Global resolution of the support vector machine regression parameters selection problem with LPCC
Global resolution of the support vector machine regression parameters selection problem with LPCC
复制标题
用LPCC全局求解支持向量机回归参数选择问题
DOI：
10.1007/s13675-015-0041-z
复制
发表时间：
2015
影响因子：
2.4
通讯作者：
J. Mitchell
中科院分区：
文献类型：
--
作者：
Yu;J. Pang;J. Mitchell
支持向量机回归是一种鲁棒的数据拟合方法，可以最小化回归的扣除残差之和，因此对回归超平面附近的数据变化不太敏感。两个设计参数，不敏感的管尺寸（$$\varepsilon _\mathrm{e}$$εe）和分配给回归误差权衡赋范支持向量（$$C_\mathrm{e}$$Ce）的权重，由用户选择，以获得更好的预测。支持向量机回归的全局训练和验证参数选择过程可以表示为一个双层优化模型，该模型可以等价地表示为具有线性互补约束的线性规划（LPCC）。我们提出了一个矩形搜索全局优化算法来解决这个LPCC。该算法在参数平面（$$（C_\mathrm{e}，\varepad_\mathrm{e}）$$（Ce，εe）-plane）上耗尽不变区域，而不显式地识别区域的边缘。该算法在多达数百个数据点的合成和真实世界支持向量机回归问题上进行了测试，并与几种方法进行了效率比较。所得到的全局最优参数是其他参数选择的重要基准。
Support vector machine regression is a robust data fitting method to minimize the sum of deducted residuals of regression, and thus is less sensitive to changes of data near the regression hyperplane. Two design parameters, the insensitive tube size ($$\varepsilon _\mathrm{e}$$εe) and the weight assigned to the regression error trading off the normed support vector ($$C_\mathrm{e}$$Ce), are selected by user to gain better forecasts. The global training and validation parameter selection procedure for the support vector machine regression can be formulated as a bi-level optimization model, which is equivalently reformulated as linear program with linear complementarity constraints (LPCC). We propose a rectangle search global optimization algorithm to solve this LPCC. The algorithm exhausts the invariancy regions on the parameter plane ($$(C_\mathrm{e},\varepsilon _\mathrm{e})$$(Ce,εe)-plane) without explicitly identifying the edges of the regions. This algorithm is tested on synthetic and real-world support vector machine regression problems with up to hundreds of data points, and the efficiency are compared with several approaches. The obtained global optimal parameter is an important benchmark for every other selection of parameters.