超球面

基于HMM核超球面支持向量机的超宽带SAR未爆物检测

Ultra-Wideband Synthetic Aperture Radar Unexploded Ordnance Detection Using HMM Kernel Hypersphere Support Vector Machine

作为单类分类器，SVDD方法是支持向量机（supportVectorMachine，SVM）的变种，可以建立正常数据超球面实现故障检测和建立各类故障超球面实现故障诊断。

As one class classifier , which is a variant of support vector machine , can establish the normal data hypersphere realize fault detection and the establishment of various fault hypersphere to realize fault diagnosis .

新超球面SVM方法及其在入侵检测中的应用

Application of Quarter-sphere SVM to Network Intrusion Detection

在分析方位角与SAR目标分布关系的基础上，提出了基于超球面投影空间的特征提取方法，通过超球面投影获得SAR样本的全方位分布特性，进而消除了方位角对SAR目标识别的影响。

With the analyzing on the relationship between azimuth and SAR target distribution , another feature extraction method based on hyper-sphere projection space is proposed .

改进的UKF滤波应用了超球面采样和平方根滤波方法，降低了算法的计算量，提高了滤波过程中的数值稳定性。

Aiming at this problem , an improved UKF algorithm based on spherical sampling and square-root filtering is presented .

针对训练样本是未标定的不均衡数据集的情况，把攻击检测问题视为一个孤立点发现或样本密度估计问题，采用了超球面上的One-ClassSVM算法来处理这类问题；

When a training sample set is unlabelled and unbalanced , attack detection is treated as outlier detection or density estimation of samples and one-class SVM of hypersphere can be utilized to solve it .

基于超球面交叉机制，提出了VB-ERL节点定位算法。

A VB-ERL localization algorithm is proposed based on the hyper-sphere intersection mechanism .

针对异常入侵检测中训练样本是未标定的不均衡数据集的情况，将其视为一个孤立点发现问题。提出了适用于孤立点检测的超球面One-ClassSVM的异常检测算法。

As for the problem that training samples in anomaly detection are unlabelled and unbalanced data sets , attack detection is treated as outlier detection and one-class SVM of hypersphere can be utilized to solve it .

针对相同粒度中如何得到学习规则问题，提出了多侧面递进MIDA的基本框架，对原有的超球面覆盖算法进行了必要的改进。

How to gain learning rules of the same granule , a multi-side increasing by degrees algorithm ( MIDA ) is proposed .

模糊超球面支持向量机（FHS-SVM）在处理一类分类问题时比超平面支持向量机泛化能力更强，特别是在雷达目标检测中得到了成功应用。

Fuzzy hypersphere support vector machine ( FHS-SVM ) has stronger generalization capability than hyperplane support vector machine in the one-class classification problem , being successful in radar target detection .

提出了一个基于同心超球面分割的支持向量预抽取方法，并在此基础上给出了HD-SVM训练算法。

A method for pre-extracting support vectors based on concentric hyperspheres division is presented in this paper , and HD-SVM algorithm based on this method is presented also .

为了改善聚类分离的精度，该方法选取混合空间中半径给定的、中心位于原点的超球面以外的所有数据点，然后将这些数据点映射到中心位于原点的单位超球面上以得到集合Cy。

In order to improve the accuracy of clustering separation , this paper selects all data-points outside the hypersphere of a given radius centered at origin , in mixture space , and then projects the data points onto the unit hypersphere centered at origin to obtain the aggregate Cy.

当把Oja学习规则描述的连续型全反馈神经网络（Oja-N）用于求解矩阵特征值特征向量时，网络初始向量需位于单位超球面上，这给应用带来不便。

While using continuous time neural network described by the E. Oja . learning rule ( Oja-N ) for computing real symmetrical matrix eigenvalues and eigenvectors , the initial vector must be on Rn unit hyper-sphere surface , otherwise , the network may produce limit-time overflow .

算法利用核空间中样本特征差异突出的特性，首先对样本在核空间进行K-均值聚类，然后使用OC-SVMs对各子类训练建立多超球面分类模型，实现分类判决。

Considering that the data features were expected to be more separable in kernel space , we first performed the K-means clustering in kernel space , then trained the sub-class data separately using OC-SVMs and established a multiple hyperspheres classification model to decide the class label of new data .

超球面模型应用于股票排序的探讨

An Application of Multi Dimensional Sphere Model on Stock Market Ordination

基于同心超球面分割的支持向量预抽取方法

Method for Pre-extracting Support Vectors Based on Concentric Hyperspheres Division

模糊线性判别函数与权重初始化超球面

Fuzzy Linear Discriminant Functions and the Weight - Initialization Hyperspheres

证明了平衡解向量位于由非零初始向量确定的超球面上的结论。

The equilibrium vector is on the hyper-sphere surface decided by the initial vector .

欧氏空间超球面的特征

Characteristics of the hypersphere in Euclidean space

采用改进的超球面支持向量机作为分类器，实现了刀具磨损状态的自动识别。

The improved hyper-sphere support vector machine was adopted as classifier to implement tool wear state automatic recognition .

并通过一系列近似推理与实验验证，提出了将隐层权重矢量初始值均匀地分布在权重空间的一个圆（超球面）上的方法。

Based on a series of approximate reasoning and experiment verifications , the method of initializing weights is inducted .

在对超球面性状的目标的侦测方面，这种聚类算法大大优于传统的算法。

In the case of detection of hyperspherical-shaped objects , this clustering algorithm is much better than traditional algorithms .

针对这一问题，提出一种基于改进超球面支持向量机的故障分类方法，并将其应用于刀具磨损状态的自动识别。

To solve the problem , A tool wear state recognition method based on improved hyper-sphere support vector machine was proposed after research .

在分类器方面，考虑到各类样本的疏松程度不同，利用引力法对超球面支持向量机的决策函数进行改进，经过优化分析得到最佳分类引力公式。

In the aspect of classification algorithm , considering the difference of samples ' distribution , gravitation method was used to improve the decision function of hyper-sphere support vector machine for acquiring the optimized classification formula .

该方法借鉴了最优超球面思想，通过构造一个二次规划问题，运用支持向量代替样本构造相似度度量矩阵，从而解决了不确定问题维度对计算复杂性的影响。

Through adopting the ideas of optimal hypersphere and constructing a quadratic programming problem , we can construct a similarity measurement matrix by support vectors taking place of samples , which can solve uncertain problem dimensionality .

然后在特征空间里构造超球面，以逼近样本点分布的几何轮廓，从而将神经网络训练问题转化为点集包含问题。

And then hyperspheres are constructed to draw up the distribution of the sample data in feature space . The training problem of neural networks can be transformed into the " including " problem of a point set .

设计的基于超椭球面的分类规则用来对过程数据分类，建立的多PCA模型用于过程监测，SOFM网络用于故障诊断。

Hyper-ellipsoid bound clustering rules are adopted to classify the process data , multi-PCA models are then built up for process monitoring . SOFM network is used in fault diagnosis .

推导了基于超椭球面支持向量机的马田系统阈值确定公式。

The function of threshold of MTS based on the hyper ellipsoidal support vector machine is established .

超精密非球面磨削加工微振动试验系统研究

Study on microvibration experiment system of ultra-precision grinding optical aspheric surfaces

超精密非球面镜面计算机辅助设计与应用

Study and Applications of Computer Aided Design for Ultra-precision Aspheric Lens