动态粒度支持向量回归机

粒度支持向量机(granular support vector machine,简称GSVM)可以有效提高支持向量机(support vectormachine,简称SVM)的学习效率,但由于经典GSVM 通常将粒用个别样本替代,且粒划和学习在不同空间进行,因而不可避免地改变了原始数据分布,从而可能导致泛化能力降低.针对这一问题,通过引入动态层次粒划的方法,设计了动态粒度支持向量回归(dynamical granular support vector regression,简称DGSVR)模型.该方法首先将训练样本映射到高维空间,使得在低维样本空间无法直接得到的分布信息显示出来,并在该特征空间中进行初始粒划.然后,通过衡量样本粒与当前回归超平面的距离,找到含有较多回归信息的粒,并通过计算其半径和密度进行深层次的动态粒划.如此循环迭代,直到没有信息粒需要进行深层粒划时为止.最后,通过动态粒划过程得到的不同层次的粒进行回归训练,在有效压缩训练集的同时,尽可能地使含有重要信息的样本在最终训练集中保留下来.在基准函数数据集及UCI 上的回归数据集上的实验结果表明,DGSVR 方法能够以较快的速度完成动态粒划的过程并收敛,在保持较高训练效率的同时可有效提高传统粒度支持向量回归机(granular support vector regression machine,简称GSVR)的泛化性能.

Dynamical Granular Support Vector Regression Machine

Although granular support vector machine (GSVM) can improve the learning speed, the generalization performance may be decreased because the original data distribution will be changed inevitably by two reasons: (1) A granule is usually replaced by individual datum; (2) Granulation and learning are carried out in different spaces. To address this problem, this study presents a granular support vector regression (SVR) model based on dynamical granulation, namely DGSVR, by using the dynamical hierarchical granulation method. With DGSVR, the original data are mapped into the high-dimensional space by mercer kernel to reveal the distribution features implicit in original sample space, and the data are divided into some granules initially. Then, some granules are obtained with important regression information by measuring the distances of granules and regression hyperplane. By computing the radius and density of granules, the deep dynamical granulation process executes until there are no informational granules need to be granulated. Finally, those granules in different granulation levels are extracted and trained by SVR. The experimental results on benchmark function datasets and UCI regression datasets demonstrate that the DGSVR model can quickly finish the dynamical granulation process and is convergent. It concludes this model can improve the generalization performance and achieve high learning efficiency at the same time.