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    光滑CHKS孪生支持向量回归机

    Smooth CHKS Twin Support Vector Regression

    • 摘要: 针对目前光滑孪生支持向量回归机(smooth twin support vector regression, STSVR)中采用的Sigmoid光滑函数逼近精度不高,从而导致算法泛化能力不够理想的问题,引入一种具有更强逼近能力的光滑(chen-harker-kanzow-smale, CHKS)函数,采用CHKS函数逼近孪生支持向量回归机的不可微项,并用Newton-Armijo算法求解相应的模型,提出了光滑CHKS孪生支持向量回归机(smooth CHKS twin support vector regression, SCTSVR).不仅从理论上证明了SCTSVR具有严格凸,能满足任意阶光滑和全局收敛的性能,而且在人工数据集和UCI数据集上的实验表明了SCTSVR比STSVR具有更好的回归性能.

       

      Abstract: Twin support vector regression (TSVR) was proposed recently as a novel regressor that tries to find a pair of nonparallel planes, i.e., ε insensitive down- and up- bounds, by solving two related SVM-type problems. However, it may incur suboptimal solution since its objective function is positive semi-definite and it is lack of complexity control. In order to address this shortcoming, smooth twin support vector regression (STSVR) is introduced using sigmoid function as smoothing technique to convert the original problems into unconstrained minimization, which can improve the training speed. However, its accuracy needs to be improved. In this paper, aiming at the low approximation ability of sigmoid function of STSVR, using CHKS (chen-harker-kanzow-smale) function which has better approximation ability as the smooth function, a new version of smooth TSVR called smooth CHKS twin support vector regression (SCTSVR) model is proposed. In SCTSVR, CHKS function is used to approximate the non-differential term of twin support vector regression. Then Newton-Armijo algorithm is used to solve the corresponding model. We have proved that SCTSVR is not only strictly convex, but also can meet the arbitrary order smooth performance. Meanwhile, the experimental results on several artificial and benchmark datasets show that SCTSVR has better regression performance than STSVR.

       

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