Suppose we have a set E of entities. Each entity is described by a set P of binary properties (i.e. each element e of E has a defined true/false value for each element p of P).
|P| >> |E|
We now want to select a subset of fixed size (e.g., 10) of P that will enable us distinguish the elements in E as accurately as possible.
In extensions of this basic scenario, the properties could assume numeric values.
Has this problem been studied? Under what name?
A practical example: there is a set of 100 bacterial species that are characterized for the presence or absence of 1000 genes. We now want to select a subset of 10 genes that, upon typing of a novel sample, will tell us which bacterial species that sample represents.