A convex relaxation framework for a class of semi-supervised learning methods and its application in pattern recognition

• We propose a semi-definite program relaxation framework for a class of S3VMs.
• One significant feature of this SDP framework is that it can implement L1-norm.
• This SDP framework needs only to solve the primal problems.
• The proposed approach is applied directly to identify the purity of maize seeds.

Semi-supervised learning has been an attractive research tool for using unlabeled data in pattern recognition. Applying a novel semi-definite programming (SDP) relaxation strategy to a class of continuous semi-supervised support vector machines (S3VMs), a new convex relaxation framework for the S3VMs is proposed based on SDP. Compared with other SDP relaxations for S3VMs, the proposed methods only require solving the primal problems and can implement L1-norm regularization. Furthermore, the proposed technique is applied directly to recognize the purity of hybrid maize seeds using near-infrared spectral data, from which we find that the proposed method achieves equivalent performance to the exact solution algorithm for solving the S3VM in different spectral regions. Experiments on several benchmark data sets demonstrate that the proposed convex technique is competitive with other SDP relaxation methods for solving semi-supervised SVMs in generalization.