1. Linear Discriminant x2x2 x1x1 class 1 class 2 g 1 (x|w 1 )= w 10 + w 11 x 1 + w 12 x 2 e.g.: 1 - 5x 1 + 4x 2 (5,7) (8,7)

2. Tree classifier x2x2 x1x1 class 1 class 2

3. Bayesian x2x2 x1x1 class 1 class 2 p(C|x 1,x 2 )=p(C) p(x 1 |C) p(x 2 |C) / p(x 1,x 2 )

4. Quadratic Discriminant Example x2x2 x1x1 class 1 class 2 (x 1 - a) 2 + (x 2 - b) 2 = r 2 ex: g 1 =(x 1 - 7) 2 + (x 2 - 4) 2 - 4 (6,5) (5,2)

5. Quadratic Discriminant Example, continued convert quadratic form to linear: g 1 =ax 1 2 +bx 2 2 +cx 1 x 2 +dx 1 +ex 2 +f example: g 1 = (x 1 - 7) 2 + (x 2 - 4) 2 - 2f = 1x 1 2 +1x 2 2 +0x 1 x 2 -14x 1 - 8x 2 +61 = 1z 1 +1z 2 +0z 3 -14z 4 - 8z 5 +61

6. Quadratic Discriminant Example, continued x2x2 x1x1 class 1 class 2 ex: g 1 =x 1 2 – 14x 1 + x 2 2 – 8x 2 +61 (6,5) → (36, 25, 30, 6, 5) (5,2) → (25, 4, 10, 5, 2) g 1 =1z 1 + 1z 2 – 14z 4 – 8z 5 +61