Efficient and Effective Optimal Transport-Based Biclustering: Supplementary Material

For w, v, r and c containing no zeros, the resulting optimal coupling matrices Z and W are always an h-almost hard clustering with h {0,..., k 1}. W) represents a hard clustering Z Γ(n, n) (resp. The Kantorovich OT problem is a bounded linear program since Π(w, v) is a polytope i.e. a bounded polyhedron. The fundamental theorem of linear programming states that if the feasible set is non-empty then the solution lies in the extremity of the feasible region. This means that a solution Z to the OT problem is an extreme point of Π(w, v).