A Functional Link Network Using Ordered Basis Functions

Abstract

A new function approximation and classification network based on Functional Link Network (FLN) with orthonormal Polynomial Basis Functions (PBF) is presented. By using an iterative Gram-Schmidt procedure, the PBF's are orthonormalized, ordered and selected based on their contribution to minimize the Mean Square Error (MSE). Linearly dependent and less useful PBF are detected and eliminated at an early stage thereby improving the approximation capabilities and reducing the possibility of combinatorial explosion. The number of passes through the data during network training is minimized through the use of correlations. A one-pass method is used for validation and network sizing. Equivalent function approximation and classification networks are designed and simulation examples are presented. Results for the Ordered FLN are compared with those for the FLN, Group Method of Data Handling (GMDH), and Multi-Layer Perceptron (MLP), Nearest Neighbor Classifier (NNC) and Piecewise Linear Classifier (PLNC).