Research On Multiview Learning Methods Based On Margin Distribution Theory

Similar to the central idea of maximizing the minimum margin of support vector machine,margin distribution has been proven to play a crucial role in improving generalization ability.In recent studies,many methods considering the margin distribution have been proposed successively,showing attractive performance.However,these methods are usually proposed based on single-view data,which easily leads to the curse of dimensionality and the loss of statistical characteristic for multiview data.Considering that there is almost no research on multiview margin distribution,in order to explore the optimization of margin distribution in multiview learning,a new multiview margin distribution model is proposed in this paper,and two fast models are proposed to reduce the computational cost.The details are as follows:According to the characteristics of multiview data,this paper constructs the multiview margin mean and margin variance,and proposes a new multiview margin distribution model,called MVLDM.MVLDM takes the weight of different views,the multiview margin distribution,the experience loss within views and the consistency loss between views into consideration at the same time,and jointly optimizes all views under a unified framework.MVLDM provides a new way to explore the utilization of complementary information in multiview learning from the perspective of margin distribution and satisfies both the consistency principle and the complementarity principle.In the optimization method,the original problem of MVLDM is transformed into a quadratic programming problem by Lagrange dual transformation,and the calculation process is accelerated by the alternating direction method of multipliers.In the theoretical analysis,this paper uses the Rademacher complexity theory to analyze the consistency error bounds and generalization error bounds of MVLDM,which guarantees the generalization performance of MVLDM theoretically.In the experiments,this paper constructs a new performance metric,the view consistency rate(VCR),for the characteristics of multiview data.The effectiveness of MVLDM is evaluated by using both VCR and other traditional performance metrics.The experimental results show that MVLDM is superior to other benchmark methods.Based on MVLDM,this paper proposes a general multiview large margin distribution framework(MVLDF).In order to reduce the computational cost,based on MVLDF,this paper proposes the least squares multiview large margin distribution machine(LS-MVLDM)and the weighted linear loss multiview large margin distribution machine(WL-MVLDM).LS-MVLDM and WL-MVLDM apply the quadratic loss and the weighted linear loss as the intra-view empirical loss function respectively,and the coupling loss as the inter-view consistency loss function.The original problems of LS-MVLDM and WL-MVLDM can be transformed into two linear equation problems by Lagrange dual transformation,which reduces the computational cost significantly.Experiments on real datasets show that the performance of the two models is superior to other benchmark methods,and illustrate the mechanism of MVLDF.