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Given n samples and p >> n (discrete) data points for each of the n samples, what is a good algorithm for finding a smallest possible set of k data points such that those k data points discriminate between all n samples?
For my purposes, a good algorithm that finds an approximately smallest set would also suffice.
It sounds as though your problem is closely related to the test cover problem. The test cover problem is, given a ground set X = {1, …, n} and a collection T = {T1, …, Tm} of subsets of X, to find the smallest subcollection U of T such that for all y ≠ z in X, there exists a set S in T such that either (x in S and y not in S) or (x not in S and y in S).
The test cover problem is NP-hard, so in practice, optimal solutions are found using branch and bound techniques. See De Bontridder et al.