1.1 Decision Functions and into Class 2 if g1(x)<g2(x) (1.5) In this case, the class boundary is given by(see the dotted curve in Fig 12) (1.6) This means that the class boundary is indirectly obtained by solving(1.6) for x. We call this type of decision function an indirect decision function Class 2 Fig. 1.2 Class boundary for Fig. 1.1 If we define the decision functions by 1(x) (1.7) we classify x into Class l if 91(x)>0 and into Class 2 if g2(x)>0. Thus the class boundary is given by (x)=-92(x)=0. Namely, the class boundary corresponds to the curve where the decision func tion vanishes. We call this type of decision function a direct decision function. If the decision function is linear, namely, g1 (x)is given by1.1 Decision Functions 3 and into Class 2 if g1(x) < g2(x). (1.5) In this case, the class boundary is given by (see the dotted curve in Fig. 1.2) g1(x) = g2(x). (1.6) This means that the class boundary is indirectly obtained by solving (1.6) for x. We call this type of decision function an indirect decision function. Class 1 x1 x2 0 Class 2 g1 (x) = 0 g2 (x) = 0 Class boundary Fig. 1.2 Class boundary for Fig. 1.1 If we define the decision functions by g1(x) = −g2(x), (1.7) we classify x into Class 1 if g1(x) > 0 (1.8) and into Class 2 if g2(x) > 0. (1.9) Thus the class boundary is given by g1(x) = −g2(x)=0. (1.10) Namely, the class boundary corresponds to the curve where the decision func￾tion vanishes. We call this type of decision function a direct decision function. If the decision function is linear, namely, g1(x) is given by