Convex Optimization

8.6.2 Nonlinear discrimination

We can just as well seek a nonlinear function f, from a given subspace of functions, that is positive on one set and negative on another:

Provided f is linear (or affine) in the parameters that define it, these inequalities can be solved in exactly the same way as in linear discrimination. In this section we examine some interesting special cases.

Quadratic discrimination

Suppose we take f to be quadratic: f(x) = x^T P x + q^T x + r. The parameters P ∈ Sⁿ, q ∈ Rⁿ, r ∈ R must satisfy the inequalities

which is a set of ...