Discriminant function and steroids

The R script considers a binary classification task where $\mathbf x\in \mathbb R^2$ and the inverse conditional distributions of the two classes are $\mathcal{N}(\mu_1,\sigma ^2 I)$ and $\mathcal{N}(\mu_2,\sigma ^2 I)$, respectively. Suppose that the two a priori probabilities are identical, that $\sigma =1$, $\mu_1=[-1,-2]^ T$ and $\mu_2=[2,5]^ T$. The positions of 100 points randomly drawn from $\mathcal{N}(\mu_1,\sigma ^2 I)$, of 100 points drawn from $\mathcal{N}(\mu_2,\sigma ^2 I)$ together with the optimal decision boundary computed by  are plotted in Figure .