模糊数学方法在孢粉分析中的应用

运用模糊聚类分析的方法将已知的孢粉样本进行了分类 ,得到了动态聚类图 ,并利用方差分析的原理给出了最佳的分类 .     

Sparse Convex Clustering

Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational and statistical properties have been recently studied, the performance of convex clustering has not yet been investigated in the high-dimensional clustering scenario, where the data contains a large number of features and many of them carry no information about the clustering structure. In this article, we demonstrate that the performance of convex clustering could be distorted when the uninformative features are included in the clustering. To overcome it, we introduce a new clustering method, referred to as Sparse Convex Clustering, to simultaneously cluster observations and conduct feature selection. The key idea is to formulate convex clustering in a form of regularization, with an adaptive group-lasso penalty term on cluster centers. To optimally balance the trade-off between the cluster fitting and sparsity, a tuning criterion based on clustering stability is developed. Theoretically, we obtain a finite sample error bound for our estimator and further establish its variable selection consistency. The effectiveness of the proposed method is examined through a variety of numerical experiments and a real data application. Supplementary material for this article is available online.     

基于对象多属性差异的灰色发展聚类方法及应用

在现实决策问题中,决策对象在不同时期行为状态和所属类型往往呈现一定的发展规律,而现有聚类方法难以充分挖掘聚类对象的发展信息、对象间的关系信息和发展属性的差异信息。为有效处理此类问题,考虑到研究对象的发展趋势、发展行为和发展绝对量与增长量的属性差异,采用GM(1,1)和灰色定权聚类方法,构建了基于对象多属性差异的灰色发展聚类方法,并以我国区域高新技术产业化聚类评估问题为例验证了模型的有效性与合理性。结果表明,所构建模型能够有效描述研究对象呈现发展趋势或未来行为,并实现对研究对象的有效聚类。     

Space-Time Point-Process Models for Earthquake Occurrences

Several space-time statistical models are constructed based on both classical empirical studies of clustering and some more speculative hypotheses. Then we discuss the discrimination between models incorporating contrasting assumptions concerning the form of the space-time clusters. We also examine further practical extensions of the model to situations where the background seismicity is spatially non-homogeneous, and the clusters are non-isotropic. The goodness-of-fit of the models, as measured by AIC values, is discussed for two high quality data sets, in different tectonic regions. AIC also allows the details of the clustering structure in space to be clarified. A simulation algorithm for the models is provided, and used to confirm the numerical accuracy of the likelihood calculations. The simulated data sets show the similar spatial distributions to the real ones, but differ from them in some features of space-time clustering. These differences may provide useful indicators of directions for further study.     

基于加权相似性的BIRCH聚类算法

BIRCH方法是一个集成的层次聚类方法.它克服了凝聚层次聚类方法所面临的两个难点:可伸缩性和不能撤销前一步工作的问题.基于BIRCH聚类的多阶段聚类算法思想,结合基于权重的欧式距离度量和基于划分的K-means算法,提出了一种基于加权相似性的BIRCH聚类方法,并将方法应用在时间序列的气象数据分析中.     

Consistency of regularized spectral clustering

Clustering is a widely used technique in machine learning, however, relatively little research in consistency of clustering algorithms has been done so far. In this paper we investigate the consistency of the regularized spectral clustering algorithm, which has been proposed recently. It provides a natural out-of-sample extension for spectral clustering. The presence of the regularization term makes our situation different from that in previous work. Our approach is mainly an elaborate analysis of a functional named the clustering objective. Moreover, we establish a convergence rate. The rate depends on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers. Some new methods are exploited for the analysis since the underlying setting is much more complicated than usual. Some new methods are exploited for the analysis since the underlying setting is much more complicated than usual.     

高维稳健主成分聚类方法及其应用研究

随着信息技术的高速发展,每条数据所包含的信息越来越丰富,使得数据不可避免地含有异常值,且随着维数的增加,异常值出现的可能性更大。传统的主成分聚类分析对异常值特別敏感,基于MCD估计的主成分聚类方法虽然对异常值具有防御作用,但是在高维数据下MCD估计的偏差过大,其稳健性显著降低,而且当维数大于观测值个数时MCD估计失效。为此本文提出了基于MRCD估计的稳健主成分聚类方法,数值模拟和实证分析表明,基于MRCD估计的主成分聚类分析的效果优于传统的主成分聚类分析和基于MCD估计的主成分聚类分析,尤其是在维数大于样本观测值的情况下,MRCD估计更为有效。     

Pseudo-orthogonality for graph 1-Laplacian eigenvectors and applications to higher Cheeger constants and data clustering

The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data. This is an NP-hard problem that can be relaxed in the spectral graph theory, where the optimal cuts of a graph are related to the eigenvalues of graph 1-Laplacian. In this paper, we first give new notations to describe the paths, among critical eigenvectors of the graph 1-Laplacian, realizing sets with prescribed genus. We introduce the pseudo-orthogonality to characterize m₃(G), a special eigenvalue for the graph 1-Laplacian. Furthermore, we use it to give an upper bound for the third graph Cheeger constant h₃(G), that is, h₃(G) 6 m₃(G). This is a first step for proving that the k-th Cheeger constant is the minimum of the 1-Laplacian Raylegh quotient among vectors that are pseudo-orthogonal to the vectors realizing the previous k - 1 Cheeger constants. Eventually, we apply these results to give a method and a numerical algorithm to compute m₃(G), based on a generalized inverse power method.     

关于“信息熵”分析及其应用的研究

本文用Ｓｈａｎｎｏｎ熵函数的观点及最大离散熵原理，探讨了对随机试验项目的优选问题：即压缩某种“不确定性”试验项目的实施与探索．并通过应用实例的计算，获得了满意的聚类效果．这种方法对于信息资料的数据处理及压缩“不确定性“验项目具有普遍意义．     

改进的K均值聚类红外目标检测方法

利用图像方差能很好地反映目标边缘信息的特点,提出一种基于方差的K均值聚类红外目标检测算法。利用形态学方法对红外图像进行预处理,运用相应的模板计算得到红外图像的方差图像,利用K均值聚类算法对方差图像进行聚类,从而分离出目标类别和背景类别。实验表明,该算法提取的红外图像中目标信息的兰德指数最高,说明该算法能有效地提取红外图像中目标信息,从而达到目标检测的目的。