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Robust least squares projection twin SVM and its sparse solution

Journal of Systems Engineering and Electronics 2023年第4期34卷 827-838页

作者： ZHOU Shuisheng ZHANG Wenmeng CHEN Li XU Mingliang School of Mathematics and Statistics Xidian UniversityXi’an 710126China School of Physical Education Zhengzhou UniversityZhengzhou 450001China School of Computer and Artificial Intelligence Zhengzhou UniversityZhengzhou 450001China

Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.

关键词： outliers robust least squares projection twin support vector machine(R-LSPTSVM) low-rank approximation sparse solution

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Outlier deletion based improvement on the StOMP algorithm for sparse solution of large-scale underdetermined problems

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Science China(Information Sciences) 2014年第9期57卷 242-255页

作者： ZHANG WanHong ZHOU Tong HUANG BoXue Department of Automation Tsinghua University Department of Chemical Machinery Qinghai University Tsinghua National Laboratory for Information Science and Technology Tsinghua University

StOMP algorithm is well suited to large-scale underdetermined applications in sparse vector estimations.It can reduce computation complexity and has some attractive asymptotical statistical properties.However,the estimation speed is at the cost of accuracy violation.This paper suggests an improvement on the StOMP algorithm that is more efficient in finding a sparse solution to the large-scale underdetermined problems.Also,compared with StOMP,this modified algorithm can not only more accurately estimate parameters for the distribution of matched filter coefficients,but also improve estimation accuracy for the sparse vector itself.Theoretical success boundary is provided based on a large-system limit for approximate recovery of sparse vector by modified algorithm,which validates that the modified algorithm is more efficient than StOMP.Actual computations with simulated data show that without significant increment in computation time,the proposed algorithm can greatly improve the estimation accuracy.

关键词： stagewise orthogonal matching pursuit sparse solution linear underdetermined equations systems biology outlier deletion

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