4.1 ( ) Given a set of data points {xn}, we can define the convex hull to be the set of all points x given by x =



n

αnxn (4.156)

where αn  0 and



n αn = 1. Consider a second set of points {yn} together with their corresponding convex hull. By definition, the two sets of points will be linearly separable if there exists a vector
w and a scalar w0 such that
wTxn +w0 > 0 for all xn, and
wTyn+w0 < 0 for all yn. Show that if their convex hulls intersect, the two sets of points cannot be linearly separable, and conversely that if they are linearly separable, their convex hulls do not intersect.