Pairwise Constraint Propagation by Semidefinite Programming for Semi-Supervised Classification

author: Zhenguo Li, Department of Information Engineering, Chinese University of Hong Kong
published: Aug. 4, 2008,   recorded: July 2008,   views: 4041


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We consider the general problem of learning from pairwise constraints and unlabeled data. The pairwise constraints specify whether two objects belong to the same class or not, known as the must-link constraints and the cannot-link constraints. We propose to learn a mapping that is smooth over the data graph and maps the data onto a unit hypersphere, where two must-link objects are mapped to the same point while two cannot-link objects are mapped to be orthogonal. We show that such a mapping can be achieved by formulating a semidefinite programming problem, which is convex and can be solved globally. Our approach can effectively propagate pairwise constraints to the whole data set. It can be directly applied to multi-class classification and can handle data labels, pairwise constraints, or a mixture of them in a unified framework. Promising experimental results are presented for classification tasks on a variety of synthetic and real data sets.

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