Neural Networks

Artificial neural networks (ANN) are used as a statistical analysis tool. They are designed to simulate a biological nervous system. These networks begin "ignorant", but build through a learning process to output answers. ANNs have the ability to create, learn, and memorize relationships in the data that it is given. There are several different kinds of ANN: Kohonen, Self-Organizing Map, and Back Propagation ANN being the most popular.

Neural networks (NN) use very sophisticated non-linear modeling techniques. In the past, most relationships between data were determined with linear models and optimization. Also, NNs learn by example. The NN user gathers certain data, and then uses training algorithms to automatically learn the structure and relationship of the data. Although the NN user needs knowledge to implement the NN, for example in selecting and preparing the data, interpreting the results, the amount of knowledge needed is significantly less than what is needed to use a traditional statistical method.

The structure of a neural network appears like the following:

The bottom layer represents the input layer, in this case with 5 inputs labeled X1 through X5. In the middle is something called the hidden layer, with a variable number of nodes. It is the hidden layer that performs much of the work of the network. The output layer in this case has two nodes, Z1 and Z2 representing output values we are trying to determine from the inputs. For example, we may be trying to predict sales (output) based on past sales, price and season (input).

Each node in the hidden layer is fully connected to the inputs. That means what is learned in a hidden node is based on all the inputs taken together. This hidden layer is where the network learns interdependencies in the model. The following diagram provides some detail into what goes on inside a hidden node.

Simply speaking a weighted sum is performed: X1 times W1 plus X2 times W2 on through X5 and W5. This weighted sum is performed for each hidden node and each output node and is how interactions are represented in the network.
Each summation is then transformed using a nonlinear function before the value is passed on to the next layer.

ANNs are used mostly for classification, modeling, and prediction.

In classification, its uses span from medical diagnosis, to signature verification, to cell types, to voice and image recognition. In prediction, its uses range from sales forecasting, to performance, to weather, and to gambling. In modeling, ANNs are used in many ways including signal compression, robotics, and systems control.

Programmers decided that instead of using the "traditional" method of carrying instructions one at a time, neural network software enables the computer to analyze data by sending it through simulated processors that are interconnected through weights. Although ANN technologies are complex, their sheer results are very useful. Just by using some data that was collected, one can send it through the ANN to "learn". By feeding data that is collected through the neural network, the ANN will constantly refine itself and then give out an accurate response. After analyzing the data, the network begins to organize itself. It is similar to how humans learn by example.

Neural networks are quickly gaining popularity because of today's technology and processing power. What once took days to analyze, now can take a several minutes. Traditional statistical methods will never be the same.