Abstract
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.
Highlights
Support vector machine (SVM) [1] proposed by Vapnik and his cooperators has become an excellent tool for machine learning
For θ = 0%, compared with SVM and twin support vector machine (TWSVM), twinhypersphere support vector machine (THSVM) and QHSVM have better classification accuracies, which shows that the nonparallel hyper-planes and inner-class clustering of samples strengthen the performance of classifiers
All these results show that QHSVM performs the best in accuracy for datasets with noise samples, which is due to pinball losses, two nonparallel support hyper-spheres and inner-class clustering of samples
Summary
Support vector machine (SVM) [1] proposed by Vapnik and his cooperators has become an excellent tool for machine learning. Different versions of classifiers have been extended from SVDD because the inner-class of samples can be gathered to the greatest extent These classifiers include maximal-margin spherical-structured multi-class SVM (MSM-SVM) [20], twin support vector hyper-sphere (TSVH) [21], twinhypersphere support vector machine (THSVM) [22], maximum margin and minimum volume hyper-spheres machine with pinball loss (Pin-M3HM) [23] and least squares twin support vector hyper-sphere (LS-TSVH) [24]. A novel support vector machine with quantile hyper-spheres (QHSVM) for pattern classification is proposed. It inherits the excellent genes of SVDD_neg, TWSVM and Pin-SVM.
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