从岩石力学系统运动稳定性研究滑坡问题

从岩石力学系统运动稳定性的基本理论出发,将边坡力学系统的破坏分成五类,对其中的连续协调变形边坡的稳定性问题进行了描述,并分析了该系统的稳定性及其判据,找出了系统的控制变量是系统的广义刚度系数,同时对影响系统控制变量的因素进行了初探,指出影响边坡系统稳定性的控制变量主要是系统的几何结构因素和系统的力学参数性质,最后提出对系统控制变量进行人为的调控,达到调整系统、加强系统稳定性和防灾的目的．     

DETECTING AND ADJUSTING FOR NON-LINEARITIES IN CALIBRATION OF NEAR-INFRARED DATA USING PRINCIPAL COMPONENTS

A new regression method for non-linear near-infrared spectroscopic data is proposed.The technique isbased on a model which is linear in the principal components and simple functions(squares and products)of them.Added variable plots are used to determine which squares and products to incorporate into themodel.The regression coefficients are estimated by a Stein estimate which shrinks towards the estimatedetermined by the first several principal components and the selected non-linear terms.The technique isnot computationally intensive and is appropriate for routine predictions of chemical concentrations.Themethod is tested on three data sets and in all cases gives more accurate predictions than does linearprincipal components regression.     

黄土丘陵小流域土壤水分空间预测的统计模型

在6个土层和10次土壤含水量测定的基础上,利用土地利用与地形等6类20个环境因子变量,建立了黄土丘陵区小流域土壤水分空间预测的6种多元线性回归模型,并提出了5类13个指标对模型进行了评价与比较。研究表明,各模型组之间的差异较大,以直接回归模型组为最优,PCA线性转换回归模型组次之,DCA非线性转换回归模型组最差。在每一组内,模型之间的差异相对较小,以变量全部入选模型稍优于变量逐步筛选模型。6种模型中,通用多元线性回归模型的拟合性最好、预测精度最高,但模型结构最为复杂、需要的环境因子最多;多元线性逐步回归模型不仅拟合性和无偏性方面很好,而且结构最为简单、需要的环境变量最少,因而为最优模型     

SOIL AND VEGETATION PATTERNS IN BARRIER-ISLAND DUNE ENVIRONMENTS

Plant species distributions often have been attributed to landform characteristics or their associated geomorphic processes. This complicates interpretation of vegetation patterns in that geomorphic processes shape, and are shaped by, landforms. To characterize the biogeographic impacts of this interaction, I used principal components analysis (PCA) to examine hypotheses regarding the structure of variation among soil properties in active barrier-island dune systems. Dune soils and vegetation were sampled on two well-recognized barrier-island morphologies. On low-profile, wave-dominated microtidal barrier islands (South Core Banks, North Carolina) frequent overwash exerts a greater control on the distribution of soil properties. On mixed-energy mesotidal barrier islands (Sapelo Island, Georgia), overwash is less frequent, and the distribution of soil properties is shaped by a complex dune topography. Nontrivial principal components on both islands captured an equivalent amount of variance in the soil data. However, there were inter-island differences in the dimensionality of these nontrivial principal components, and differences in the distribution of variance and factor loadings. Suites of topography-modifying species, unique to each island, were uniform in the strength of their individual correlation with local edaphic variability. I posit that soil variance structure is a useful criterion to distinguish the relative influence on vegetation patterns of soil properties expressed through landforms (Sapelo Island) versus sediment transport processes (South Core Banks). [Key words: dune vegetation, barrier islands, principal components analysis (PCA), overwash.]     

SHORT COMMUNICATION VARIATIONS IN ESSENTIAL OILS OF MANDARINE RELATED TO PROCESSING AND RIPENING

Mandarine essential oils are extracted from green unripened fruits as well as from red fruits at ripening,both oils having specific uses as natural additives in the food industry.Two processes of production,pressing and peeling,are currently adopted in their production.Capillary gas chromatography with flameionization detection has been suggested as a sensitive method for the fractionation of volatile componentsof the essential oils.Principal component analysis was proposed as an exploratory chemometric methodfor the differentiation of essential oils from fruits at different degrees of ripening,taking into accountthe processes of production.Product-moment correlations between variables(concentrations of 17components)were used as starting matrices and the explained variance was adopted as a criterion foreigenvalue selection.Bi-plots and three-dimensional plots of unrotated principal component scores weresystematically used as well as those of orthogonally rotated factor scores.The 17 variables were reducedto four principal components,which explained 87% of the total variance.Projection on the first threeeigenvectors of all data as unrotated component scores allowed for a tentative differentiation of 59 oilsaccording to their degree of ripening.The two processes of production were also differentiated in asample of 55 oils.     

