Neural Network Toolbox User's Guide

Neuron ModelAll of the neurons in this toolbox have provision for a bias, and a bias is usedin many of our examples and will be assumed in most of this toolbox. However,you may omit a bias in a neuron if you want.As previously noted, the bias b is an adjustable (scalar) parameter of theneuron. It is not an input. However, the constant 1 that drives the bias is aninput and must be treated as such when considering the linear dependence ofinput vectors in Chapter 4, “Linear Filters.”Transfer FunctionsMany transfer functions are included in this toolbox. A complete list of themcan be found in “Transfer Function Graphs” on page 14-14. Three of the mostcommonly used functions are shown below.a+1n0-1a = hardlim(n)Hard-Limit Transfer FunctionThe hard-limit transfer function shown above limits the output of the neuronto either 0, if the net input argument n is less than 0; or 1, if n is greater thanor equal to 0. We will use this function in Chapter 3 “Perceptrons” to createneurons that make classification decisions.The toolbox has a function, hardlim, to realize the mathematical hard-limittransfer function shown above. Try the code shown below.n = -5:0.1:5;plot(n,hardlim(n),'c+:');It produces a plot of the function hardlim over the range -5 to +5.All of the mathematical transfer functions in the toolbox can be realized witha function having the same name.The linear transfer function is shown below.2-3