To reduce the influences of outliers on support vector machine(SVM) classification problem,a new tangent loss function was constructed.Since the tangent loss function was not smooth in some interval,a smoothing functi...To reduce the influences of outliers on support vector machine(SVM) classification problem,a new tangent loss function was constructed.Since the tangent loss function was not smooth in some interval,a smoothing function was used to approximate it in this interval.According to this loss function,the corresponding tangent SVM(TSVM) was got.The experimental results show that TSVM is less sensitive to outliers than SVM.So the proposed new loss function and TSVM are both effective.展开更多
A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for ...A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for compact supported infinitely differentiable zonal functions.Making use of the property of this sequence somehow similar to that of approxination kernels,the authors deduce that the inversion formula is true for continuous zonal functions on SL(2, R)under some condition. The classical result can be viewed as a corollary of the results here.展开更多
基金National Natural Science Foundations of China(Nos.61272015,11201123)the Scientific Research Foundation for the Doctor of Henan University of Science&Technology,China(No.09001476)School Foundation of Henan University of Science&Technology,China(No.2012QN011)
文摘To reduce the influences of outliers on support vector machine(SVM) classification problem,a new tangent loss function was constructed.Since the tangent loss function was not smooth in some interval,a smoothing function was used to approximate it in this interval.According to this loss function,the corresponding tangent SVM(TSVM) was got.The experimental results show that TSVM is less sensitive to outliers than SVM.So the proposed new loss function and TSVM are both effective.
文摘A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for compact supported infinitely differentiable zonal functions.Making use of the property of this sequence somehow similar to that of approxination kernels,the authors deduce that the inversion formula is true for continuous zonal functions on SL(2, R)under some condition. The classical result can be viewed as a corollary of the results here.
