values with the familiar framework. For example, think back to the daily temperature values for the previous week. If you look at these values plotted on a graph, are you looking at the absolute values? Or, are you comparing them to room temperature or their position relative to the freezing point of water? For most of us, the answer is in the comparison, because the comparisons have more meaning to us than the raw values themselves.

Multidimensional Scaling

Multidimensional scaling extends the scaling idea to more than one dimension. In the daily temperature example, we are using two dimensions, the temperature value and the day of the week. This type of representation is quite natural because it can be easily displayed on a piece of paper or a computer screen. More dimensions are certainly possible but present some problems. The biggest being how to represent the extra dimensions on paper or a computer screen. Three dimensions, for example, isn't usually too bad, as there are 3D techniques available. But what about four, or five? The problem becomes obvious.

Uses for Multidimensional Scaling

The daily temperature comparison is just one example of multidimensional scaling at work. From a more general perspective, multidimensional scaling tries to provide a visual representation of the similarities or distances between values in an information set. This idea can be applied to a lot of things. Here are some examples:

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