1.1 Decision Functions Class 1 马2(x)=0 Fig. 1. 3 Class boundaries by one-against-all formulation 1.1.2.3 Decision-Tree formulation The second approach is based on a decision tree. It is considered to be a variant of one-against-all formulation. We determine the ith decision function gi (x)(i=l,., n-1), so that when x belongs to class i, (x)>0 and when x belongs to one of the classes i+1,.,n g1(x)<0 (1.16) In classifying x, starting from g1(x), we find the first positive gi (x)and classify x into class i. If there is no such i among gi(x)(i=l,-., n-1),w classify x into class n. Figure 1. 4 shows an example of decision functions for four classes. The decision functions change if we determine decision functions in descending order or in an arbitrary order of class labels. Therefore, in this architecture, we need to determine the decision functions so that classification performance in he upper level of the tree is more accurate than in the lower one. Otherwise the classification performance may not be good1.1 Decision Functions 5 Class 1 x1 x2 0 g Class 2 1 (x) = 0 g2 (x) = 0 g3 (x) = 0 Class 3 Fig. 1.3 Class boundaries by one-against-all formulation 1.1.2.3 Decision-Tree Formulation The second approach is based on a decision tree. It is considered to be a variant of one-against-all formulation. We determine the ith decision function gi(x) (i = 1,...,n − 1), so that when x belongs to class i, gi(x) > 0, (1.15) and when x belongs to one of the classes {i + 1,...,n}, gi(x) < 0. (1.16) In classifying x, starting from g1(x), we find the first positive gi(x) and classify x into class i. If there is no such i among gi(x) (i = 1,...,n − 1), we classify x into class n. Figure 1.4 shows an example of decision functions for four classes. The decision functions change if we determine decision functions in descending order or in an arbitrary order of class labels. Therefore, in this architecture, we need to determine the decision functions so that classification performance in the upper level of the tree is more accurate than in the lower one. Otherwise, the classification performance may not be good