New MDS API

[wildart]

Changed cMDS to have a standard fit/transform API

New:

• include eigenvalues in a result (Returning eigenvalues from classical_mds? #60)

Added:

• stress calculation (Any plans for stress evaluation of MDS? #51)
• out-of-sample extension

[kmundnic]

I've been trying to use the implementation classical_mds and the new API in the master branch, and it seems that both are making the assumption that the distance matrix has entries D[i,j] = norm(X[:,i] - X[:,j], 2). However, by definition a Euclidean Distance Matrix (EDM) uses square Euclidean distances for its entries (this can be found in your reference, chapter 12), and on this paper (which follows the same approach: https://arxiv.org/pdf/1502.07541.pdf).

The result is that when computing an embedding Z from a distance matrix D, where D[i,j] = norm(X[:,i] - X[:,j], 2)^2 and X is our original (underlying) embedding, X and Z do not match up to an affine transformation, as they should (see Section II. C. Orthogonal Procrustes Problem of the paper referenced from ArXiv).

Given the reference in use in the documentation, I think it should be good to use distance matrices with squared Euclidean distances. However, if there is no consensus on this idea, I would suggest stating in the documentation that the distances matrices are assumed to have Euclidean distance entries.

Thanks!

Edit: Please let me know if I should open an issue instead of including this comment here.