The normalization factor is introduced because the nominator of the proposed kernel depends on the length of the compared documents.
given the adjacency matrices of the transformed graph representations of two documents A 1 , A 2 where the value of each entry in the adjacency matrix is set equal to the label of the corresponding edge, and the diagonal matrices D 1 , D 2 with diagonal entries set to 1 if the corresponding term exists in the corresponding document, we first compute the matrices M 1 , M 2 as shown below: and we then compute the normalization factor using the following formula: where • F is the Frobenius norm for matrices.