Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification

3 Wavelet Neural Networks

In the literature, various versions of wavelet networks have been proposed. A wavelet network usually has the form of a three-layer network. The lower layer represents the input layer, the middle layer is the hidden layer, and the upper layer is the output layer. The way that the three layers are connected and interact defines the structure of the network. In the input layer, the explanatory variables are inserted in the model and transformed to wavelets. The hidden layer consists of wavelons, or hidden units. Finally, all the wavelons are combined to produce the output of the network, , at the output layer, which is an approximation of the target value, y_p.

In this chapter we present and discuss analytically the structure of the wavelet network proposed. More precisely, in this book, a multidimensional WN with a linear connection between the wavelons and the output is implemented. In addition, there is a direct connection from the input layer to the output layer that will help the network to perform well in linear applications. In other words, a wavelet network with zero hidden units is reduced to a linear model.

Furthermore, the initialization phase, the training phase, and the stopping conditions are discussed. A wavelet is a waveform of effectively limited duration that has an average value of zero and localized properties. Hence, in wavelet networks, ...