CAJ | 학술논문

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 vector machine,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。
립도지지향량궤(granular support vector machine,간칭 GSVM)가이유효제고지지향량궤(support vector machine,간칭 SVM)적학습효솔,단유우경전GSVM 통상장립용개별양본체대,차립화화학습재불동공간진행,인이불가피면지개변료원시수거분포,종이가능도치범화능력강저。침대저일문제,통과인입동태층차립화적방법,설계료동태립도지지향량회귀(dynamical granular support vector regression,간칭DGSVR)모형。해방법수선장훈련양본영사도고유공간,사득재저유양본공간무법직접득도적분포신식현시출래,병재해특정공간중진행초시립화。연후,통과형량양본립여당전회귀초평면적거리,조도함유교다회귀신식적립,병통과계산기반경화밀도진행심층차적동태립화。여차순배질대,직도몰유신식립수요진행심층립화시위지。최후,통과동태립화과정득도적불동층차적립진행회귀훈련,재유효압축훈련집적동시,진가능지사함유중요신식적양본재최종훈련집중보류하래。재기준함수수거집급 UCI 상적회귀수거집상적실험결과표명,DGSVR 방법능구이교쾌적속도완성동태립화적과정병수렴,재보지교고훈련효솔적동시가유효제고전통립도지지향량회귀궤(granular support vector regression machine,간칭GSVR)적범화성능。
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.