Fig. 1.

The rankprop algorithm. Given a set of objects (in this case, proteins) X = x_1,..., x_m, let x₁ be the query and x_2,..., x_m be the database (targets) we would like to rank. Let K be the matrix of object–object similarities, i.e., K_ij gives a similarity score between x_i and x_j, with K normalized so that for all i. For computational efficiency, we set K_1i = K_i1 for all i, so that we can compute weights involving the query using a single execution of psi-blast. Let y_i, i = 2,..., m, be the initial ranking “score” of a target. In practice, for efficiency, the algorithm is terminated after a fixed number I of iterations, and y_i(I) is used as an approximation of . The parameter α ∈ [0,1] is set a priori by the user. For α = 0, no global structure is found, and the algorithm's output is just the ranking according to the original distance metric. These experiments use α = 0.95, looking for clear cluster structure in the data.