ABSTRACT
An artificial neural network (ANN) is a functional abstraction of the biologic neural
structures of the central nervous system (Aleksander and Morton 1993; Rudomin et al.
1993; Arbib 1995; Anderson 1995). It is essentially a simple mathematical model
representing a nonlinear mapping function from a set of inputs x to outputs y, i.e., / x ->
y. The most commonly used ANN model is the feedforward neural network. This
network usually consists of input, hidden, and output layers. The information moves only in the forward direction, from the input nodes, through the hidden nodes and to the output
nodes. There are no loops in the network. As an example, Fig. 2.1 shows a widely used three-layer feedforward ANN model,
with arrows depicting the dependencies between variables at each layer. Its single output
у (i.e., model prediction) is the nonlinear weighted sum of the inputs x. In Fig. 2.1, the
input vector x consists of p variables x, (/ = 1 ,..., p). The parameter ay (/ = 1 ,..., p; j = 1,
...,K ) represents the weight of the link connecting the input node і to node j in the hidden
layer, in which K is the number of nodes in the hidden layer. The parameter wj represents
the weight of the link connecting the hidden node j to the node in the output layer, and
the variable d represents the weight of the bias. The bias term (a constant value, typically one) allows the neural network to return a nonzero value at the origin. The parameters αβ,
Wj, and d need to be estimated using a learning algorithm which will be discussed later.
