关键词: 最小二乘双支持向量回归, 结构风险最小化, 稀疏性, 不完全Choesky分解, 大规模

Abstract: The Least Squares Twin Support Vector Regression（LSTSVR） machine simplifies the quadratic programming problem in the Twin Support Vector Regression（TSVR） machine to the solution of two linear equations by introducing the least squares loss, thus greatly reducing the training time. However, LSTSVR minimizes the empirical risk based on least squares loss, which will lead to the following shortcomings：（1）the problem of “over-learning”; （2）the solution of model lacks sparsity and it is difficult to train large-scale data. For（1）, the Structured Least Squares Twin Support Vector Regression（S-LSTSVR） is given to improve the generalization ability of the model. For（2）, the low rank approximation is carried out to the kernel matrix by using incomplete Choesky decomposition, and an sparse algorithm is given for solving S-LSTSVR model（SS-LSTSVR）, which makes the model train large-scale data effectively. Experiments on artificial data and UCI data sets show that SS-LSTSVR can avoid “over learning” and can solve large-scale training problems efficiently.

Key words: Least Squares Twin Support Vector Regression（LSTSVR）, structural risk minimization, sparsity, incomplete Choesky decomposition, large-scale