| 1. | The maximum distance in high dimensional spaces
高维空间的最大距离 |
| 2. | Moreover the algorithm can be used in any high dimensional space
且这一算法可以用于任意维空间。 |
| 3. | As a matter of fact , cancers and all incurable diseases are nothing but a uniform kind of outwardly different phenomenon which occurs in higher dimensional space - time and that is reflected in the visible 3 - dimensional space - time
其实，癌症和所有的不治之症，全部都不是病，全部都仅仅是同一种发生在高维时空的反映到三维可见时空的一种不同的表面现象。 |
| 4. | It is important to determine the associated multiwavelet generated by a multi - scaling function for the flexible application of the multiwavelet analysis , and this can be converted equivalently into a problem of optimization in a high dimensional space under some conditions
确定多尺度函数所生成的多子波是灵活运用多子波理论的一个重要环节，在一定的条件下，它可以等价地转化为一个高维空间中的优化问题。 |
| 5. | This dissertation mainly discusses issues on the applications of wavelet analysis in the control of nonlinear systems . the main topics are : ( 1 ) the problem of modeling and identification of nonlinear systems in the high dimensional space using wavelet analysis is studied
本文对小波分析在非线性系统控制中应用的若干问题作了较深入地研究和探索，主要的研究内容包括： ( 1 )研究了小波分析在高维空间中对非线性系统建模的问题。 |
| 6. | One is the performance of data mining algorithms degrades , the other is many distance - based and density - based algorithms maybe not effective . these problems can be solved by the following methods : l ) transport the data from high dimensional space to lower dimensional space by dimensionality reduction , then process the data as lower dimensional data . 2 ) to improve the performance of mining algorithms , we can design more effective indexing structures , adopt incremental algorithms and parallel algorithms and so on
解决的方法可以有以下几种：一个可以通过降维将数据从高维降到低维，然后用低维数据的处理办法进行处理；对算法效率下降问题可以通过设计更为有效的索引结构、采用增量算法及并行算法等来提高算法的性能；对失效的问题通过重新定义使其获得新生。 |
| 7. | The majority of our work is summarized here : ( 1 ) a new function hsim ( ) to measure the proximity of objects in high dimensional spaces is presented by analyzing the characteristic of the high dimensional data . the function can not only avoid the problem which the lp - norm lead to the non - contrasting behavior of distance in high dimensional space , but also adapt to both binary and numerical data . we also made a comparison between hsirn ( ) and other similarity functions
本文的主要工作如下： ( 1 )通过对高维数据特点的分析，提出了一种新的相似性度量函数hsim ( ) ，该函数可以避免在高维空间中分辨能力下降的问题，还可以将数值型的数据和二值型数据相似性的计算整合在一个统一的框架中。 |
| 8. | The performance of similarity indexing structures in high dimensions degrades rapidly . in lower dimensional space , we often use lp - norm to measure the proximity between two points , but in many case the concept of this proximity is never meaningless in high dimensional space . these issues bring high dimensional data mining two challenges
随着数据维数的升高，高维索引结构的性能迅速下降，在低维空间中，我们经常采用l _ p距离作为数据之间的相似性度量，在高维空间中很多情况下这种相似性的概念不复存在，这就给高维数据挖掘带来了很严峻的考验，一方面引起基于索引结构的数据挖掘算法的性能下降，另一方面很多基于全空间距离函数的挖掘方法也会失效。 |
| 9. | The document space is generally of high dimensionality and clustering in such a high dimensional space is often infeasible due to the curse of dimensionality . so the primary step in document clustering is to project the document into a lower - rank semantic space in which the documents related to the same semantics are close to each other
基于文本空间的文本聚类因为其具有高维的特征而不容易直接实现,所以文本聚类的首要步骤就是将文本空间的数据投影到较低维的语义空间里,使在文本空间里相邻的数据向量在语义空间里根据某些提取的特征参数而相似。 |
| 10. | Support vector machine ( svm ) is a machine learning method based on the structural risk minimization principle and vc dimension of statistical learning theory . by using kernel functions , svm eliminates the problem of " curse of dimensionality " in high dimensional space and has better generalization performance than traditional statistical based learning methods
支持向量机是基于统计学习理论中结构风险最小化归纳原则和vc维原理的一种机器学习方法，它通过使用核函数巧妙的解决高维空间的维数灾难问题，并且具有比传统的基于统计的学习方法更好的推广性能。 |
