超平面

在分类过程中，位于分类超平面附近的样本点很有可能成为支持向量，对分类的结果影响比较大，因此在隶属度设计中，对这些样本赋予了较大的隶属度权值。

In the classification process , the sample points near to the separating hyper plane might become the support vector and affect the results of the classification .

直线与超平面求交的软件设计

Software Design On Evaluating The Intersec-tion of A Line And A hyper plane

用遗传算法求SVM的最优超平面

Using GA to Obtain Optimal Hyperplane of SVM

R~n中有限点集的Chebyshev超平面拟合

Finite point set fitting by a hyperplane under the sense of Chebyshev in Rn

支持向量机（SVM）是一种基于超平面分类的新的学习方法，具有很强的泛化能力。

Support Vector Machine ( SVM ) is a new learning method based on hyperplane classification , and its powerful in common use .

首先通过分析非线性核映射的特征空间超平面的最小VC维数，提出了多分辨率核函数参数的自适应优化准则。

First - ly a multi-resolution kernel parameters optimal scheme is presented by deeply analyzing the high dimensional feature space produced by nonlinear mapping .

Fuzzy凸集分离定理的研究有两种方式：一是利用分离度；二是利用Fuzzy超平面。

There are two ways in the study of separation theorems of convex fuzzy sets , one , using the separation degree [ 1 & 5 ] , and the other using the fuzzy hyperplane .

支持向量机（SVM）是一种崭新的机器学习方法，建立在结构风险最小化原理基础上，寻找一个最优分类超平面，引进核函数将低维空间向量映射到高维空间。

Support Vector Machine ( SVM ) is based on Structure Risk Minimization principle ( SRM ) is a kind of machine learning method .

把Logistic回归算法训练得到的分类超平面用于指导演化过程，提高了电路的容错性能。

We use the classification hyperplane trained by logistic regression to guide the evolutionary process and this method is beneficial to improve the fault tolerance of circuit .

代谢组学数据中的噪音属性很可能会对SVM最优超平面的构建产生影响，进而影响到对特征的评价。

Noise features in metabolomics data are likely to impact the construction of the optimal hyper-plane in SVM . thus can affect the evaluation of features .

训练过程是用大量人脸样本、非人脸样本训练SVM分类器，使之获得一个最优分类超平面。

A lot of face samples and " not face " samples are used to train the SVM classifier , to get optimal separating hyperplane in the training .

M3网络中已采用了随机划分、超平面划分、等分割聚类、谱聚类和基于先验知识等多种数据划分方法。

Some methods have been presented in M3 network , such as randomly division , hyper-planes division , spectral clustering and so on .

然后详细阐述了统计学习理论的基本理论，包括VC维理论、推广性的界和结构风险最小化；接下来介绍了最优超平面及其构造；

At first , basic theory of SLT including the VC dimension , the bound of extending and the principle of structural risk minimization ( SRM ) are presented .

该算法首先使用二叉树进行多类决策，将原始分类数据分解成3个二类分类问题，然后利用SVM进行二类分类，使3个分类超平面得到优化。

This algorithm uses binary tree to construct the multi-class frame by decomposing the problem into three 2-class classification problems , then uses Support Vector Machine optimizing the three hyperplanes .

引入数据包络分析方法，提出了一种基于贷款可接受案例集的DEA型信用评估模型和分类边界为分段线性分离超平面的分类方法。

In this paper , we develop a DEA model based on accepted cases set and propose a classification method with piece wise linear separating hyperplane as its boundary .

检测时，首先利用基于最大间隔超平面的支持向量分类器（SVC）对输入模式进行分类判决；

Firstly the first layer of support vector classifier ( SVC ) with maximum margin between two classes will be used for classifying the input pattern ;

实际电力系统的实用动态安全域（practicaldynamicsecurityregion，PDSR）的临界边界可表示为节点注入空间的一个或几个超平面，这为最优安全控制提供了有效的解析工具。

The fact of that the critical boundary of practical dynamic security region ( PDSR ) in real power systems can be described as one or a few hyper planes in injection space provides an effective tool for optimizing security control .

