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# Neural Networks Provide Solutions to Real-World Problems: Powerful new algorithms to explore, classify, and identify patterns in data

By Matthew J. Simoneau, MathWorks and Jane Price, MathWorks

Inspired by research into the functioning of the human brain, artificial neural networks are able to learn from experience. These powerful problem solvers are highly effective where traditional, formal analysis would be difficult or impossible. Their strength lies in their ability to make sense out of complex, noisy, or nonlinear data. Neural networks can provide robust solutions to problems in a wide range of disciplines, particularly areas involving classification, prediction, filtering, optimization, pattern recognition, and function approximation.

### Popcorn?

A look at a specific application using neural networks technology will illustrate how it can be applied to solve real-world problems. An interesting example can be found at the University of Saskatchewan, where researchers are using MATLAB and the Neural Network Toolbox to determine whether a popcorn kernel will pop.

Knowing that nothing is worse than a half-popped bag of popcorn, they set out to build a system that could recognize which kernels will pop when heated by looking at their physical characteristics. The neural network learns to recognize what differentiates a poppable from an unpoppable kernel by looking at 16 features, such as roughness, color, and size.

The goal is to design a neural network that maps a set of inputs (the 16 features extracted from a kernel) to the proper output, in this case a 1 for popped, and -1 for unpopped. The first step is to gather this data from hundreds of kernels. To do this, the researchers extract the characteristics of each kernel using a machine vision system, then heat the kernel to see if it pops. This data, when combined with the proper learning algorithm, will be used to teach the network to recognize a good kernel from a bad one.

### Designing the network

As the name suggests, a neural network is a collection of connected artificial neurons. Each artificial neuron is based on a simplified model of the neurons found in the human brain. The complexity of the task dictates the size and structure of the network. The popcorn problem requires a standard feed-forward network. An example of this type of network is shown in Figure 1. But the popcorn problem needs 16 inputs, 15 neurons in the first hidden layer, 35 in the second, and 1 output neuron. Each neuron has a connection to each of the neurons in the previous layer. Each of these connections has a weight that determines the strength of the coupling.

Figure 1. Here is an example of a simple three- layer, feed-forward network. It has four inputs, two neurons in the first layer, three in the second layer, and one in the third (output) layer. There is a connection from each neuron to all the neurons in the previous layer, and each connection has a weight associated with it. The neuron takes signals from previous layers, multiplies each signal by the connection's weight, and adds them together. The neuron then passes the sum through a transfer function. The result becomes the neuron's output.

For this problem, the backpropagation algorithm guides the network's training. It holds the network's structure constant and modifies the weight associated with each connection. This is an iterative process that takes these initially random weights and adjusts them so the network will perform better after each pass through the data. Each set of features is presented to the neural network along with the corresponding desired output. The input signal propagates through the network and emerges at the output. The network's actual output is compared to the desired output to measure the network's performance. The algorithm then adjusts the weights to decrease this error. This training process continues until the network's performance can no longer improve.

The desired result is a neural network that is able to distinguish a poppable kernel from an unpoppable one. The key to the training is that the network doesn't just memorize specific kernels. Rather, it generalizes from the training sample and builds an internal model of which combinations of features determine “poppability.” The test, of course, is to give the network some data extracted from kernels it has never seen before and have it classify them. Illustrated in Figure 2, the network is correct three out of four times, providing the manufacturer with a method to significantly increase popcorn quality.

Figure 2. This graph shows the performance of the trained network on 130 kernels, 65 that popped (shown in blue) and 65 that didn't pop (shown in red). The neural network output is continuous, but the value 0.40 forms the boundary between kernels that are classified by the network as poppable and not poppable based on their extracted features. Red dots above the line and blue dots below the line are correctly classified.

### More Than Popcorn

Neural network technology has been proven to excel in solving a variety of complex problems in engineering, science, finance, and market analysis. Examples of the practical applications of this technology are widespread. For example, NOW! Software uses the Neural Network Toolbox to predict prices in futures markets for the financial community. The model is able to generate highly accurate, next-day price predictions. Meanwhile researchers at Scientific Monitoring, Inc., are using MATLAB and the Neural Network Toolbox to apply a neural network-based, sensor validation system to a simulation of a turbofan engine. Their ultimate goal is to improve the time-limited dispatch of an aircraft by deferring engine sensor maintenance without a loss in operational safety or performance.

### Highlights of the Neural Network Toolbox version 3.0

The latest release offers several new features, including new network types, learning and training algorithms, improved network performance, easier customization, and increased design flexibility.

• New modular network representation: all network properties can be easily customized and are collected in a single network object
• New reduced memory: Levenberg-Marquardt algorithm for handling very large problems
• New supervised networks - Generalized Regression - Probabilistic
• New network training algorithms
- Resilient Backpropogation (Rprop)
- Two Quasi-Newton methods
• Flexible and easy-to-customize network performance, initialization, learning and training functions
• Automatic creation of network simulation blocks for use with Simulink
• New training options - Automatic regularization - Training with validation - Early stopping
• New pre- and post-processing functions

Published 1998