1.3 Data sets used in the book the training data. Although the generalization ability is directly affected by the positions, conventional training methods do not consider this x …, Fig. 1.7 Class boundary when classes do not overlap In a support vector machine, the direct decision function that maximizes the generalization ability is determined for a two-class problem. Assuming that the training data of different classes do not overlap the decision function is determined so that the distance from the training data is maximized. We call this the optimal decision function. Because it is difficult to determine a nonlinear decision function, the original input space is mapped into a high- dimensional space called feature space. And in the feature space, the optimal decision function, namely, the optimal hyperplane is determined Support vector machines outperform conventional classifiers, especially when the number of training data is small and the number of input vari ables is large. This is because the conventional classifiers do not have the mechanism to maximize the margins of class boundaries. Therefore, if we troduce some mechanism to maximize margins, the generalization ability is 1. 3 Data sets Used in the book In this book we evaluate methods for pattern classification and function ap- proximation using some benchmark data sets so that and disad-1.3 Data Sets Used in the Book 9 the training data. Although the generalization ability is directly affected by the positions, conventional training methods do not consider this. Class 1 x1 x2 0 Class 2 g1 (x) = 0 g2 (x) = 0 Fig. 1.7 Class boundary when classes do not overlap In a support vector machine, the direct decision function that maximizes the generalization ability is determined for a two-class problem. Assuming that the training data of different classes do not overlap, the decision function is determined so that the distance from the training data is maximized. We call this the optimal decision function. Because it is difficult to determine a nonlinear decision function, the original input space is mapped into a high￾dimensional space called feature space. And in the feature space, the optimal decision function, namely, the optimal hyperplane is determined. Support vector machines outperform conventional classifiers, especially when the number of training data is small and the number of input vari￾ables is large. This is because the conventional classifiers do not have the mechanism to maximize the margins of class boundaries. Therefore, if we in￾troduce some mechanism to maximize margins, the generalization ability is improved. 1.3 Data Sets Used in the Book In this book we evaluate methods for pattern classification and function ap￾proximation using some benchmark data sets so that advantages and disad-