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.