Nonparallel Support Vector Machine Research Articles

Efficient sparse nonparallel support vector machines for classification

In this paper, we propose a novel nonparallel classifier, named sparse nonparallel support vector machine (SNSVM), for binary classification. Different with the existing nonparallel classifiers, such as the twin support vector machines (TWSVMs), SNSVM has several advantages: It constructs two convex quadratic programming problems for both linear and nonlinear cases, which can be solved efficiently by successive overrelaxation technique; it does not need to compute the inverse matrices any more before training; it has the similar sparseness with standard SVMs; it degenerates to the TWSVMs when the parameters are appropriately chosen. Therefore, SNSVM is certainly superior to them theoretically. Experimental results on lots of data sets show the effectiveness of our method in both sparseness and classification accuracy and, therefore, confirm the above conclusions further.

Nonparallel Support Vector Machines for Multiple-Instance Learning

In this paper, we proposed a new multiple-instance learning (MIL) method based on nonparallel support vector machines (called MI-NPSVM). For the linear case, MI-NPSVM constructs two nonparallel hyperplanes by solving two SVM-type prob- lems, which is different from many other maximum margin SVM-based MIL methods. For the nonlinear case, kernel functions can be easily applied to extend the linear case, which is different from other nonparallel SVM-based MIL methods. Further- more, compared with the existing MIL method based on nonparallel SVM – MI-TSVM, MI-NPSVM has two main advantages. Firstly the method enforces the structural risk minimization; secondly it does not need to solve a bilevel programming prob- lem anymore, but to solve a series of standard Quadratic Programming Problems (QPPs). All experimental results on public datasets show that our method is superior to the traditional MIL methods like MI-SVM, MI-TSVM etc.

A feature selection method for nonparallel plane support vector machine classification

Over the past decades, 1-norm techniques based on algorithms are widely used to suppress input features. Quite different from traditional 1-norm support vector machine (SVM), direct 1-norm optimization based on the primal problem of nonparallel plane classifiers like generalized proximal support vector machine, twin support vector machine (TWSVM) and least squares twin support vector machine (LSTSVM) are not capable of generating very sparse solutions that are vital for classification and can make them easier to store and faster to compute. To address the issue, in this paper, we develop a feature selection method for LSTSVM, called a feature selection method for nonparallel plane support vector machine classification (FLSTSVM), which is specially designed for strong feature suppression. We incorporate a Tikhonov regularization term to the objective of LSTSVM, and then minimize its 1-norm measure. Solution of FLSTSVM can follow directly from solving two smaller quadratic programming problems (QPPs) arising from two primal QPPs as opposed to two dual ones in TWSVM. FLSTSVM is capable of generating very sparse solutions. This means that FLSTSVM can reduce input features, for the linear case. When a nonlinear classifier is used, few kernel functions determine the classifier. In addition to having strong feature suppression, the edge of our method still lies in its faster computing time compared to that of TWSVM, Newton Method for Linear Programming SVM (NLPSVM) and LPNewton. Lastly, this algorithm is compared on public data sets, as well as an Exclusive Or (XOR) example.