Research On Robustness And Sparsity Of L2P Norm Distance Metrics

In traditional pattern recognition algorithms,the distance metric is often based on the square L2-norm distance.In practical applications,the squared L2-norm distance often amplifies the distance of the noise data in the overall data distance,resulting in the algorithm being not robust.Due to the non-robust defects of the square L2-norm distance,the paper improves the robustness of traitional algorithms by using the L2P-norm distance and the L21-norm distance respectively on the classification methods and feature selection methods.Twin Support Vector Machine is an efficient classifier especially suitable for XOR data.It is usually studied based on the square L2 norm distance metric.Since the squared L2 norm distance is susceptible to outliers,TWSVM requires a more robust distance metric.In this paper,we propose a new robust twin support vector machine based on the L2P-norm distance,because the L2P-norm distance can better suppress the influence of outliers than the L1-norm distance or the squared L2-norm distance.However,the new objective function is non-smooth and non-convex,this makes it difficult to solve the objective function.As an important work of this paper,we systematically deduced an effective iterative algorithm to minimize the p-th order of L2-norm distance.Theoretical studies have proved that this iterative algorithm based on L2P-norm distance metric is effective in improving TWSVM.A large number of experiments show that the L2P-norm distance support vector machine(pTWSVM)can effectively deal with noise data and has better accuracy.Data dimension reduction is mainly divided into feature selection and feature extraction.However,they are always discussed separately.Feature extraction aims at finding new feature subspaces,while feature selection focuses on selecting a subset of the original feature set.In order to obtain a better dimension reduction method,this paper proposes a new feature selection method based on L21-norm linear discriminant analysis(LDA).The new objective function provides better robustness.However,solving this objective function is very challenging because it requires minimizing and maximizing non-smooth L21 norm terms at the same time.To solve this problem,we propose an iterative algorithm.A series of theories proves the convergence and computational efficiency of the algorithm.The experimental results on various datasets shows the effectiveness of our new method.