6.3 Graph kernel. Let G = (V; E) be an undirected graph with vertex set V and edge set E. V could represent a set of documents or biosequences and E the set of connections between them. Let w[e] 2 R denote the weight assigned to edge e 2 E. The weight of a path is the product of the weights of its constituent edges. Show that the kernel K over VV where K(p; q) is the sum of the weights of all paths of length two between p and q is PDS (Hint: you could introduce the matrix W = (Wpq), where Wpq = 0 when there is no edge between p and q, Wpq equal to the weight of the edge between p and q otherwise).