Abstract

We introduce a semi-supervised support vector machine (S3yM) method. Given a training set of labeled data and a working set of unlabeled data, S3YM constructs a support vector machine us-ing both the training and working sets. We use S3YM to solve the transduction problem using overall risk minimization (ORM) posed by Yapnik. The transduction problem is to estimate the value of a classification function at the given points in the working set. This contrasts with the standard inductive learning problem of estimating the classification function at all possible values and then using the fixed function to deduce the classes of the working set data. We propose a general S3YM model that minimizes both the misclassification error and the function capacity based on all the available data. We show how the S3YM model for I-norm lin-ear support vector machines can be converted to a mixed-integer program and then solved exactly using integer programming. Re-sults of S3YM and the standard I-norm support vector machine approach are compared on ten data sets. Our computational re-sults support the statistical learning theory results showing that incorporating working data improves generalization when insuffi-cient training information is available. In every case, S3YM either improved or showed no significant difference in generalization com-pared to the traditional approach. Semi-Supervised Support Vector Machines 369 1