Enhanced piecewise regression based on deterministic annealing

Regression is one of the important problems in statistical learning theory. This paper proves the global convergence of the piecewise regression algorithm based on deterministic annealing and continuity of global minimum of free energy w.r.t temperature, and derives a new simplified formula to compute the initial critical temperature. A new enhanced piecewise regression algorithm by using "migration of prototypes" is proposed to eliminate "empty cell" in the annealing process. Numerical experiments on several benchmark datasets show that the new algorithm can remove redundancy and improve generalization of the piecewise regression model.