### MultiDimensional Scaling (MDS) in Excel/VBA

Information
visualization technique multidimensional scaling (MDS) has its roots in the
field of psychometrics and is used for
exploring similarity/dissimilarity data. The case in point is once again the
city distance matrix for the U.S. (see the post on PCA).

As a result a
two-dimensional representation of data is constructed, where each Euclidean distance
approximates the corresponding dissimilarity/distance
in the
original matrix. There is an objective function (called stress/Kruskal’s
stress/energy) that is minimized.

This file is based on methods
put forth in the dissertation of Wojciech Basalaj and uses Newton-Raphson method for optimization. There is a problem with convergence,
though, as solution seems to get stuck in the local minima.

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