一种基于密度敏感的自适应谱聚类算法

针对传统的谱聚类算法不适合处理多尺度问题,引入一种新的相似性度量—密度敏感的相似性度量,该度量可以放大不同高密度区域内数据点间距离,缩短同一高密度区域内数据点间距离,最终有效描述数据的实际聚类分布.本文引入特征间隙的概念,给出一种自动确定聚类数目的方法.数值实验验证本文所提的算法的可行性和有效性.     

基于相似性度量的改进DBSCAN算法

针对传统DBSCAN算法对高维数据集聚类效果不佳且参数的选取敏感问题,提出一种新的基于相似性度量的改进DBSCAN算法.该算法构造了测地距离和共享最近邻的数据点之间的相似度矩阵,克服欧式距离对高维数据的局限性,更好地刻画数据集的真实情况.通过分析数据的分布特征来自适应确定Eps和MinPts参数.实验结果表明,所提GS-DBSCAN算法能够有效地对复杂分布的数据进行聚类,且在高维数据的聚类准确率高于对比算法,验证了算法的准确性和可行性.     

函数型聚类分析方法研究

基于距离度量的函数型数据聚类是目前函数型聚类分析方法的主要研究方向之一,而该方法主要是基于数值距离或曲线形态的单一角度来衡量函数型数据的相似性.为了解决这种单一性,提出一种同时兼顾函数型数据的数值距离和曲线形态的相似性度量方法—基于极值点偏差补偿的相似性度量,并给出实证分析,结果显示该方法比较有效.进一步提出一种多元函数型聚类分析方法—函数型熵权法,丰富了函数型聚类分析方法.     

多标度数据几何轮廓相似性的度量与应用

在多标度数据的分类问题中,对于分布特征不清或小样本下的数据的相似性度量仍是研究的热点.对此,建立了基于样本几何轮廓相似度的判别分析模型,并应用于采动沉陷建筑物损坏等级的评价,结果表明该模型简洁、有效,无需数据预处理,较少依赖先验信息,具有推广应用的价值.     

基于差异关系案例推理的关系价值度量研究

关系价值度量的研究还非常少,少量研究也仅停留在理论公式阶段,缺乏操作层面的度量方法。本文将关系价值度量看作是一个决策问题,提出一种基于差异案例推理的方法进行关系价值的度量。首先分析了将案例推理用于关系价值度量的基本思想;在实施相似性度量阶段,用问题案例和历史案例在各个关系价值度量指标上的差异关系来替代经典的欧氏距离,并给出了基于距离比例的无差异关系、弱差异关系和强差异关系定义,通过对三种差异关系对应的差异指数进行集成实现问题案例和历史案例的相似性度量。     

模糊度量空间中多变量压缩映射的公共耦合不动点定理

本文提出了多变量映射的一致点的概念.本文的结果是模糊偏序度量空间中不动点定理的一些主要结论从低维到高维的推广.     

基于Copula函数的非线性时间序列聚类

时间序列数据的聚类是对面板数据或多维时间序列根据序列相似度进行分组。聚在同一组的时间序列具有相近的模型参数,尤其是当序列较短时聚类后能够得到更精确的参数估计。现存的时间序列聚类方法的距离度量大都基于时间序列的线性假设,但是现实中时间序列通常是非线性的。本文提出了一种基于Copula距离测度的非线性时间序列数据的聚类方法,它利用了Copula函数获取时间序列的非线性相依结构。作为一种非参数的距离度量,基于Copula函数的距离度量能够识别动态相关结构的相似性。大量的模拟实验和实证研究验证了我们所提方法的有效性。     

关于共形Berwald的Kropina度量(英文)

本文利用导航数据研究了共形Berwald的Kropina度量.首先利用导航数据刻画了Berwald Kropina度量.在此基础上,本文得到了Kropina度量是共形Berwald度量的一个充分必要条件.进一步,刻画了具有弱迷向旗曲率的共形Berwald Kropina度量的局部结构.     

一类由概率分布生成的新度量

主要得到了一类由概率分布生成的新度量.以信息理论中的重要概念-相对熵为基础,对前人文章中的重要结论进行推广,通过利用改进的初等方法在离散的可测空间中得到了这类新度量,并且证明了得到的新度量成立的充要条件.由此再将这类新度量推广到连续的可测空间中,得到了同样的结果.最后讨论了新度量的最值问题.     

高维纵向数据的模型平均估计

高维数据的模型选择是当今统计学研究的一个热点问题,但关于高维纵向数据方面的模型平均却少见研究,文章提出了一种利用删组交叉验证准则对高维纵向数据进行模型平均估计的方法,在最小化预测残差意义下,以删组交叉验证为准则,证明了其渐近最优性,并通过模拟研究表明,该模型平均方法在估计效果上要优于其它一些传统的模型选择和平均方法.     

A novel fractional moments-based maximum entropy method for high-dimensional reliability analysis

High-dimensional reliability analysis is still an open challenge in structural reliability community. To address this problem, a new sampling approach, named the good lattice point method based partially stratified sampling is proposed in the fractional moments-based maximum entropy method. In this approach, the original sample space is first partitioned into several orthogonal low-dimensional sample spaces, say 2 and 1 dimensions. Then, the samples in each low-dimensional sample space are generated by the good lattice point method, which are deterministic points and possess the property of large variance reduction. Finally, the samples in the original space can be obtained by randomly pairing the samples in low-dimensions, which may also significantly reduce the variance in high-dimensional cases. Then, this sampling approach is applied to evaluate the low-order fractional moments in the maximum entropy method with the tradeoff of efficiency and accuracy for high-dimensional reliability problems. In this regard, the probability density function of the performance function involving a large number of random inputs can be derived accordingly, where the reliability can be straightforwardly evaluated by a simple integral over the probability density function. Numerical examples are studied to validate the proposed method, which indicate the proposed method is of accuracy and efficiency for high-dimensional reliability analysis.     

