Brain–Computer Interfaces - Index of

320 Y. Li et al.
5.1.2 Support Vector Machine
The support vector machine (SVM) [45] is a linear discriminant tool that maximizes
the margin of separation between two classes based on the assumption that it
improves the classifier’s generalization capability. In contrast, Fisher linear discriminant
maximizes the average margin, i.e., the margin between the class means [34].
Figure 6 illustrates a typical linear hyperplane learned by a SVM.
From articles such as [34, 45], an optimal classifier for unseen data is that with
1
the largest margin
||w|| 2 , i.e. of minimal Euclidean norm ||w|| 2 . For a linear SVM,
the large margin (i.e. the optimal hyperplane w) is realized by minimizing the cost
function on the training data
under the constraints
J (w, ξ) = 1
2 �w�2 + C
n�
ξi, (20)
� T
yi w xi + b � ≥ 1 − ξi, ξi ≥ 0, ∀i = 1, ··· , n, (21)
Fig. 6 An example that illustrates the training of a support vector machine that finds the optimal
hyperplane with maximum margin of separation from the nearest training patterns. The nearest
training patterns are called the support vectors
i=1