Extend the logistic regression method in Section $6\mathrm{.}3$ to deal with pattern$-$classification prob$-$

lems involving K $>2$ classes. Specify how to use the softmax function in Eq$.(6\mathrm{.}18)$ for K$-$class

pattern classification and give a training algorithm based on the gradient descent method.

Hint: i$)$ substitute linear models xk $=$ w$$

k x $($k $=\{1,2,...,$ K$)$ into the softmax function to derive

the multiclass classifier; ii$)$ use K$-$dimensional one$-$hot vectors to represent K$-$class labels.