A proof of the convergence theorem of maximum-entropy clustering algorithm

In this paper, we point out that the counterexample constructed by Yu et al. is incorrect by using scientific computing software Sage. This means that the example cannot negate the convergence theorem of maximum entropy clustering algorithm. Furthermore, we construct an example to negate Theorem 1 in Yu's paper, and we propose Proposition 3 to prove that the limit of the iterative sequence is a local minimum of the objective function while v varies and u remains stable. Finally, we give a theoretical proof of the convergence theorem of maximum entropy clustering algorithm.