1.1 Decision functions more than one class(see the hatched region in Fig. 1.5). These can be re- solved by decision-tree formulation or by introducing membership functions as discussed in Chapter 3 Class 1 Class 2 Fig. 1. 5 Class boundaries by pairwise formulation 1.1. 2.5 Error-Correcting Output Codes he fourth approach is to use error-correcting codes for encoding outputs 12 One-against-all formulation is a special case of error-correcting code with no error-correcting capability, and Chapter3,if“dont” care bits are introduced 1.1.2.6 All-at-Once Formulation The fifth approach is to determine decision functions all at once, namely, we determine the decision functions gi(x) by gi(x)>9i(x)for j*i, j=1, (1.21) In this formulation we need to determine n decision functions at all once[13, pp. 174-176, 8, pp. 437-440,[14-20. This results in solving a problem with a larger number of variables than the previous methods.1.1 Decision Functions 7 more than one class (see the hatched region in Fig. 1.5). These can be re￾solved by decision-tree formulation or by introducing membership functions as discussed in Chapter 3. Class 1 x1 x2 0 Class 2 g12(x) = 0 g23(x) = 0 g13(x) = 0 Class 3 Fig. 1.5 Class boundaries by pairwise formulation 1.1.2.5 Error-Correcting Output Codes The fourth approach is to use error-correcting codes for encoding outputs [12]. One-against-all formulation is a special case of error-correcting code with no error-correcting capability, and so is pairwise formulation, as discussed in Chapter 3, if “don’t” care bits are introduced. 1.1.2.6 All-at-Once Formulation The fifth approach is to determine decision functions all at once, namely, we determine the decision functions gi(x) by gi(x) > gj (x) for j = i, j = 1, . . . , n. (1.21) In this formulation we need to determine n decision functions at all once [13, pp. 174–176], [8, pp. 437–440], [14–20]. This results in solving a problem with a larger number of variables than the previous methods.