高维空间

k-LDCHD&高维空间k邻域局部密度聚类算法

K-LDCHD & A Local Density Based k-Neighborhood Clustering Algorithm for High Dimensional Space

高维空间上的一类自映射嵌入n周期轨的构造方法

A Construction Method for a Class of Self-mapping in Higher Dimensional Space Embedded in n-Period Orbit

DNA序列高维空间数字编码的运算法则是：（1）根据DNA序列数码的奇偶性质，可以推导出其与末位碱基的对应关系。

According to the parity of DNA digital sequences , the last nucleotide bases can be determined .

一种采用Z曲线高维空间范围查询算法

High-dimensional Spatial Range Query Algorithm Based on Z Curve

高维空间下求解MDA的扰动算法及其在人脸识别中的应用

A perturbation algorithm for MDA in high dimensional space and its application to face recognition

高维空间上的迭代方程及Wiener型Banach代数

Iterative Equations on High Dimensional Space and Wiener Type Banach Algebra

Q式非线性映射分析方法是将一组高维空间的数据映射到低维空间，同时保持数据固有结构的一种方法。

Q nonlinear mapping method works by mapping high-dimensional data into low-dimensional data , with data interrelation unchanged .

研究高维空间中代数流形上多项式空间的Lagrange插值问题。

We researched the problem of Lagrange interpolation of polynomial space on the algebraic manifold .

研究四能级N-型EIT系统中的稳定高维空间光孤子。

High-dimensional spatial optical solitons in N-type four-level EIT are studied .

用马氏距离客观确定样本的空间结构后，我们可定义在E最小意义下高维空间到低维空间的映射。

After the space structure is fixed objectively with Mahalanobis 's distance the image from a higher-dimensional space to a lower-dimensional space is defined based upon the minimum E.

高维空间中半线性波动方程的Sobolev指数

The Sobolev Exponent of Semilinear Wave Equations in High Space Dimensions

高维空间中代数流形上多项式空间的维数与Lagrange插值适定结点组的构造

The Dimension of Polynomial Space and the Construction of Properly Posed Set of Nodes for Lagrange Interpolation on Algebraic Manifold

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 .

主曲线强调寻找通过数据分布的中间（middle）并满足自相合的光滑一维曲线，其理论基础是寻找嵌入高维空间的非欧氏低维流形。

They emphasize for finding ' self-consistent ' smooth one dimensional curves that pass through the middle of a multidimensional data set , and the theoretical foundation is to seek lower-dimensional non-euclidean manifolds embedded multidimensional data space .

提出DNA序列高维空间的表观维数Nv，数值维数Nx及差异维数Nd的概念。

The difference between the visual dimension Nv and the digital dimension Nx is called the difference dimension Nd of DNA sequence .

使用该双层MEC算法进行MEC高维空间的性能的实验研究。

Experimental study has been carried out with this two-level MEC algorithm in high-dimension space .

研究利用MatchingPursuit（MP）方法实现的图像稀疏分解算法，针对其中关键难题，提出利用在低维空间的搜索实现高维空间的搜索的快速方法。

To overcome the key problem in image sparse decomposition by Matching Pursuit ( MP ), a fast algorithm is presented which realizes high space search in a lower space .

高维空间的对称及非对称反常与Atiyah－Singer指标定理

Symmetric and antisymmetric anomalies of high dimensional space and Atiyah-Singer index theorem

利用Z曲线聚类和降维特性，本文给出网格划分方法、搜索区域分解过程，提出一种高维空间范围查询算法。

Based on Z curve , the paper presents a method of grid partition , a procedure of partitioning search region , and a high-dimensional spatial range query algorithm .

在处理非线性问题时，SVM通过引入核函数，避免了在高维空间中的内积运算，从而解决了维数灾问题。

When dealing with nonlinear problems , SVM avoid computing inner product in the high dimension space through the introduction of kernel function , thus solved the dimension disaster problem .

此外还讨论了在高维空间的和有质量标量场引起的Casimir效应。

The Casimir effects in high dimensional space and relevant to massive scalar field are also discussed .

不论是寻优函数还是分类函数都只涉及训练样本之间的内积运算（χi·χj），因此在高维空间实际上只需进行内积运算。

Both optimizing function and classification function are only involve with inner product operation between the training samples , so the method of calculation in high-dimensional space is only require inner product operation .

k-means聚类通常采用欧氏距离作为距离度量方法，但由于高维空间数据存在噪声且具有稀疏性，使得聚类效果显著降低，影响图像的表达。

The performance of k-means clustering severely degraded when Euclidean distance was used as the similarity measurement method because of the existence of the sparsity and noise in high-dimensional data .

小波分析比Fourier分析能更稀疏地表示一维分段光滑或者有界变差函数，而新的多尺度分析方法在高维空间中对多变量函数的稀疏表示具有较小波分析更好的逼近性能。

Wavelet analysis can give more " sparse " expression than Fourier analysis in piecewise smooth signal or bounded variance function . New multiscale methods can give better performance in approximating multivariate function in high-dimension space than wavelet analysis .

高维空间的一个Heilbronn型问题

On a Problem of Heilbronn Type in Higher Dimensional Space

众所周知，Wavelet分析能够对具有点奇异性信号进行有效的描述，但对于高维空间中沿各种曲线、曲面和超曲面分布的奇异性信号来讲，Wavelet分析就失去了它的分析优势。

As well known , wavelet analysis can be used to describe the signal with point singularities effectively . However , for the signals with singularities distributed along various curves , curve surface and hyper-curve-surface in high dimensional space , Wavelet analysis loses its advantages .

KDA算法是通过非线性映射将高维空间的原始数据样本投影到低维特征空间中，然后在该空间中实施LDA特征提取。

KDA algorithm projects the high-dimensional of original data samples to the low-dimensional feature space through non-linear mapping , and then uses the LDA method to extract feature .

基于高维空间划分的原理，提出了一种非线性神经元CC模型和基于CC模型的神经网络的构造算法。

On the basis of the space partition in high_dimension space , the paper has put forward a new nonlinear neural model - CC model and the construct algorithm of neural networks based on the CC model .

Quasi-Regression主要用于解决高维空间的函数逼近问题。

Quasi-Regression is introduced for approximation of a function in high dimensional space in recent literature .

数据流聚类是数据流挖掘研究的一个重要内容，已有的数据流聚类算法大多采用k中心点（均值）方法对数据进行聚类，不能对数据分布不规则以及高维空间数据流进行有效聚类。

Data stream clustering is an important issue in data stream mining . Most of the existing algorithms adopted K medians ( means ) method to solve this problem , which are not suitable to address the problem of clustering high dimensional or abnormal distributed data streams .