首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 78 毫秒
1.
王泽兴 《数学杂志》2023,(3):229-246
LUMs(Large-margin Unified Machines)在分类学习中受到广泛关注,LUMs是一类最大化间隔分类器,它提供了一种独特的软分类到硬分类转化的方式.本文研究的是基于独立不同分布样本和LUM损失函数的二分类在线学习算法.同时,在线算法的每一步迭代,涉及的LUM损失函数的参数是随着迭代在逐渐减小的.在这种假设下,我们基于再生核希尔伯特空间(RKHS),给出了在线算法的收敛阶.  相似文献   

2.
研究了软拓扑空间的相关性质.采用经典拓扑学的定义方法,定义了新的软点和软连续,证明了软拓扑空间及乘积拓扑空间有关的分离性质,通过例子说明了各种分离性质之间的关系,进一步推广了软拓扑空间.  相似文献   

3.
利用模糊软拓扑空间族,构造出模糊软和拓扑,得到相应的模糊软和拓扑空间的系列拓扑性质。最后给出模糊软Ti-空间族的和空间(i=0,1,2,3,4)的一些结论。  相似文献   

4.
关于概率度量空间的等距同构   总被引:2,自引:0,他引:2  
概率度量空间理论中有两种等距同构,一种是一个概率度量空间等距同构于另一个概率度量空间。另一种是一个概率度量空间等距同于一个准度量族生成空间。该文建立了这两种等距同构之间的联系。  相似文献   

5.
双曲虚单位对应一类Minkowski复空间并具有方向异性的特点.四维时空中特殊方向上两时空点间的减法对应类时区与类光区的几何关联,在物理中表示粒子和场的相互作用.通过定义拟(虚)距离使Minkowsk空间的时空映射和间隔不变量进行度量公理化.四维时空中不同方向的距离或度量需要用线度因子和角度因子共同刻画,其中角度因子对应模糊集合,决定了Minkowski度量空间的奇异性质.  相似文献   

6.
本文提出了基于支持向量回归机(SVR)的一种新分类算法.它和标准的支持向量机(SVM)不同:标准的支持向量机(SVM)采用固定的模度量间隔且最优化问题与参数有关.本文中我们可以用任意模度量间隔,得到的最优化问题是无参数的线性规划问题,避免了参数选择.数值试验表明了该算法的有效性.  相似文献   

7.
本文给出了超空间上Hausdorff概率度量的一种简明形式,用以讨论了超空间上Hausdorff概率度量所决定的收敛及空间的某些拓扑性质。  相似文献   

8.
针对多观测样本分类问题,提出一种基于Kernel Discriminant CanonicalCorrelation(KDCC)来实现多观测样本分类的模型.该算法首先把原空间样本非线性的投影到高维特征空间,通过KPCA得到核子空间,然后在高维特征空间定义一个使类内核子空间的相关性最大,同时使类间核子空间的相关性最小的KDCC矩阵,通过迭代法训练出最优的KDCC矩阵,把每个核子空间投影到KDCC矩阵上得到转换核子空间,采用典型相关性作为转换核子空间之间的相似性度量,并采用最近邻准则作为多观测样本的分类决策,从而实现多观测样本的分类.在三个数据库上进行了一系列实验,实验结果表明提出的方法对于多观测样本分类具有可行性和有效性.  相似文献   

9.
随机结构空间理论初探   总被引:6,自引:3,他引:3  
提出了随机结构空间的概念,引出了随机拓扑空间、随机度量空间、随机赋范空间、随机内积空间、随机关系等随机数学结构的概念,初步研究了随机度量空间、随机赋范空间、随机内积空间的基本构造以及与概率度量空间、概率赋范空间、概率内积空间的关系。  相似文献   

10.
研究了基于数据的区间数智能决策分析,提出了一种基于区间数的支持向量域多分类软计算方法,该方法可以直接处理特征空间为区间数的多分类问题,拓展了支持向量域多分类算法应用的范围.  相似文献   

