Pattern Recognition

and the decision boundaries are given by

$\begin{array}{l}P\left({\omega }_1|m\right)>P\left({\omega }_1|m\right)\\ \iff \ln P\left({\omega }_1|m\right)>\ln P\left({\omega }_1|m\right)\\ \iff \ln P\left({\omega }_1|m\right)+\ln P\left({\omega }_1\right)>\ln P\left({\omega }_1|m\right)+\ln P\left({\omega }_1\right),\left(3.50\right)\end{array}$

The decision boundaries are hyperplanes that are perpendicular to the connection lines between the expectation. If the a priori probabilities of the classes are equal, i.e., ln $\frac{P\left({\omega }_i\right)}{P\left({\omega }_j\right)}=0,$ then the hyperplanes lie at the center points between the expectation vectors. If the a priori probabilities are not equal, the hyperplanes move toward the component with lower a priori probability. Examples with one and two features are shown in Figure 3.10.

For the second step, continue ...