If you have c classes/categories and the targets are the columns of the c-dimensional unit matrix, then the outputs are estimates of the input conditional posterior probabilities for each class.
The input is assigned to the class corresponding to the maximum output regardless of the type of activation function when one of the following are used:
softmax: 0 < P(i=c|x) < 1, sum(i=1:c){P(i=c|x)} = 1
logsig: 0 < P(i=c|x) < 1
purelin: sum(i=1:c){P(i=c|x)} = 1
Typically, the most important goal is correct classification and not necessarily the best estimate of the posteriors.
Use softmax if the best posterior estimates are desired. Otherwise use logsig and normalize to a unity sum after training. Since the estimates using purelin can be negative and/or exceed unity, you can dream up a number of ways to make them look appealing. But why bother when you can just as easily use the other functions?
Hope this helps.
Greg