11.
In this paper, we take the case of soft points into consideration and propose a new metric structure called soft $D_a$-metric space for a specific orbit defined with soft points. In order to establish fixed point results in the modified metric space, we modify a few existing definitions in the sense of soft points.  相似文献   

12.
In this paper, we consider the problem of signal classification. First, the signal is translated into a persistence diagram through the use of delay-embedding and persistent homology. Endowing the data space of persistence diagrams with a metric from point processes, we show that it admits statistical structure in the form of Fréchet means and variances and a classification scheme is established. In contrast with the Wasserstein distance, this metric accounts for changes in small persistence and changes in cardinality. The classification results using this distance are benchmarked on both synthetic data and real acoustic signals and it is demonstrated that this classifier outperforms current signal classification techniques.  相似文献   

13.
In the theory of physical structures the classification of metric functions (both on a single set and on two ones) plays an important role. A metric function represents a two-point invariant of a certain local Lie transformation group. Moreover, one can uniquely restore this group with the help of the invariance condition. According to this theorem, in order to find all metric functions, it suffices to construct the complete classification of local Lie transformation groups. In this paper we classify Lie algebras of simply transitive local Lie groups of local transformations of a four-dimensional space, and then we define metric functions. The obtained results admit application in physics, in particular, in thermodynamics.  相似文献   

14.
15.
Support Vector Machines (SVMs) are now very popular as a powerful method in pattern classification problems. One of main features of SVMs is to produce a separating hyperplane which maximizes the margin in feature space induced by nonlinear mapping using kernel function. As a result, SVMs can treat not only linear separation but also nonlinear separation. While the soft margin method of SVMs considers only the distance between separating hyperplane and misclassified data, we propose in this paper multi-objective programming formulation considering surplus variables. A similar formulation was extensively researched in linear discriminant analysis mostly in 1980s by using Goal Programming(GP). This paper compares these conventional methods such as SVMs and GP with our proposed formulation through several examples.Received: September 2003, Revised: December 2003,  相似文献   

16.
For hypersurfaces with regular Weingarten operator in nonflat space forms we study the relations between the intrinsic geometry of the third fundamental form metric and the extrinsic geometry of the hypersurface. We prove a theorema-egregium-type result for this metric and, in particular, give a local classification of hypersurfaces in case of an Einstein structure of this metric.Partially supported by the project 19701003 of NSFC.The geometry groops at TU Berlin and KU Leuven cooperate within the GA DGET program.  相似文献   

17.
We present a stationary axisymmetric space–time admitting circular closed timelike geodesics everywhere within a finite region of space. The space–time is free from curvature divergence and is locally isometric to a nonvacuum pp-wave space–time. The matter–energy content is a pure radiation field and satisfies the null energy condition (NEC), and the metric is of type N in the Petrov classification scheme. Finally, we demonstrate the existence of timelike and null circular geodesic paths for this metric.  相似文献   

18.
In this paper, we introduce a G metric on the G-cone metric space and then prove that a complete G-cone metric space is always a complete G metric space and verify that a contractive mapping on the G-cone metric space is a contractive mapping on the G metric space. At last, we also give a new way to obtain the unique fixed point on G-cone metric space.  相似文献   

19.
胡和生 《数学学报》1956,6(2):320-332
<正> 在歐氏空間E_(m+1)中的安裝及變形問題在近一世紀的幾何學者的工作中得到了解决,而所確定的V_m E_(m+1)一般是不能變形的。就是說,能够變形的只是狹窄的一類超曲面.運用了外微分形式的方法,很詳細地綜合了這些工作,並且完全地給出  相似文献   

20.
We introduce new types of convergence of sequences of measurable functions stronger than convergence in measure for each pair of positive real numbers p, q and we obtain a classification of convergences in measure. Also in the space M of sequences of measurable functions converging in measure to zero, we introduce in a natural way an equivalence relation ∼, and in the quotient space M=M/∼ a metric, under which M turns to be a complete metric space.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号