﻿ Multi-Dimensional Scaling | Applied Maths

# Multi-Dimensional Scaling

Question:

What exactly is Multi-Dimensional Scaling (MDS) doing? Is it using the similarity matrix generated by the cluster analysis or does it generate its own? What are the labels for the x, y, and z axis?

In a comparison of N entries, each entry is characterized by an array of N-1 distance values (converted from the similarity values). These arrays are used in a method very similar as PCA, also producing a set of components, not from the characters, but from the distance values. The first component is the most discriminative; the second is second most, etc. When this is done, the method will compare the distances between the entries as plotted on the MDS coordinate system (usually 2 or 3 first components) with the distance values in the matrix. It will iteratively adjust the positions of the entries in the coordinate system until the differences with the distance matrix are minimal. With MDS (as opposed to PCA) there is no physical interpretation that can be given to the axes of the coordinate system. Any scale assigned would be arbitrary.

A very good reference handbook, which you can safely use in your publication as well (also for PCA, Discriminant analysis, MANOVA) is:

J.D. Jobson. Applied Multivariate Data Analysis (2nd Vol.). Springer Verlag. ISBN 0 387 97804 6

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