In recent years, modern optical processing technologies, such as single point diamond turning, ion beam etching, and magneto-theological finishing, arc getting break- throughs. Machining precisions of super-smooth opt...In recent years, modern optical processing technologies, such as single point diamond turning, ion beam etching, and magneto-theological finishing, arc getting break- throughs. Machining precisions of super-smooth optics have also been significantly improved. However, with increasing demands for the optical surface quality,展开更多
This article puts forward a novel smooth rotated hyperbola model for support vector machine( RHSSVM) for classification. As is well known,the support vector machine( SVM) is based on statistical learning theory( SLT)a...This article puts forward a novel smooth rotated hyperbola model for support vector machine( RHSSVM) for classification. As is well known,the support vector machine( SVM) is based on statistical learning theory( SLT)and performs its high precision on data classification. However,the objective function is non-differentiable at the zero point. Therefore the fast algorithms cannot be used to train and test the SVM. To deal with it,the proposed method is based on the approximation property of the hyperbola to its asymptotic lines. Firstly,we describe the development of RHSSVM from the basic linear SVM optimization programming. Then we extend the linear model to non-linear model. We prove the solution of RHSSVM is convergent,unique,and global optimal. We show how RHSSVM can be practically implemented. At last,the theoretical analysis illustrates that compared with other three typical models,the rotated hyperbola model has the least error on approximating the plus function. Meanwhile,computer simulations show that the RHSSVM can reduce the consuming time at most 54. 6% and can efficiently handle large scale and high dimensional programming.展开更多
基金supported by the National Natural Science Foundation of China(Nos.61627825 and 11275172)the State Key Laboratory of Modern Optical Instrumentation Innovation Program(MOI)(No.MOI2015 B06)
文摘In recent years, modern optical processing technologies, such as single point diamond turning, ion beam etching, and magneto-theological finishing, arc getting break- throughs. Machining precisions of super-smooth optics have also been significantly improved. However, with increasing demands for the optical surface quality,
基金supported by the National Nature Science Foundation of China under Grant ( 61100165, 61100231, 61472307 )Natural Science Foundation of Shaanxi Province ( 2016JM6004)
文摘This article puts forward a novel smooth rotated hyperbola model for support vector machine( RHSSVM) for classification. As is well known,the support vector machine( SVM) is based on statistical learning theory( SLT)and performs its high precision on data classification. However,the objective function is non-differentiable at the zero point. Therefore the fast algorithms cannot be used to train and test the SVM. To deal with it,the proposed method is based on the approximation property of the hyperbola to its asymptotic lines. Firstly,we describe the development of RHSSVM from the basic linear SVM optimization programming. Then we extend the linear model to non-linear model. We prove the solution of RHSSVM is convergent,unique,and global optimal. We show how RHSSVM can be practically implemented. At last,the theoretical analysis illustrates that compared with other three typical models,the rotated hyperbola model has the least error on approximating the plus function. Meanwhile,computer simulations show that the RHSSVM can reduce the consuming time at most 54. 6% and can efficiently handle large scale and high dimensional programming.
