Extracting Certainty from Uncertainty: Transductive Pairwise Classification from Pairwise Similarities
نویسندگان
چکیده
In this work, we study the problem of transductive pairwise classification from pairwise similarities 1. The goal of transductive pairwise classification from pairwise similarities is to infer the pairwise class relationships, to which we refer as pairwise labels, between all examples given a subset of class relationships for a small set of examples, to which we refer as labeled examples. We propose a very simple yet effective algorithm that consists of two simple steps: the first step is to complete the sub-matrix corresponding to the labeled examples and the second step is to reconstruct the label matrix from the completed sub-matrix and the provided similarity matrix. Our analysis exhibits that under several mild preconditions we can recover the label matrix with a small error, if the top eigen-space that corresponds to the largest eigenvalues of the similarity matrix covers well the column space of label matrix and is subject to a low coherence, and the number of observed pairwise labels is sufficiently enough. We demonstrate the effectiveness of the proposed algorithm by several experiments.
منابع مشابه
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 space...
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