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I am using NVI (Normalized Variation of Information) to measure the quality of clustering obtained ( a family of them) compared to the Ground Truth and also to the result obtained with another method.

Since NVI is a metric, it satisfies the triangular inequality and hence I thought it would be nice to plot the result graphically.

For that, I need a tool that given the distances among points can plot them in such a way that all the distances are respected among the different reference points. The graph should be 2D.

Do you know of any tool that can do like that? i.e. receiving a matrix of distances The matrix will not be complete, that is, the distance between all the partitions is not calculated. All the distances to the 3 references (2 GT and the additional method) and the distances among the 3 references are calculated.

If not a tool, using Matlab or Python and doing some programming is also fine for me. I have around 200 points to plot.

EDIT: I have found this answer in SO: https://stackoverflow.com/questions/13513455/drawing-a-graph-or-a-network-from-a-distance-matrix but it doesn't work properly, even for 7 nodes (that can be visually verified the correctness")

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It seems what you're looking for is Multidimensional Scaling. It takes a distance matrix and processes coordinates such that the distances between the points approximately respect the values in the matrix. There are implementations in many languages, such as R (see this page).

However, you might need (much) more than 2 dimensions if you want to obtain coordinates exactly resulting in the same distances.

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  • $\begingroup$ I found the same solution from Matlab webpage. As you suggest, the results are not very satisfactory as to represent in a 2D or 3D space. In any case, since you provided the solution, I award you the Correct Answer. $\endgroup$
    – Picarus
    Mar 23, 2014 at 20:20

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