拉格朗日支持向量回归的有限牛顿算法

Finite Newton algorithm for Lagrangian support vector regression

拉格朗日支持向量回归是一种有效的快速回归算法,求解时需要对维数等于样本数加一的矩阵求逆,求解需要较多的迭代次数才能收敛。采用一种Armijo步长有限牛顿迭代算法求解拉格朗日支持向量回归的优化问题,只需有限次求解一组线性等式而不需要求解二次规划问题,该方法具有全局收敛和有限步终止的性质。在多个标准数据集上的实验验证了所提算法的有效性和快速性。

Lagrangian Support Vector Regression （SVR） is an effective algorithm and its solution is obtained by taking the inverse of a matrix of order equaling the number of samples plus one, but needs many times to terminate from a starting point. This paper proposed a finite Armijo-Newton algorithm solving the Lagrangian SVR＇s optimization problem. A solution was obtained by solving a system of linear equations at a finite number of times rather than solving a quadratic programming problem. The proposed method has the advantage that the result optimization problem is solved with global convergence and finite-step termination. The experimental results on several benchmark datasets indicate that the proposed algorithm is fast, and shows good generalization performance.