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In this article, an improved nonparallel support vector machine (INPSVM) is proposed for pattern classification. INPSVM inherits almost all advantages of nonparallel support vector machine (NPSVM), i.e., the kernel trick can be directly applied for the nonlinear case and the matrix inversion is avoided. These are completely different from the twin support vector machine (TSVM). Moreover, the INPSVM classifier has some incomparable advantages over TSVM and NPSVM. First, it can effectively eliminate the negative effect of noise, especially feature noise around the decision boundary. Second, the novel classifier has higher classification accuracy for both linear and nonlinear data sets compared with the other algorithms. Finally, a large number of experiments show that INPSVM is superior to other algorithms in efficiency, accuracy, and robustness.

This paper formulates a support vector machine with quantile hyper-spheres (QHSVM) for pattern classification. The idea of QHSVM is to build two quantile hyper-spheres with the same center for positive or negative training samples. Every quantile hyper-sphere is constructed by using pinball loss instead of hinge loss, which makes the new classification model be insensitive to noise, especially the feature noise around the decision boundary. Moreover, the robustness and generalization of QHSVM are strengthened through maximizing the margin between two quantile hyper-spheres, maximizing the inner-class clustering of samples and optimizing the independent quadratic programming for a target class. Besides that, this paper proposes a novel local center-based density estimation method. Based on it, ρ-QHSVM with surrounding and clustering samples is given. Under the premise of high accuracy, the execution speed of ρ-QHSVM can be adjusted. The experimental results in artificial, benchmark and strip steel surface defects datasets show that the QHSVM model has distinct advantages in accuracy and the ρ-QHSVM model is fit for large-scale datasets., Competing Interests: The authors have declared that no competing interests exist.