Perceptron and linear models
Let's consider the example of a regression problem where we have two input variables and one output or dependent variable and illustrate the use of ANN for creating a model that can predict the value of the output variable for a set of input variables:
Figure 4.2 Sample training data
In this example, we have x1 and x2 as input variables and y as the output variable. The training data consists of five data points and the corresponding values of the dependent variable, y. The goal is to predict the value of y when x1 = 6 and x2 = 10. Any given continuous function can be implemented exactly by a three-layer neural network with n neurons in the input layer, 2n + 1 neurons in the hidden layer and m neurons in the hidden layer. Let's represent this with a simple neural network:
Figure 4.3 ANN notations
Component notations of the neural network
There is a standardized way in which the neural networks are denoted, as follows:
- x1 and x2 are inputs (It is also possible to call...
