Universal Approximation by Using the Correntropy Objective Function

Abstract

Several objective functions have been proposed in the<br><br>literature to adjust the input parameters of a node in constructive<br><br>networks. Furthermore, many researchers have focused on the universal<br><br>approximation capability of the network based on the existing objective<br><br>functions. In this brief, we use a correntropy measure based on the<br><br>sigmoid kernel in the objective function to adjust the input parameters of<br><br>a newly added node in a cascade network. The proposed network is shown<br><br>to be capable of approximating any continuous nonlinear mapping with<br><br>probability one in a compact input sample space. Thus, the convergence is<br><br>guaranteed. The performance of our method was compared with that of<br><br>eight different objective functions, as well as with an existing one hidden<br><br>layer feedforward network on several real regression data sets with and<br><br>without impulsive noise. The experimental results indicate the benefits<br><br>of using a correntropy measure in reducing the root mean square error<br><br>and increasing the robustness to noise.