  We define and study the link prediction problem in bipartite networks,
specializing general link prediction algorithms to the bipartite case. In a
graph, a link prediction function of two vertices denotes the similarity or
proximity of the vertices. Common link prediction functions for general graphs
are defined using paths of length two between two nodes. Since in a bipartite
graph adjacency vertices can only be connected by paths of odd lengths, these
functions do not apply to bipartite graphs. Instead, a certain class of graph
kernels (spectral transformation kernels) can be generalized to bipartite
graphs when the positive-semidefinite kernel constraint is relaxed. This
generalization is realized by the odd component of the underlying spectral
transformation. This construction leads to several new link prediction
pseudokernels such as the matrix hyperbolic sine, which we examine for rating
graphs, authorship graphs, folksonomies, document--feature networks and other
types of bipartite networks.
