Support vector machine with hypergraph-based pairwise constraints

Qiuling Hou, Meng Lv, Ling Zhen, Ling Jing
2016 SpringerPlus  
Introduction Support vector machine (SVM) (Vapnik 1995; Cortes and Vapnik 1995), founded on Vapnik's statistical learning theory, has already reached many achievements in practical problems. For binary classification problems, its target is to find a separating hyperlane being the middle one between two parallel hyperplanes, where the two hyperplanes are constructed following the maximum margin principle. As for its solution, obtained by solving a quadratic programming problem (QPP) in the dual
more » ... space, is global optimal. Furthermore, the kernel function (Shawe-Taylor and Cristianini 2004) introduced into SVM not only maps training vectors into a high-dimensional space, but also successfully transforms the nonlinear case into linear case. Thus, the case of nonlinear kernels is handled along lines similar to that used for linear kernels. Although the classical SVM has many good properties, one of the main challenges for it is the high computational complexity of the QPP. In addition, the trained performance also depends on the optimal parameters, which are usually found by cross-validation method. These shortcomings not only cause SVM to take a long time to train on a large database, but also prevent it Abstract Although support vector machine (SVM) has become a powerful tool for pattern classification and regression, a major disadvantage is it fails to exploit the underlying correlation between any pair of data points as much as possible. Inspired by the modified pairwise constraints trick, in this paper, we propose a novel classifier termed as support vector machine with hypergraph-based pairwise constraints to improve the performance of the classical SVM by introducing a new regularization term with hypergraphbased pairwise constraints (HPC). The new classifier is expected to not only learn the structural information of each point itself, but also acquire the prior distribution knowledge about each constrained pair by combining the discrimination metric and hypergraph learning together. Three major contributions of this paper can be summarized as follows: (1) acquiring the high-order relationships between different samples by hypergraph learning; (2) presenting a more reasonable discriminative regularization term by combining the discrimination metric and hypergraph learning; (3) improving the performance of the existing SVM classifier by introducing HPC regularization term. And the comprehensive experimental results on twenty-five datasets demonstrate the validity and advantage of our approach.
doi:10.1186/s40064-016-3315-x pmid:27722068 pmcid:PMC5035294 fatcat:rpw4szhxr5dgfb5zhapstfoani