Generalization Ability Of Support Vector Machine In The Environment Of Big Data

The basic problem of machine learning is to fit data by model,and the goal is to pursue the generalization ability.Although deep learning is regarded as the second wave in the evolution of machine learning,it typically requires large-scale data.However,in practical problems,we often encounter the situations that the data is not large-scale.It can be solved well by using shallow machine learning methods such as support vector machine(SVM).In this paper,we study the learning performance of Lagrangian SVM,incremental SVM and online pairwise SVM with hinge loss function by using SVM as a breakthrough point under the environment of big data.The main research contents and innovations are as follows:(1)The generalization bounds of Lagrangian SVM based on uniformly ergotic Markov chain,strongly mixed sequence and other non-independent and identically distributed cases are established and the optimal rates are obtained.As these applications,we also establish the generalization bound and convergence rate of Lagrangian SVM for independent and identically distributed setting.(2)For independent and identically distributed samples,the generalization bounds of incremental learning based on the classical SVM,least squares SVM,Lagrangian SVM and structural SVM are established,and fast learning rates are obtained.At the same time,we also obtain the generalization bounds and convergence rates of incremental learning based on the above four SVM algorithms for uniformly ergotic Markov chain samples.(3)For geometrically ?-mixing sequence,V-geometrically ergodic Markov chain and uniformly ergodic Markov chain,the generalization bounds of online pairwise SVM with hinge loss function are established,and the fast convergence rates are obtained.As a special case of exponentially strongly mixing sequence,we also obtain the generalization bound for online pairwise SVM based on hinge loss function for independent and identically distributed samples and obtain the fast convergence rate.In addition,we propose online pairwise SVM algorithm based on Markov selective sampling on the basis of theoretical research.The experimental results based on the public database show that,compared to the classical online pairwise SVM algorithm,the proposed online pairwise SVM algorithm based on Markov selective sampling not only has smaller misclassification rate,but also the sampling and training total time is shorter.