Extreme Learning Machine Based Functional Link Neural Network

Inspired by the biological neurons, Neural networks have been shown a high capability of building a class of very flexible models by generating complex mapping between input and output space and providing an effective solutions for function approximation, prediction, and classification. Radial Basis Function (RBF), multi-Layer Perceptrons (MLP), networks, and Support Vector Machines (SVM) have been widely applied in many engineering and science fields. The research topics vary from a theoretical view of learning algorithms such as learning and generalization properties of the networks for a variety of applications in control, classification, biomedical, manufacturing, and business forecasting, etc.The RBF networks have shown their own approximation properties, paralleling the multilayer perceptrons properties. The RBF networks family is broad enough to uniformly approximate any continuous function on a compact set in addition to their satisfactory generalization capability in solving different classification and prediction problems. The single layered feedforward networks (SLFNs) with extra high order input referred to as higher order neural networks (HONN) or functional link networks (FLN), they are rapidly expanding, young, and very active field of research. These networks are more powerful than the standard SLFNs because they include linear input-output relationships in addition to nonlinear ones. By constructing the linearly independent basis functions the nonlinearity is endowed in the input layer in addition to the original variables. we can form a radial basis functional link network (RBFL) by considering a radial basis functional as a high order terms of network.There are a various algorithms for training different kinds of neural networks including radial basis function networks (RBF) and RBFLN networks, such as the gradient descent algorithms. Which is needed more time to choose appropriate learning parameters (learning rates) by trial-and-error in order to train the networks.When the learning rate is too small, it’s affect the learning speed and the learning algorithm became so slow. However, when it is too large, the algorithm becomes unstable and diverges. Another feature of the error surface that affects the performance of the traditional learning algorithm is the presence of local minima. It is undesirable that the learning algorithm stops at local minima if it is located far above global minima. Therefore, other learning technique than these traditional algorithms, like extreme learning machine (ELM) have been studied in this thesis with the aim to develop a fast and accurate RBFL networks. This perfect learning method for SLFNs has been proposed by Huang et al developed and improved and widely used by many researchers in real world applications but no such study exists for RBFL. The ELM algorithm root out the drawbacks of these popular learning techniques, in ELM, the input weights of SLFNs do not need to be tuned and can be randomly generated, whereas the output weights are analytically determined using the least-square method, which is making it suitable to find an optimal weight of the RBFL network. After formulating the network as linear systems, and because the system equations of the RBFL network have a similar form to the RBFL network and both networks share similar "flat" architecture. So the ELM algorithm can be successfully applied for RBFL as same as RBF.Some experimental results on benchmarks and the real world approximation and classification problems are reported to clearly show a superior generalization performance of presented network comparing with ELM-RBF models. This thesis also makes another considerable contribution to high-density polyethylene (HDPE) process in chemical industrial area. The thesis is ended with the conclusion and future research work.