二次判别函数的决策面是超二次曲面包括超平面、超平面对、超球面、超椭球面、超抛物面、超双曲面。二次判别函数f(x1,x2)f(x_1, x_2)f(x1​,x2​)f(x1,x2)x⊤Wxw⊤xb f(x_1, x_2) {\boldsymbol x}^ { \top} {\boldsymbol{{W}}}{\boldsymbol x} \boldsymbol{w}^ { \top} \boldsymbol{x} {b}f(x1​,x2​)x⊤Wxw⊤xbW[w11w12w21w22] {\boldsymbol W} \begin{bmatrix} w_{11} w_{12} \\ w_{21} w_{22} \end{bmatrix}W[w11​w21​​w12​w22​​]w[w1w2] {\boldsymbol w} \begin{bmatrix} w_1 \\ w_2 \end{bmatrix}w[w1​w2​​]x[x1x2] {\boldsymbol x} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}x[x1​x2​​]f(x1,x2)w11x12(w12w21)x1x2w22x22w1x1w2x2w0 f(x_1, x_2) w_{11}x_1^2 (w_{12} w_{21})x_1x_2 w_{22}x_2^2 w_1x_1 w_2x_2 w_{0}f(x1​,x2​)w11​x12​(w12​w21​)x1​x2​w22​x22​w1​x1​w2​x2​w0​决策面方程f(x1,x2)0 f(x_1, x_2) 0f(x1​,x2​)0球面椭球面双曲面平面对抛物面超平面