Equivalent Discriminant Function and Examples

The Discriminant function can be modified without changing the classification results.

$$\begin{array}{rl}& g_i(\mathbf{x})\to \alpha g_i(\mathbf{x}),\alpha >0\\ & g_i(\mathbf{x})\to \alpha +g_i(\mathbf{x}),\alpha \in \mathbb{R}\\ & g_i(\mathbf{x})\to f\left(g_i(\mathbf{x})\right)\end{array}$$

Where $f(\cdot )$ is a monotonically increasing function

Use cases

• Improving the confidence of the decision by having a very high $\alpha$
• Using $\alpha$ in the context of a multi-class problem to normalize each classification.