Research On Classification Algorithms Based On L1-norm Distance Metric

In order to alleviate the influence of outliers,to improve the classification accuracy of the classifier,and at the same time to reduce the computational complexity,this dissertation is focused on the model of three classifiers,such as Proximal SVM based on Generalized Eigenvalues(GEPSVM),Twin Support Vector Machine(TWSVM)and Twin Bounded Support Vector Machine(TBSVM).On the basis of the three classifiers,we improved them,which further improves the generalization ability and robustness of the classifiers.The main works of this dissertation can be described as follows:1.By introducing the L1-norm distance in the objective function of GEPSVM,this thesis proposes a GEPSVM classification algorithm based on L1-norm distance metric,referred to as L1-GEPSVM,which can mitigate the effects of outliers.In this thesis,the theory of L1-GEPSVM is introduced in detail,and the feasibility and effectiveness of the improved algorithm are proved theoretically.In addition,an effective iterative algorithm is developed to solve the L1-norm optimal problems,so L1-GEPSVM can converge quickly and can obtain a local optimal solution.To test the practicability and feasibility of the L1-GEPSVM,a large number of comparative experiments were done on the three datasets(artificial datasets,UCI datasets and NDC datasets),The experimental results are analyzed in different ways(graphs and tables),to evaluate the classification performance of improved algorithms.The Gaussian noise is introduced into the experimental data on the UCI datasets,for L1-GEPSVM and related classification algorithms,and compare their anti-noise abilities.2.In order to alleviate the effect of outliers on TWSVM classification performance,in this dissertation,the L1-norm distance is applied to the TWSVM,the L1-TWSVM algorithm is proposed,which has the global optimal solution.This dissertation analyzes and proves the feasibility and effectiveness of the L1-TWSVM algorithm from the theory,which makes the feasibility and validity of L1-TWSVM theoretically guaranteed.Besides,L1-TWSVM is compared with other related algorithms on artificial datasets,UCI datasets and NDC datasets.The experimental results are analyzed in detail,so the practicability of L1-TWSVM is tested.On UCI datasets,Gaussian noise is introduced into the experimental data,the robustness of L1-TWSVM is further verified.3.To alleviate the influence of outliers on TBSVM and shorten its training time,this thesis introduces the L1-norm distance and the sense of least squares into TBSVM,and proposes a least squares TBSVM based on L1-norm distance metric for classification(L1-LSTBSVM).In this thesis,the formula derivation of L1-LSTBSVM is introduced in detail,and the feasibility and validity of L1-LSTBSVM is analyzed theoretically.L1-LSTBSVM and other related classification algorithms have done a lot of contrast experiments on artificial datasets and UCI datasets.Furthermore,on UCI datasets,the anti-noise ability of L1-LSTBSVM is tested by introducing 10% and 20% Gaussian noise to the experimental data respectively.Through the detailed observation and analysis of the experimental results,it is concluded that the classification performance of L1-LSTBSVM is stronger than other classifiers.