Quadratic Decision Boundary

Definition

Quadratic Decision Boundary

A quadratic decision boundary in is a boundary represented by the zero set of a polynomial score of degree at most two:

where is symmetric, and . Opposite signs of assign points to opposite classes; the zero set represents a class boundary where the score changes sign.

If and , is a linear decision boundary. Non-zero permits curved boundaries, including circles, ellipses and hyperbolas, as well as degenerate cases.

Independent quadratic terms

Symmetry gives

Each pair contributes one cross-term, not two independently adjustable terms. Thus the quadratic part has

independent coefficients. See why this affects estimation.