Discriminant Function

Use-case

The Bayesian Classifier uses the Discriminant function to make the classification $g_i(x)$ Depending on the application, discriminant function is described as.

Class Problems

$$\boxed{s^{\ast }=\arg \underset{i\in \mathcal{S}}{\max }{g}_i(\mathbf{x})}$$

where, $g_i(\mathbf{x})=P(s=i|\mathbf{x})$, gives the minimum error rate classification.

Decision Problems

$$\boxed{a^{\ast }=\arg \underset{j\in \mathcal{A}}{\max }{g}_i(\mathbf{x})}$$

where, $g_i(\mathbf{x})=-R(a=i|\mathbf{x})$, gives the minimum risk decision.