1 Introduction

Neural Networks is a Mathematica package designed to train, visualize, and validate neural network models. A neural network model is a structure that can be adjusted to produce a mapping from a given set of data to features of or relationships among the data. The model is adjusted, or trained, using a collection of data from a given source as input, typically referred to as the training set. After successful training, the neural network will be able to perform classification, estimation, prediction, or simulation on new data from the same or similar sources. The Neural Networks package supports different types of training or learning algorithms.

More specifically, the Neural Networks package uses numerical data to specify and evaluate artificial neural network models. Given a set of data, , from an unknown function, y=f(x), this package uses numerical algorithms to derive reasonable estimates of the function, f(x). This involves three basic steps. First, a neural network structure is chosen that is considered suitable for the type of data and underlying process to be modeled. Second, the neural network is trained by using a sufficiently representative set of data. Third, the trained network is tested with different data, from the same or related sources, to validate that the mapping is of acceptable quality.

The package contains many of the standard neural network structures and related learning algorithms. It also includes some special functions needed to address a number of typical problems, such as classification and clustering, time series and dynamical systems, and function estimation problems. In addition, special performance evaluation functions are included to validate and illustrate the quality of the desired mapping.

The documentation contains a number of examples that demonstrate the use of the different neural network models. You can solve many problems simply by applying the example commands to your own data.

Most functions in the Neural Networks package support a number of different options that you can use to modify the algorithms. However, the default values have been chosen so as to give good results for a large variety of problems, allowing you to get started quickly using only a few commands. As you gain experience, you will be able to customize the algorithms by changing the options.

Choosing the proper type of neural network for a certain problem can be a critical issue. The package contains many examples illustrating the possible uses of the different neural network types. Studying these examples will help you choose the network type suited to the situation.

Solved problems, illustrations, and other facilities available in the Neural Networks package should enable the interested reader to tackle many problems after reviewing corresponding parts of the guide. However, this guide does not contain an exhaustive introduction to neural networks. Although an attempt was made to illustrate the possibilities and limitations of neural network methods in various application areas, this guide is by no means a substitute for standard textbooks, such as those listed in the references at the end of most chapters. Also, while this guide contains a number of examples in which Mathematica functions are used with Neural Networks commands, it is definitely not an introduction to Mathematica itself. The reader is advised to consult the standard Mathematica reference: Wolfram, Stephen, The Mathematica Book, 4th ed. (Wolfram Media/Cambridge University Press, 1999).