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given a matrix of distances between points is there an algorithm for determining a set of n-dimensional points that has these distances? (or at least minimises the error)
sort of like a n-dimensional version of the turnpike problem.
The best I can come up with is using multidimensional scaling.
You are on the right track with multi-dimensional scaling (MDS), but MDS is impractical for large datasets, as its time complexity is quadratic in the number of points. You may want to look at FastMap, which has linear time complexity and is better suited to indexing. See: