AIDAID202 · Lectures 9–10

Lecture 10 · K-class discriminants

Argmax of linear scores creates regions

A K-class linear discriminant uses one affine score per class. The winning class is the one with the largest score.

Predict first: Can one class occupy two disconnected islands when all class scores are linear?

Three-class score map

Winning class—
Runner-up margin—
Why are the decision regions convex?

Region k is an intersection of half-spaces y_k(x)≥y_j(x). Intersections of convex sets are convex, so a region cannot split into disconnected islands.