Exponential C-Loss for data fitting

As a robust measure of similarity, C-Loss can be successfully used for data fitting such as regression and classification, especially when data contain large outliers. In this paper, we propose a modified C-Loss function, called exponential C-Loss (EC-Loss), which is defined as an exponential function of the C-Loss. The EC-Loss inherits the robustness and smoothness of the C-Loss but may have a better performance surface that favors the usage of a gradient-based learning algorithm, particularly at a region far from the optimal solution. In order to avoid the flatness of the performance surface near the optimal solution and obtain a fast convergence speed during the overall adaptation process, we also propose a novel switching strategy between C-Loss and EC-Loss. A simple simulation example is presented to demonstrate the performance surface and desirable performance of the new method.