Abstract

We examine mathematical models for semi-supervised support vector machines (S VM). Given a training set of labeled data and a working set of unlabeled data, S VM constructs a support vector machine using both the training and working sets. We use S VM to solve the transductive inference problem posed by Vapnik. In transduction, the task is to estimate the value of a classification function at the given points in the working set. This contrasts with inductive inference which estimates the classification function at all possible values. We propose a general S VM model that minimizes both the misclassification error and the function capacity based on all the available data. Depending on how poorly-estimated unlabeled data are penalized, different mathematical models result. We examine several practical algorithms for solving these model. The first approach utilizes the S VM model for 1-norm linear support vector machines converted to a mixedinteger program (MIP). A global solution of the ...

Citations