This repositorie of codes accompanies our paper on: "Qualitative Euclidean Embedding of Disjoint Sets of Points"
The codes can be used to test the sufficient conditions, provided in our paper above, for obtaining a positive semi-definite matrix M with components
Mij = (h(i, 0)2 + h(j, 0)2 - h(i, j)2 )/2, where h is a specific non-negative symmetric function with defined properties. We term M as cosine law matrix because it is obtained from the cosine law between points in Euclidean space.
This is important because M is Gram matrix of a set of Euclidean points iff it is positive semi-definite (M = E ET). That is any arbitrary set of points generating the cosine law matrix M can be embedded into the set of Euclidean points with coordinates obtained on the rows of E (Schoenberg criterion).
working_points.ipynb: jupyter notebook to demonstrate that the theory works for two sets of points with point coordinated constructed from a contingency dataset and using their representations in Correspondence Analysis.
rand_points.ipynb: jupyter notebook to demonstrate that the theory works on randomly generated points (at least it works for the few trials done with our computers)
rand_points_chgdist.ipynb: same as rand_points.ipynb but the distance within set was increased by a positive constant
Mathematical statements and proofs are provided in our paper: "Qualitative Euclidean Embedding of Disjoint Sets of Points"