Supplementary Material: Extracting Certainty from Uncertainty: Transductive Pairwise Classification from Pairwise Similarities

We first prove Theorem 1 regarding the perfect recovery of the sub-matrix Ẑ, which is essentially a Corollary of the following Theorem for matrix completion. Corollary 1. (Theorem 1.1 [2]) Let M be an n1 × n2 matrix of rank r with singular value decomposition UΣV >. Without loss of generality, impose the conventions n1 ≤ n2, U is n1 × r, and V is n2 × r. Assume that (i) The row and column spaces have coherences bounded above by some positive μ0, and (ii) the matrix UV has a maximum entry bounded by μ1 √ r/(n1n2) in absolute value for some positive μ1. Suppose N entries of M are observed with locations sampled uniformly at random denoted by Σ. Then if