I am given a set of multi-dimensional vectors (e.g. 7D) and I need to select a subset of maximally "different" ones, in the sense of "pointing in as many different directions as possible" and "maximising the spread of the selected vectors". (I'm not really sure what the correct terminology for this would be, so I'm using the least technical description I can.) This is illustrated in 2D in the figure below, where the thick black vectors on the right are one possible answer, given the input vectors shown on the left.
I primarily need to know what mathematical criterion I can use, and I can deal with the ensuing numerical optimisation problem myself--however, if there is a known algorithm for solving this problem, of course I'd appreciate a reference to it as well.
Thanks!
