Nelder-mead enhanced extreme learning machine

Many algorithms such as Support Vector Regression (SVR), Incremental Extreme Learning Machine (I-ELM), Convex Incremental Extreme Learning Machine (CI-ELM), and Enhanced random search based Incremental Extreme Learning Machine (EI-ELM) are being used in current research to solve various function approximation problems. This paper presents a modification to the I-ELM family of algorithms targeted specifically at Single Layer Feedforward Networks (SLFN) using Radial Basis Function (RBF) nodes. The modification includes eliminating randomness in both the center positions of the RBF units as well as the widths of the RBF units. This is accomplished by assigning the center of each incrementally added node to the highest point in the residual error surface and using Nelder-Mead's Simplex method to iteratively select an appropriate radius for the added node. Using this technique, the properties of I-ELM that allow for universal approximation and appropriate generalization are preserved, while the sizes of the RBF networks are greatly reduced.