Cyber-Physical Systems

192  ◾  Cyber-Physical Systems

In a multidimensional space, the line in Figure 14.2 will be a hyperplane. e points x on the

hyperplane satisfy wx + b = 0, where w is normal to the hyperplane. If ∥w∥ is the Euclidean norm

of w, |b|/∥w∥ is the perpendicular distance from the hyperplane to the origin. Suppose d

+

and

d

−

are the shortest distance from the hyperplane to the nearest positive and negative subjects, the

“margin” of a hyperplane can be defined as d

+

+ d

−

. e linear SVMs are looking for the separating

hyperplane with the largest margin, which can be expressed [20] as

x

i

w + b ≥ +1 for y

i

= +1, (14.5)

x

i

w + b ≤ −1 for y

i

= −1, (14.6