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**1 - 2**of**2**### Extracting Certainty from Uncertainty: Transductive Pairwise Classification from Pairwise Similarities

"... In this work, we study the problem of transductive pairwise classification from pairwise similarities 1. The goal of transductive pairwise classification from pair-wise similarities is to infer the pairwise class relationships, to which we refer as pairwise labels, between all examples given a subse ..."

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In this work, we study the problem of transductive pairwise classification from pairwise similarities 1. The goal of transductive pairwise classification from pair-wise 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 sec-ond step is to reconstruct the label matrix from the completed sub-matrix and the provided similarity matrix. Our analysis exhibits that under several mild precon-ditions 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. 1

### SCALABLE APPROXIMATION OF KERNEL FUZZY C-MEANS By

, 2014

"... This report has been approved in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE in Computer Engineering. ..."

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This report has been approved in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE in Computer Engineering.