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Abstract:
We introduce a semi-supervised support vector machine method
(SSSVM). Given a training set of labeled data and a working set of
unlabeled data, SSSVM constructs a support vector machine using
both the training and working sets. We use SSSVM to solve the
overall risk minimization problem (ORM) posed by Vapnik. The ORM
problem is to estimate the value of a classification function at
the given points in the working set. This contrasts with the
standard learning problem of empirical risk minimization which
estimates the classification function at all possible values. We
propose a general SSSVM model that minimizes both the
misclassification error and the function capacity based on all the
available data. We show how the SSSVM model for 1-norm linear
support vector machines can be converted to a mixed-integer program
(MIP) and then solved exactly using integer programming. Results of
SSSVM-MIP and the standard ERM approach are compared on eleven data
sets. Our computational results support the statistical learning
theory results showing that incorporating working data improves
generalization when insufficient training information is available.
In every case, SSSVM either improved or showed no significant
difference in generalization compared to the standard
approach.
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