核函数

We combine two typical kernel functions by means of convex combination. The weighting coefficient and other kernel parameters are optimized by an improved GA.

具体地说，本文主要有以下几个创新点：1、适当核函数的选择和核参数的优化一直是核方法应用的关键和难点。

Considering that the covariance function could not exist in some conditions, we put forward the idea of using the variogram function as a substitute for the covariance function and prove their equivalence.

考虑到在某些情况下协方差函数可能不存在，因此考虑用变异函数来代替协方差函数估计径向基核函数的宽度参数。

Inspired by the intuitive geometric interpretation of SVM based on convex hulls, KNNCH maps the data in the original space to the kernel space with the kernel trick and constructs a nearest neighbor classifier in the kernel space, which takes the convex hulls of training sets as the extended class sets.

该算法的设计受到支持向量机几何解释启发，利用核函数方法将数据映射到高维核空间，并在核空间构造以训练集凸包为扩展类集的最近邻分类器。

This project studies the scale-dependent deformation behavior of the metal matrix composite, the void nucleation and void growth mechanisms at the micron/submicron scale. The main results are:(1) In prophase, growth and coalescence of the void embedded in the graded matrix are analyzed in detailed;(2) Based on the infinite solid model containing a micro-void, coupling effects of the void shape and the void size on the void growth are studied carefully, the results show that it seems to exist a critical equivalent void radius, which is associated with the material length. When radius of a microvoid is close to or smaller than the critical void radius, the micro-void growth rate is essentially eliminated;(3) The coupling effects of the particle shape and size on the mesoscopic stress fields within the particle and matrix are also investigated by introducing the conception of inclusion/matrix interfacial energy. The results show that the stress concentration factors within the particle and on the matrix/particle interface are also strongly size-dependent,so the void nucleation mechanism is size-dependent.(4) By employing a specific orthogonal curve coordinate frame and a 'kernel function' conception, a 'unified method'solving the spheriodal and spherical void problems is suggested; by this unified method, size-dependent plastic potentials of the porous materials containing the spheriodal or spherical voids are obtained, which extend the traditional Gurson model for the spherical void and GLD model for the spheriodal voids to the micron scale.(5) Based on the RVE model containing the spheriodal or spherical particles, the influences of the particle shape and size on the size-dependent mechanical behavior of metal matrix composite are studied.

中文摘要：本项目对金属基复合材料在微细观尺度下的尺度相关变形行为、孔洞形核及长大的机理和模型进行了研究，取得了如下主要结果：1）在前期研究中，探讨了基体的梯度分布对孔洞长大和聚合的影响；2）基于含孔洞的无限大体模型，探讨了孔洞形状和孔洞尺寸对其长大的耦合作用，结果表明：可能存在一个与材料特征长度相关的临界孔洞尺寸，当椭球孔洞的等效半径小于临界孔洞半径时，孔洞的长大受到明显抑制；3）通过引入基体/夹杂界面能的概念，分析了夹杂尺寸、夹杂形状对材料细观应力场的耦合影响，结果表明：颗粒内部和界面上的应力集中因子强烈地依赖于夹杂的尺寸和形状，因此，孔洞的形核机理是尺寸相关的；4）采用一种特殊的正交曲线坐标系和引入"核函数"的概念，"统一"地得到了含椭球和球形孔洞的材料的尺寸相关塑性势，它将传统的Gurson球形孔洞模型和GLD椭球孔洞模型推广到微尺度范围；5）基于含椭球和球形夹杂的体胞模型，初步研究了夹杂形状、夹杂尺寸对金属基复合材料尺寸相关力学行为的影响。

The main work of this paper is to study the sampling theorem in domain of the fraction and the sampling relationship. We will try to obtain the theoretic sampling rate and the proof of feasibility. And we also give some relationship between the kernels under the meaning of sampling.

本文的主要工作就是，研究了分数傅立叶变换算子核函数的采样定理及采样关系，给出了一种能够达到理论的最佳采样频率的尝试，也给出了这种做法的可行性的证明，更进一步由采样关系给出了核函数的一些关系。

This method constructs a quasi-conformal transaction with the sech function. It improves the respective of SVM by modifying the polynomial kernel function. The text emphasizes on the parameter analysis of quasi-conformal transaction.

该方法用双曲正割函数构造拟共形变换函数，对多项式核函数进行修正来提高SVM的分辨率，并侧重于拟共形变换函数中的参数分析，确定了参数的取值方法，缩小了参数选取的范围。

At the same time, considering the close relationship between splice sites selection and the composition of adjoined sequences,a new kernel, position weight subsequence kernel, is built.

考虑到剪接位点的选取与位点附近的核酸序列有着重要的关联，特别为支持向量机构造了一个新的核函数——位置权重子序列核函数。

By using the kernel function, the input space is mapped to a high dimension feature space where the data are expected to be more separable, the initial centroids in the feature space are selected by applying the KRA algorithm, and the large and small clusters are partitioned and the outliers can be split from the large clusters iteratively after the kk-means clustering. As a result, the audit data can be clustered better. Secondly, the closed sequential patterns mining algorithm CloSpan is improved according to the restrictions that is composed of the axis properties and reference properties.

该方法通过核函数把数据样本空间映射到一个高维的特征空间，使数据在新的空间中具有更好的可分离性；在特征空间采用KRA算法选取初始聚类中心，然后在核k-means聚类的基础上，划分出大簇小簇并在大簇中分离出异类再次进行核聚类，从而不断地优化聚类结果。

In this paper, a kernel quantification theory IV is proposed through organical combining kernel function theory and quantification theory IV. The algorithm framework for the new model with large scale-sampling data is established on the basis of Lanczos algorithm which is an iterative method for finding the eigenpairs of a square matrix.

把核函数理论与数量化理论IV模型有机结合，提出了核数量化理论IV模型，并以高阶对称矩阵端部特征对求解的Lanczos算法为基础设计了大样本核数量化理论IV模型的算法框架。

I will show systematically how we induce the kernel functions of support vector machine to the Riemannian metric,which makes possible for studying the support vector machine in geometry.

系统的 讲述了SVRM问题、如何构造SVRM的核函数和B样条核函数的几何修正。在这章我们详细的介绍了怎样来用支撑向量回归机解决拟合或逼近问题。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。