Synthesising cluster operators

摘要

Let Γi ⊂ Rm denote pattern classes with means γi and covariances Ri, i = 1, …, l respectively. The set {ψi} ⊂ Rk denotes signatures for the pattern classes. A function f : Rm → Rk is said to be a cluster function provided (i) f (γi) = ψi, i = 1, …, l and (ii) f minimizes a dispersion functional. This paper develops a complete theory for realization of polynomic cluster functions, including the linear case.