In this paper we obtained the asymptotic formula of the orthogonal rational function on the unit circle with respect to the weight function μ(z) with preasigned poles, which are in the exterior of the unit disk.
Support vector machines （SVMs） have been intensively applied in the domains of speech recognmon, text categorization, and faults detection. However, the practical application of SVMs is limited by the non-smooth fea...Support vector machines （SVMs） have been intensively applied in the domains of speech recognmon, text categorization, and faults detection. However, the practical application of SVMs is limited by the non-smooth feature of objective function. To overcome this problem, a novel smooth function based on the geometry of circle tangent is constructed. It smoothes the non-differentiable term of unconstrained SVM, and also proposes a circle tangent smooth SVM （CTSSVM）. Compared with other smooth approaching functions, its smooth precision had an obvious improvement. Theoretical analysis proved the global convergence of CTSSVM. Numerical experiments and comparisons showed CTSSVM had better classification and learning efficiency than competitive baselines.展开更多
文摘In this paper we obtained the asymptotic formula of the orthogonal rational function on the unit circle with respect to the weight function μ(z) with preasigned poles, which are in the exterior of the unit disk.
文摘Support vector machines （SVMs） have been intensively applied in the domains of speech recognmon, text categorization, and faults detection. However, the practical application of SVMs is limited by the non-smooth feature of objective function. To overcome this problem, a novel smooth function based on the geometry of circle tangent is constructed. It smoothes the non-differentiable term of unconstrained SVM, and also proposes a circle tangent smooth SVM （CTSSVM）. Compared with other smooth approaching functions, its smooth precision had an obvious improvement. Theoretical analysis proved the global convergence of CTSSVM. Numerical experiments and comparisons showed CTSSVM had better classification and learning efficiency than competitive baselines.
