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kernel form
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  核形式
     In this paper, the minimum squared error algorithm is modified by using kernel functions satisfying Mercer condition and regularization technique, and a nonlinear minimum squared error algorithm based on kernels and regularization technique, i.e., the regularized kernel form of minimum squared error algorithms is proposed. Its objective function includes squared error summation between the output of nonlinear function based on kernels and the desired output, and a proper regularization term.
     该文应用满足Mercer条件的核函数和正则化技术,改造经典的最小平方误差算法,提出了基于核函数和正则化技术的非线性最小平方误差算法,即最小平方误差算法的正则化核形式,其目标函数包含基于核的非线性函数的输出与期望输出的误差平方和,及一个适当的正则项.
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  “kernel form”译为未确定词的双语例句
     The pertinence of kernel form and necessity of using fractal were certified by the excellent fitness of experiment and numerical solution.
     模拟结果与实验数据的良好吻合初步表明用分形理论描述硅胶粒子聚集的必要性,并说明导出的碰撞矩阵形式基本正确。
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  相似匹配句对
     On form
     “形式”论
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     ESTIMATES FOR KERNEL DENSITY OF GENERAL FORM
     一般形式的密度估计
短句来源
     Free-form surface reconstruction based on reproducing kernel
     基于再生核的自由曲面重构
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     Form and thought
     形与思
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     kernel technology?
     NET的实质和一些核心技术、.
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  kernel form
In particular, we investigate under what conditions conservation laws analogous to those holding for the Boltzmann equation hold for the scattering kernel form as well.
      
The extra programming effort involved is to prepare data in an appropriate kernel form.
      
This tells us that we only need to define a kernel form of an inner product instead of computing the explicit form of this mapping.
      


Minimum squared error algorithm is one of the classical pattern recognition and regression analysis methods, whose objective is to minimize the squared error summation between the output of linear function and the desired output. In this paper, the minimum squared error algorithm is modified by using kernel functions satisfying Mercer condition and regularization technique, and a nonlinear minimum squared error algorithm based on kernels and regularization technique, i.e., the regularized kernel form of...

Minimum squared error algorithm is one of the classical pattern recognition and regression analysis methods, whose objective is to minimize the squared error summation between the output of linear function and the desired output. In this paper, the minimum squared error algorithm is modified by using kernel functions satisfying Mercer condition and regularization technique, and a nonlinear minimum squared error algorithm based on kernels and regularization technique, i.e., the regularized kernel form of minimum squared error algorithms is proposed. Its objective function includes squared error summation between the output of nonlinear function based on kernels and the desired output, and a proper regularization term. The regularization technique can handle ill-posed problems, reduce the solution space and control the generalization. Three regularization terms of square form are utilized in this paper. According to the probabilistic interpretation of regularization terms, the difference among three regulari2ation terms is given in detail. The synthetic and real data are used to analyze the algorithm performance.

最小平方误差算法是最常用的一种经典模式识别和回归分析方法,其目标是使线性函数输出与期望输出的误差平方和为最小.该文应用满足Mercer条件的核函数和正则化技术,改造经典的最小平方误差算法,提出了基于核函数和正则化技术的非线性最小平方误差算法,即最小平方误差算法的正则化核形式,其目标函数包含基于核的非线性函数的输出与期望输出的误差平方和,及一个适当的正则项.正则化技术可以处理病态问题,同时可以减小解空间和控制解的推广性,文中采用了三种平方型的正则项,并且根据正则项的概率解释,详细比较了三种正则项之间的差别.最后,用仿真资料和实际资料进一步分析算法的性能.

In machine learning the nonlinear kernel forms of classical linear algorithms are a class of nonlinear techniques developed in the last ten years.The most attractive idea is that by using kernel functions satisfying Mercer condition the classical linear algorithms are skillfully extended to construct their nonlinear kernel forms.These nonlinear algorithms are described by optimization problems that depend on the size of training sets rather than the dimension of sample vectors.In order to improve...

In machine learning the nonlinear kernel forms of classical linear algorithms are a class of nonlinear techniques developed in the last ten years.The most attractive idea is that by using kernel functions satisfying Mercer condition the classical linear algorithms are skillfully extended to construct their nonlinear kernel forms.These nonlinear algorithms are described by optimization problems that depend on the size of training sets rather than the dimension of sample vectors.In order to improve numerical stability,control generalization ability and improve convergence of iterative procedures,the regularization technique is utilized in some algorithms.On the basis of summarizing the kernel idea and kernel functions and regularization technique,the nonlinear kernel forms of linear algorithms are surveyed.Related properties are disscussed and further research directions are pointed out.

经典线性算法的非线性核形式是近10年发展起来的一类非线性机器学习技术.它们最显著的特点是利用满足M ercer条件的核函数巧妙地推导出线性算法的非线性形式,并表述为与样本数目有关、与维数无关的优化问题.为了提高数值计算的稳定性、控制算法的推广能力以及改善迭代过程的收敛性,部分算法还采用了正则化技术.在概述核思想与核函数、正则化技术的基础上,系统地介绍了经典线性算法的非线性核形式,同时分析它们的优缺点,并讨论了进一步发展的方向.

 
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