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**A new semi-supervised classifier based on maximum vector-angular margin.**
*(English)*
Zbl 1364.65122

Summary: Semi-supervised learning is an attractive method in classification problems when insufficient training information is available. In this investigation,a new semi-supervised classifier is proposed based on the concept of maximum vector-angular margin, (called S\(^3\)MAMC), the main goal of which is to find an optimal vector \(c\) as close as possible to the center of the dataset consisting of both labeled samples and unlabeled samples. This makes S\(^3\)MAMC better generalization with smaller VC (Vapnik-Chervonenkis) dimension. However, S\(^3\)MAMC formulation is a non-convex model and therefore it is difficult to solve. Following that we present two optimization algorithms, mixed integer quadratic program (MIQP) and DC (difference of convex functions) program algorithms, to solve the S\(^3\)MAMC. Compared with the supervised learning methods, numerical experiments on real and synthetic databases demonstrate that the S\(^3\)MAMC can improve generalization when the labelled samples are relatively few. In addition, the S\(^3\)MAMC has competitive experiment results in generalization compared to the traditional semi-supervised classification methods.

### MSC:

65K05 | Numerical mathematical programming methods |

90C26 | Nonconvex programming, global optimization |

90C11 | Mixed integer programming |

78M50 | Optimization problems in optics and electromagnetic theory |

### Keywords:

vector-angular margin; semi-supervised learning; support vector machine; DC programming; mixed integer programming### Software:

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\textit{L. Yang} and \textit{Y. Chao}, J. Ind. Manag. Optim. 13, No. 2, 609--622 (2017; Zbl 1364.65122)

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