面向原问题求解的拟牛顿SVM回归算法研究

研究了支持向量机（SVM）的原问题优化及其回归算法．在分析原问题与对偶问题最优化关系的基础上，引入了一种原问题求解的L—MBFGS—SVR算法．该算法在求解无约束优化问题时，引入了一类新的BFGS拟牛顿算法．它利用迭代的梯度和函数值来近似逆Hessian矩阵，以降低计算复杂性；并结合有限内存技术，来解决数据存储问题．仿真表明，该算法总体上优于IHLF—SVR—RFN和SMO算法，是一种有效的大样本非线性回归建模方法．

Quasi-Newton SVM Regression Algorithm for Solving Primal Problem

The primal problem optimization of SVM （Support Vector Machine） and its regression algorithm are studied. After analyzing the relationship between primal and dual optimization, an L - MBFGS - SVR algorithm based on solving primal problem is introduced. For solving the unconstrained optimization problem, the algorithm introduces a new BFGS Quasi - Newton optimization method. It approximates the converse of Hessian matrix by the iterative gradient and function value to reduce the computation complexity, and makes use of the limited memory technique to solve the data memory problem. The experiments show that the L - MBFGS - SVR is better than IHLF- SVR -RFN or SMO in general, and it is an effective nonlinearity regression modeling method for large samples.