Research On Non-parallel Support Vector Machines For Noise Classification

Research from support vector machines to non-parallel support vector machines has attracted widespread attention in recent years.The support vector machine is mainly to find a pair of parallel hyperplanes,and to make the interval between the two parallel hyperplanes as large as possible.The non-parallel support vector machine is designed to construct an optimal hyperplane for each type of data.The constructed hyperplane does not have this definition in parallel,and it is expected that each hyperplane can be close to this class of data,away from other class data.The non-parallel support vector machine solves two problems faced by the traditional support vector machine.One is the high computational complexity required to solve the inequality quadratic programming,the other is to solve the XOR problem,and the non-parallel support vector machine pairs different types of data.Have a good classification ability.In some noisy data,noise will reduce the generalization ability of the decision function,which will easily cause over-fitting and affect its classification performance.The non-parallel support vector machine mainly considers the loss function and data structure to improve its classification performance.Therefore,based on the non-parallel support vector machine,a non-parallel support vector machine model of different models is proposed.This paper is divided into the following two main research contents:On the one hand,different non-parallel support vector machine models are constructed by using different loss functions from the perspective of support vector machine.This model introduces a new soft interval loss function,which can be applied to different types of data;this new non-parallel support vector machine can be degraded to the standard support vector machine model,so the calculation method of the model and the calculation method of support vector machine It is the same;adding the sparse loss function to the non-parallel support vector machine,while maintaining the sparse characteristics,can adapt to different types of cross data.The effectiveness was verified by a large number of public dataset experiments.On the other hand,two excellent non-parallel support vector machine models:Proximal Support Vector Machines Generalized Eigenvalues?GEPSVM?and their Improved Generalized Eigenvalue Proximal Support Vector Machine?IGEPSVM?,they have good promotional performance,but they also have some drawbacks in practical applications.First,the empirical risk in GEPSVM and IGEPSVM is calculated using the L₂-norm.The squared distance is used in the L₂-norm,which is sensitive to noise and outliers and reduces its classification performance.In fact,the above two non-parallel support vector machines do not consider the relevant structure of the data.When the data is highly correlated,its classification ability is reduced.In order to alleviate the above problems,this paper proposes a Robust Nonparallel Proximal Support Vector Machine?RNPSVM?for noise classification.On the basis of IGEPSVM,the L₂-norm is changed to L₁-norm,L₁-norm is measured by the sum of absolute values,reduces the sensitivity to noise,and aims to maximize the L₁-norm class distance while minimizing the L₁-norm class The internal distance makes it robust to outliers;the trace lasso penalty term?adaptive model based on training data?is introduced by considering the correlation of the data.This Trace Lasso penalty term not only has sparsity,but also in data correlation.The classification performance is also good at higher times.Singular value problems may be encountered in GEPSVMs.The singular value problem can be avoided by modifying the model.Finally,an effective iterative algorithm is proposed and its convergence is verified.Extensive experimental results on synthetic and realistic noise data sets demonstrate the effectiveness of RNPSVM.