On the classification of weakly symmetric Finsler spaces

In this paper, we give the classification of some special types of weakly symmetric Finsler spaces. We first present a general principle to classify weakly symmetric Finsler spaces and also give a method to figure out the Berwald spaces among the class of weakly symmetric Finsler spaces. Then we give an explicit classification of weakly symmetric Finsler spaces with reductive isometric groups as well as the left invariant weakly symmetric Finsler metrics on nilpotent Lie groups of the Heisenberg type. As an application, we obtain a large number of high-dimensional examples of reversible Finsler spaces which are non-Berwaldian and with vanishing S-curvature, a kind of spaces which are sought after in an open problem of Z. Shen.     

(3+1)维短波方程的不变子空间和精确解

利用不变子空间方法研究了(3+1)维短波方程的不变子空间和精确解.在(2+1)维短波方程增加一维的情形下,构造了更加广泛的精确解,同时也得到了超曲面的爆破解.主要结果不仅推广了不变子空间理论在高维非线性偏微分方程中的应用,而且对研究高维方程的动力系统有重要意义.     

A method for selecting the relevant dimensions for high-dimensional classification in singular vector spaces

Advances in Data Analysis and Classification - In this paper, we give a new feature selection algorithm for the binary class classification problem in sparse high-dimensional spaces. Singular value...     

投影寻踪动态聚类模型在房地产投资环境评价中的应用

将投影寻踪动态聚类模型引入到房地产投资环境评价方法中.针对房地产投资环境评价所面临的多因素高维复杂性问题,该模型能够完全根据样本数据特性将高维数据通过投影向量投影到低维数据,同时实现对低维数据的排序和自动聚类分析,进而通过研究低维数据以实现对高维数据的研究.最后通过辽宁省工业地产投资环境评价实例验证了该模型在房地产投资环境评价中的适用性.     

Discriminative variable selection for clustering with the sparse Fisher-EM algorithm

The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results. Existing approaches have demonstrated the importance of variable selection for clustering but turn out to be either very time consuming or not sparse enough in high-dimensional spaces. This work proposes to perform a selection of the discriminative variables by introducing sparsity in the loading matrix of the Fisher-EM algorithm. This clustering method has been recently proposed for the simultaneous visualization and clustering of high-dimensional data. It is based on a latent mixture model which fits the data into a low-dimensional discriminative subspace. Three different approaches are proposed in this work to introduce sparsity in the orientation matrix of the discriminative subspace through \(\ell _{1}\) -type penalizations. Experimental comparisons with existing approaches on simulated and real-world data sets demonstrate the interest of the proposed methodology. An application to the segmentation of hyperspectral images of the planet Mars is also presented.     

破坏性测量系统波动源的分析

测量系统分析是质量改进活动中的一个重要问题,评价测量系统精确度的标准方法是量具的重复性和再现性(R&R)研究,这种研究通常采用试验设计方法,而且对测量对象可以重复测量。然而在工业实践中,当遇到破坏性测量时,这种标准的R&R研究方法是无法实施的。本文给出了破坏性测量中测量系统波动源分析的一种方法,首先分析了破坏性测量中进行量具R&R研究的前提条件,进而给出了进行量具R&R研究的随机效应模型和方差分析方法;最后通过应用Minit-ab.14软件,对工业实践中的一个应用实例进行了分析。     

Efficiency measurement using independent component analysis and data envelopment analysis

Efficiency measurement is an important issue for any firm or organization. Efficiency measurement allows organizations to compare their performance with their competitors’ and then develop corresponding plans to improve performance. Various efficiency measurement tools, such as conventional statistical methods and non-parametric methods, have been successfully developed in the literature. Among these tools, the data envelopment analysis (DEA) approach is one of the most widely discussed. However, problems of discrimination between efficient and inefficient decision-making units also exist in the DEA context (Adler and Yazhemsky, 2010). In this paper, a two-stage approach of integrating independent component analysis (ICA) and data envelopment analysis (DEA) is proposed to overcome this issue. We suggest using ICA first to extract the input variables for generating independent components, then selecting the ICs representing the independent sources of input variables, and finally, inputting the selected ICs as new variables in the DEA model. A simulated dataset and a hospital dataset provided by the Office of Statistics in Taiwan’s Department of Health are used to demonstrate the validity of the proposed two-stage approach. The results show that the proposed method can not only separate performance differences between the DMUs but also improve the discriminatory capability of the DEA’s efficiency measurement.     

A combined p-value test for the mean difference of high-dimensional data

This paper proposes a novel method for testing the equality of high-dimensional means using a multiple hypothesis test. The proposed method is based on the maximum of standardized partial sums of logarithmic p-values statistic. Numerical studies show that the method performs well for both normal and non-normal data and has a good power performance under both dense and sparse alternative hypotheses. For illustration, a real data analysis is implemented.     

方差分析在复杂测量系统能力分析中的应用

测量系统分析是QS9000标准中的核心要素之一,主要用来评估测量系统对工序质量改进的保证程度。传统的测量系统能力分析主要采用极差分析或方差分析研究单台测量仪器组成的二因素交叉型简单测量系统,本文从企业的实际情况出发,采用方差分析法研究包含多台测量仪器的复杂测量系统,基于三因素套析因混合效应实验模型的方差分析和方差估计,提出了这种测量系统能力分析的方法,并给出了应用实例。