多元联系数在地基处理方案模糊选优中的应用

联系分量多于3个的集对分析联系数称为多元联系数,常用的多元联系数有四元联系数和五元联系数等等。用五元联系数中的a、b、c、d、e5个联系分量分别表述地基处理方案模糊评语“好”、“较好”、“一般”、“较差”、“差”对应的指标值,建立各个方案的五元联系数,再利用五元联系数系统态势排序等信息作进一步处理,在得到各个地基处理方案优劣排序的同时,还可以得到方案的优劣属性级别。     

Multivariate analysis of landscape wildfire dynamics in a Mediterranean ecosystem of Greece

This paper focuses on spatial distribution of long-term fire patterns versus physical and anthropogenic elements of the environment that determine wildfire dynamics in Greece. Logistic regression and correspondence analysis were applied in a spatial database that had been developed and managed within a Geographic Information System. Cartographic fire data were statistically correlated with basic physical and human geography factors (geomorphology, climate, land use and human activities) to estimate the degree of their influence at landscape scale. Land cover types of natural and agricultural vegetation were the most influential factors for explaining landscape wildfire dynamics in conjunction with topography and grazing.     

基于典型相关分析的遥感影像变化检测

多通道遥感影像由于通道之间相关性的影响,相对于单通道影像的变化检测更为困难,因此需要有效的集中分布在各个通道上的变化信息,构造出不同时相之间的差异影像,以便于变化信息的分析解译。针对多通道变化信息集中的难点和通道之间相关性的影响难以消除的问题,引入多元统计分析中的典型相关分析方法,将2个时相的多通道遥感影像示作2组多元随机变量,采用多元变化检测变换,对多个波谱通道上的所有差异信息或变化信息进行重组,分配到一组互不相关的结果变量中,最大限度地消除通道间的相关性对变化检测的不利影响,初步解决了差异影像构造的问题。     

多元统计分析在矿床指示元素组合特征研究中的应用——以山东黄埠岭金矿为例

应用相关分析、聚类分析和因子分析方法讨论了黄埠岭矿床中指示元素的组合特征。综合对该矿床具有代表性的7号矿脉和10号矿脉的分析结果，确定了黄埠岭金矿床Au的富集与Ag、Cu、Pb、Zn、Bi密切相关，矿体原生晕头晕组合为As、Sb、Hg，主成矿元素组合Au、Ag、Cu、Pb、Zn、Bi，尾晕元素组合为Co、Ni。为矿床的深边部成矿预测提供参数。     

Multivariate discrimination technique based on the Bayesian theory

A multivariate discrimination technique was established based on the Bayesian theory. Using this technique, P/S ratios of different types (e.g., Pn/Sn, Pn/Lg, Pg/Sn or Pg/Lg) measured within different frequency bands and from different stations were combined together to discriminate seismic events in Central Asia. Major advantages of the Bayesian approach are that the probability to be an explosion for any unknown event can be directly calculated given the measurements of a group of discriminants, and at the same time correlations among these discriminants can be fully taken into account. It was proved theoretically that the Bayesian technique would be optimal and its discriminating performance would be better than that of any individual discriminant as well as better than that yielded by the linear combination approach ignoring correlations among discriminants. This conclusion was also validated in this paper by applying the Bayesian approach to the above-mentioned observed data.     

Evaluation of geochemical data acquired from regular grids

Geochemical data obtained during mineral exploration often are biased by systematic as well as random errors; these may result in failures when usual methods of evaluation are used. This is true particularly in soil surveys carried out in regions where a long history of prospecting and mining activity has occurred and/or where aerial chemical pollution is likely to have occurred.A satisfactory evaluation of geochemical data even in such an unfavorable case requires sampling on a relatively dense grid and utilization of all available knowledge of types of mineralization. The evaluation procedure proposed consists of five consecutive phases: (1). Dividing the area of interest into subareas of a relatively homogeneous geological nature. (2). Processing by multivariate methods (factor analysis, in particular) without consideration of geographic relations. (3). A preliminary interpretation and search for a geochemical explanation of factors. (4). Processing of individual factors in two-dimensional geographic space by directional and frequency linear filtering methods. (5). Final interpretation and construction of a geochemical model. The procedure is illustrated by an example from a geochemical exploration survey in the vicinity of Píbram (Middle Bohemia).     

Multivariate normality in morphometric analysis

Data on some living (salamanders and grasshoppers) and fossil (Devonian brachiopods) animals are analyzed by means of recently developed methods for the large-scale treatment of multivariate normality. Multivariate nonnormality was found to exist in all situations, even if the univariate deviations in the skewness and kurtosis statistics proved to be without significance for the most part. The effect of logarithmically transforming the data appears to be a mixed blessing. Apart from the fact that the investigator is removed one step from the biological relationships in his data by carrying out a transformation of them, the betterment in the multivariate interconnections with respect to normality tends to be slight, despite the general improvement in the univariate values. The relationship between sample size and the multivariate normality measures b_1,p and b_2,p are studied empirically.     

Multivariate morphometrics and analysis of shape

Analysis of size and shape has always figured largely in interpretations of multivariate analyses of measurements on organisms, although on premises that are not always unchallengeable. A recent surge of interest has led to important advances in formal analysis of variations in shape (geometric morphometrics) and phylogenetic significance of such changes. In connection herewith, an improved philosophy for the choice of variables suitable for depicting shape variation is evolving. Important results for statistical validity of multivariate analyses now are being made available by several workers (robust estimates of canonical vectors, etc., stability of eigenvectorial elements, effects of deviations from multivariate normality) with special reference to applications in morphometric studies. Such questions have been little considered in the past with the result that many multivariate analyses of biological and geological data are inexact.Contribution Number 2 in a series of review articles by the Mathematical Geologists of United States. Accepted January 8, 1985. Invited lecture delivered to the thematic conference of Geological Shape Analysis, Wood's Hole, Massachusetts, September 8–12, 1984.     

On the Use of Multivariate Lévy-Stable Random Field Models for Geological Heterogeneity

Increasing attention has been paid to the use of non-Gaussian distributions as models of heterogeneity in sedimentary formations in recent years. In particular, the Lévy-stable distribution has been shown to be a useful model of the distribution of the increments of data measured in well logs. Frequently, the width of this distribution follows a power–law type scaling with increment lag, thus suggesting a nonstationary, fractal, multivariate Lévy distribution as a useful random field model. However, in this paper we show that it is very difficult to formulate a multivariate Lévy distribution with any nontrivial spatial correlations that can be sampled from rigorously in large models. Conventional sequential simulation techniques require two properties to hold of a multivariate distribution in order to work: (1) the marginal distributions must be of relatively simple form, and (2) in the uncorrelated limit, the multivariate distribution must factor into a product of independent distributions. At least one of these properties will break down in a multivariate Lévy distribution, depending on how it is formulated. This makes a rigorous derivation of a sequential simulation algorithm impossible. Nonetheless, many of the original observations that spurred the original interest in multivariate Lévy distributions can be reproduced with a conventional normal scoring procedure. Secondly, an approximate formulation of a sequential simulation algorithm can adequately reproduce the Lévy distributions of increments and fractal scaling frequently seen in real data.