Robust Twin Parametric-margin Support Vector Machine For Pattern Classification

Support vector classifier is one of the hot issues in research.It is widely used in text classification,pattern recognition,financial regression,computational biology and other fields.In the process of data collection,there are often small errors,and the real data value exists in an uncertain region.These uncertain region will reduce the performance of the classification model,so it is necessary to consider uncertain region to make the classification model more robust.In this paper,a robust twin parametric-margin support vector machine(RTPMSVM)is proposed for the binary classification with uncertain region.More specifically,considering that the sample is subject to multivariate Gaussian distribution,the construction methods of several covariance matrices are given.A new loss function is defined.Since the training samples obey multivariate Gaussian distribution,the loss function is the expected value of the classical SVM loss function.R-TPMSVM aims to find two nonparallel parametric-margin hyperplanes from a pair of smaller size convex optimization problems.These optimization problems are solved by stochastic gradient descent method.The formulation of R-TPMSVM approximates the TPMSVM formulation when the training example is an isotropic Gaussian with variance tends to zero.Experimental results show that the proposed approach has comparable generalization.