支持向量机通过核函数将样本从输入空间映射到高维特征空间（Hilbert空间），从而实现在特征空间中寻求线性判别超平面。

After mapping the samples from primal input space to high-dimentional feature space ( Hilbert space ) using kernel function , we can obtain linear discriminant hyperplane in the feature space .

该算法将SVM视为每类只取一个代表点的1NN分类器，在对测试数据进行分类时，依据测试样本与超平面之间的距离决定采用何种分类算法。

In the case of testing samples , the algorithm computes the distance from the test sample to the optimal super plane of SVM in feature space , and choices the classification algorithm according to the distance .

SVM回归的本质是在预定的误差范围内，只用占样本集合较少的支撑矢量就可以确定最优回归超平面，从而可以稀疏地表示原始数据集。

The essence for the SVM regression analysis is inside error margin scope , using a handful of support vectors to make sure the superior regression flat surface . It can sparsely mean the original data gathers .

证明如下结果：设X是Banach空间，则X是无限维的充分必要条件是存在不含内点的非空凸集B，使得B不在任何一个闭超平面上。

In this paper , we prove a conclusion as following : The necessary and sufficient condition that Banach space is infinite dimension is that it exists nonempty convex subset B without inner point so that B is not on any closed hyperplane .

在讨论和分析中发现，ε0的不同选取会导致信赖域和超平面L1，L2的相对位置发生变化。

Trough the discuss and the analysis , we can find that the different select of ε 0 can lead to the change of the relative position between the hyperplane and the trust-region .

提出SPSO-SVR模型，采用SPSO算法优化SVR的超平面，解决了现有利用Lagrange对偶原理求解SVR最优超平面时遇到的高阶矩阵问题，使得问题更直接、更简化。

The SVR model with optimized hyperplane by SPSO algorithm is derived , which solves the high-order matrix problem encountered in the optimal SVR hyperplane based on Lagrange duality principle .

本文在自反Banach空间中，对于闭稠定且值域为超平面的线性算子A，利用Banach空间几何方法，给出其度量广义逆A+的一般表达式。

In this paper , the representation for the metric generalized inverse of dosed linear operator with dense domain and hyperplane range in reflexive Banach space is given by means of the method of Geometry of Banach spaces .

首先选取训练集中最典型的一些样本，构造一个粗糙SVMs的分类超平面，用样本与这个超平面的相对距离定义隶属函数，将所有的训练样本都映射到一个带形区域；

Firstly , the learning machines select the most typical samples , such as the centers of two classes , to form the coarse classification hyperplane of SVMs named preformed hyperplane .

该算法通过实时增加训练序列，利用KKT条件构造当前训练样本集，实时地调整最优分类超平面。

The algorithm added one training sample every step and constructed current training set using KKT condition in order to adjust the maximal margin hyperplane dynamically .

本文对互联系统的分散变结构控制进行了研究；给出了有关分散变结构控制开关超平面（switchinghyperplane）以及开关超平面上滑模（slidingmodeontheswitchinghyperplane）存在的两定理和结论；

A study is made of the decentralized variable structure control of interconnected systems and two theorems related respectively to the existence of the switching hyperplane of the decentralized variable structure control and to the sliding mode on the switching hyperplane are given .

本文在详细分析了混合像元分解算法及GA进化原理的基础上，提出了用遗传算法进化模型拟合分解结果超平面，以实现混合像元分解并进一步分类的算法。

By researching the principles of the mixed pixel unmixing algorithm , this paper proposes a new GA-based method for mixed pixel unmixing and classification problems , which uses the GA evolution models to fit ( approximate ) the hyperplane of the unmixing results .

用超平面法对2m阶常微分方程二点边界值问题进行探讨，在已知m个初始条件下确定另外m个未知初始值的方法。

This paper studied the question of two point boundary value question for the 2m-th-order ordinary differential equation using hyperplane method to determin another m unknown original values under the condition of known m original values .

通过引入样本与超平面加权距离的概念，使得WSVM算法可以对样本的权值信息进行有效处理。

Samples ' weights are properly solved through introducing the concept of weighted distance between weighted sample and hyperplane .