A class of smooth semi-supervised SVM by difference of convex functions programming and algorithm

Owing to its wide applicability, semi-supervised learning is an attractive method for using unlabeled data in classification. Applying a new smoothing strategy to a class of continuous semi-supervised support vector machines (S3VMs), this paper proposes a class of smooth S3VMs (S4VMs) without adding new variables and constraints to the corresponding S3VMs. Moreover, a general framework for solving the S4VMs is constructed based on robust DC (difference of convex functions) programming. Furthermore, DC optimization algorithms (DCAs) for solving the S4VMs are investigated. The resulting DCAs converge and only require solving one linear or quadratic program at each iteration. Numerical experiments on some real-world databases demonstrate that the proposed smooth S3VMs are feasible and effective, and have comparable results as other S3VMs.

Highlight
► A class of smooth S3VMs (S4VMs) is proposed.
► The S4VMs add no new variables and constraints compared to the S3VMs.
► A general framework for solving S4VMs is constructed based on DC programming.
► The resulting DCA converges and needs solving one linear or quadratic programming.