what is Multidimensional scaling

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What is Multidimensional scaling from statistics.

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Assume you have a set of objects and you have a big table about how similar they are to each others (A is similar to B at 66%, to C at 14%, etc), and that you want to visualise this table by having one point per objects, and objects far away from each others when they are different but near each other when they are similar.

That’s what multidimensional scaling is about. It’s not a single method, there are a lot of methods for doing it, but that’s it.

In fact, while you have a lot of precise methods in statistics to do it, we use some informal version of it in our everyday life. The main example that come to my mind is the left/right from politics. Politics is complex, but we roughly know how similar and dissimilar some political groups are. Rather than having a big unreadable tabular, we simply put every political party on a line from left to right, and arbitrary call one of the two groups at the extreme “left” and the other “right”.

It’s very basic, and in fact its not really “multi”dimensional scaling since there is only one dimension, but it is a visual representation that help us understand politics better than what a big tabular with numbers would, which is the core of what multidimensional scaling is about.

[Note: It’s not a perfect example since political parties actually claim by themself to be on the right or on the left, while usually when you’re doing multidimensional scaling, the objects you are putting on a figure are not aware that they are being put on a figure so don’t actively try to be more on the left or on the right than what they actually are.]