A question bridging math and computer science, I have on the order of 10000 vectors each of a equal but high dimension, say 6 or 7 dimensions. I want to find a given number of 'unique' vectors in the set, the number generally equal to the dimension of the vectors. In math terms I believe I want to find a subset of vectors that has the biggest angle from its neighbours in that sub set. Vector length is also a factor, i.e. a unique but nearly zero length vector is less preferred than one less unique in angle but has a finite length.
1: [1 2 4 1 5]
2: [1 1 2 1 3]
3: [1 2 4 1 4]
9999: [2 1 1 2 2]
10000: [4 5 4 2 1]
vectors 1 and 3 are quite similar, 2 less so, 10000 is most different. I think the dot product and higher order 'angle' is the best measure of uniqueness, though there may be better.
Visually, collapsing the dimension down to 2, the vectors below in black represent the full set, the vectors in red are the subset of seven most unique.
Concept update: 03/05/2018
I have recently stumbled upon the concept of the Latin hypercube, and the higher dimensional mathematics behind it that attempt to find an even spread of higher-dimensional vectors. I don't know exactly how this could be applied, but it has been the closest concept so far. Can anyone see how it might be applicable to the problem?