A regularization on Lagrangian twin support vector regression
A regularization on Lagrangian twin support vector regression
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DOI：
10.1007/s13042-015-0361-6
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发表时间：
2015-05
影响因子：
5.6
通讯作者：
M. Tanveer;K. Shubham
中科院分区：
文献类型：
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作者：
M. Tanveer;K. Shubham
双支持向量回归机（TSVR）、拉格朗日支持向量回归机（LTSVR）和双支持向量回归机（-TSVR）通过求解一对较小的二次规划问题（QPP），比求解单个大的QPP问题具有更好的泛化能力和更快的计算速度。本文提出了一种简单的线性收敛的拉格朗日支持向量机算法。我们的公式的贡献如下：（1）我们考虑松弛变量向量的2-范数的平方，而不是通常的1-范数，使目标函数强凸。(2)我们用两个线性方程组来解决回归问题，而不是在-TSVR和TSVR中解决两个QPP或在SVR中解决一个大的QPP，这导致了非常简单和快速的算法。(3)我们所提出的方法的一个显着的优点是结构风险最小化原则的实施。然而，由于其复杂的结构，仅考虑经验风险的TSVR和LTSVR的原始问题，因此可能会导致过拟合和次优在某些情况下。(4)几个人工和基准数据集上的实验结果表明，我们提出的配方的有效性。
Twin support vector regression (TSVR), Lagrangian TSVR (LTSVR) and-TSVR obtain good generalization and faster computational speed by solving a pair of smaller sized quadratic programming problems (QPPs) than a single large QPP in support vector regression (SVR). In this paper, a simple and linearly convergent Lagrangian support vector machine algorithm for the dual of the-TSVR is proposed. The contributions of our formulation are as follows: (1) we consider the square of the 2-norm of the vector of slack variables instead of the usual 1-norm to make the objective functions strongly convex. (2) We are solving regression problem with just two systems of linear equations as opposed to solving two QPPs in-TSVR and TSVR or one large QPP in SVR, which leads to extremely simple and fast algorithm. (3) One significant advantage of our proposed method is the implementation of structural risk minimization principle. However, only empirical risk is considered in the primal problems of TSVR and LTSVR due to its complex structure and thus may incur overfitting and suboptimal in some cases. (4) The experimental results on several artificial and benchmark datasets show the effectiveness of our proposed formulation.