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nmf

NMF

### Compute Non-Metricity Fraction of a dissimilarity matrix

[F,C] = NMF(D,N)
[F,C] = D*NMF

 Input D Dissimilarity matrix or dataset N Scalar integer for a fast estimation of F from N random  triangles. Default: use all.

 Output F Non-metricity fraction C Constant to make F=0, if added to the off-diagonal elements of D.

### Description

This routine counts the number of triangle inequality violations D to  estimate the NEF of D. If D is asymmetric, it is made symmetric by  averaging. F is the fraction of violating inequalities. Hence, for F = 0,  the triangle inequality holds for all triplets of the objects that  construct the distance matrix D.

Additionally, a constant C is determined, which when added to the  off-diagonal elements of D will take care that F = 0

If N is given, a random NxN subset of D is taken to speed up and F is an  estimate. N=100 yields already a reasonably fast and accurate estimate.

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