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## Error Calculation

Error calculation is an important aspect of any neural network. Whether the neural network is supervised or unsupervised, an error rate must be calculated. The goal of virtually all training algorithms is to minimize the rate of error. In this section, we will examine how the rate of error is calculated for a supervised neural network. We will also discuss how the rate of error is determined for an unsupervised training algorithm. We will begin this section by examining two error calculation steps used for supervised training.

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## Hopfield Pattern Recognition Application

Hopfield networks can be much larger than four neurons. For the third example, we will examine a 64-neuron Hopfield network. This network is connected to an 8x8 grid, which an application allows you to draw upon. As you draw patterns, you can either train the network with them or present them for recognition.

The user interface for the application can be seen in Figure 3.3.

Figure 3.3: A pattern recognition Hopfield application.

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## Problems Commonly Solved With Neural Networks

There are many different problems that can be solved with a neural network. However, neural networks are commonly used to address particular types of problems. The following four types of problem are frequently solved with neural networks:

• Classification
• Prediction
• Pattern recognition
• Optimization

These problems will be discussed briefly in the following sections. Many of the example programs throughout this book will address one of these four problems.

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## Solving Problems with Neural Networks

A significant goal of this book is to show you how to construct neural networks and to teach you when to use them. As a programmer of neural networks, you must understand which problems are well suited for neural network solutions and which are not. An effective neural network programmer also knows which neural network structure, if any, is most applicable to a given problem. This section begins by first focusing on those problems that are not conducive to a neural network solution.

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## A Feedforward Neural Network

A feedforward neural network is similar to the types of neural networks that we have already examined. Just like many other types of neural networks, the feedforward neural network begins with an input layer. The input layer may be connected to a hidden layer or directly to the output layer. If it is connected to a hidden layer, the hidden layer can then be connected to another hidden layer or directly to the output layer. There can be any number of hidden layers, as long as there is at least one hidden layer or output layer provided.

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## Introduction

In this chapter we shall examine one of the most common neural network architectures, the feedforword backpropagation neural network. This neural network architecture is very popular, because it can be applied to many different tasks. To understand this neural network architecture, we must examine how it is trained and how it processes a pattern.

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## Error Calculation

Error calculation is an important aspect of any neural network. Whether the neural network is supervised or unsupervised, an error rate must be calculated. The goal of virtually all training algorithms is to minimize the rate of error. In this section, we will examine how the rate of error is calculated for a supervised neural network. We will also discuss how the rate of error is determined for an unsupervised training algorithm. We will begin this section by examining two error calculation steps used for supervised training.

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## Creating a Java Hopfield Neural Network

The Hopfield neural network is implemented using two classes. The first class, called HopfieldNetwork is the main class that performs training and pattern recognition. This class relies on the Matrix and MatrixMath classes, introduced in chapter 2, to work with the neural network's weight matrix. The second class, called HopfieldException, is an exception that is raised when an error occurs while processing the Hopfield network. This is usually triggered as a result of bad input.

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## Problems Commonly Solved With Neural Networks

There are many different problems that can be solved with a neural network. However, neural networks are commonly used to address particular types of problems. The following four types of problem are frequently solved with neural networks:

• Classification
• Prediction
• Pattern recognition
• Optimization

These problems will be discussed briefly in the following sections. Many of the example programs throughout this book will address one of these four problems.

Technology:
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## Solving Problems with Neural Networks

A significant goal of this book is to show you how to construct neural networks and to teach you when to use them. As a programmer of neural networks, you must understand which problems are well suited for neural network solutions and which are not. An effective neural network programmer also knows which neural network structure, if any, is most applicable to a given problem. This section begins by first focusing on those problems that are not conducive to a neural network solution.

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