Geographically weighted principal components analysis

Principal components analysis (PCA) is a widely used technique in the social and physical sciences. However in spatial applications, standard PCA is frequently applied without any adaptation that accounts for important spatial effects. Such a naive application can be problematic as such effects often provide a more complete understanding of a given process. In this respect, standard PCA can be (a) replaced with a geographically weighted PCA (GWPCA), when we want to account for a certain spatial heterogeneity; (b) adapted to account for spatial autocorrelation in the spatial process; or (c) adapted with a specification that represents a mixture of both (a) and (b). In this article, we focus on implementation issues concerning the calibration, testing, interpretation and visualisation of the location-specific principal components from GWPCA. Here we initially consider the basics of (global) principal components, then consider the development of a locally weighted PCA (for the exploration of local subsets in attribute-space) and finally GWPCA. As an illustration of the use of GWPCA (with respect to the implementation issues we investigate), we apply this technique to a study of social structure in Greater Dublin, Ireland.     

Structure and process of modernization. Some remarks on recurrent features in geographical studies of modernization

Lundqvist, J. 1974. Structure and process of modernization. Some remarks on recurrent features in geographical studies of modernization. Norsk geogr. Tidsskr. 28, 103–113.

The so-called modernization studies of some African countries are discussed. More specifically the application of principal components and factor analysis techniques is critically reviewed. Attention is focused on: 1. The basic idea behind principal components and factor analysis – that of collapsing intercorrelated variables into a few independent factors. 2. Data requirements in the light of the statistical assumptions underlying the techniques. 3. The interpretation of factors. 4. The problem of scale and proper areal or reference units. 5. The selection of variables for studies of modernization. 6. The need to link principal components and factor analysis studies and the choice of variables to theory.     

Testing spatial heterogeneity in geographically weighted principal components analysis

We propose a method to evaluate the existence of spatial variability in the covariance structure in a geographically weighted principal components analysis (GWPCA). The method, that is extensive to locally weighted principal components analysis, is based on performing a statistical hypothesis test using the eigenvectors of the PCA scores covariance matrix. The application of the method to simulated data shows that it has a greater statistical power than the current statistical test that uses the eigenvalues of the raw data covariance matrix. Finally, the method was applied to a real problem whose objective is to find spatial distribution patterns in a set of soil pollutants. The results show the utility of GWPCA versus PCA.     

DISCRIMINANT PRINCIPAL COMPONENTS ANALYSIS

When the number of variables exceeds the number of samples, one method of multivariate discriminationis to use principal components analysis to reduce the dimensionality and then to perform canonicalvariates analysis (PC-CVA). This paper proposes an alternative approach in which discriminant analysisis carried out by a weighted principal component analysis of the group means (DPCA). This method doesnot require prior data reduction and produces discriminant factors that are orthogonal in the original dataspace. The theory and performance of the two methods are compared. Although the individual factors ofDPCA are found to be less discriminating than PC-CVA, the overall discrimination, calculated bymultivariate analysis of variance, and the predictive value, estimated by the leaving-one-out error rate,are broadly comparable.     

贡嘎山东坡亚高山林区土壤结构综合评价

土壤结构状况对森林水文生态功能的发挥具有重要作用,以青藏高原东部、长江上游亚高山天然林区不同林型下土壤为研究对象,通过20个土壤结构指标的分析、计算,运用主成分-聚类分析方法综合评价了该区土壤结构。结果表明:20个土壤结构性评价常用指标所反映的信息有较大的重叠性,4个主成分表达了全部信息的90%以上,表现出土壤团聚体及稳定性、固相物质空间排列形成的孔隙、细粒物质等在土壤结构性能中具重要意义;林木生长的成熟化、混交或乔灌结合对土壤结构性能有较强促进作用。研究结果对于土壤结构综合评价方法选择、加强森林经营与培育以促进土壤结构发育、充分发挥森林水文生态效应具有一定的指导作用。     

基于主成分分析的关中地区农业粮食生产变化的影响因素研究

针对陕西省关中区域1978—2017年的农业生产数据,在分析关中40 a农业粮食生产的趋势变化后,运用主成分分析法,对影响关中农业生产中的地理环境和生产投入等主要因素进行了评价研究。结果表明：（1） 关中农业粮食生产的趋势变化呈现周期为3～7 a的循环增长方式,平均每周期峰值增长率为4.5%。（2） 主成分分析研究后得出,第一主成分全是地理因素指标,方差贡献率达到0.554,对关中地区农业粮食生产起着非常显著的决定影响作用,包括受灾农田面积（不含病虫害）、主要粮食作物播种面积、成灾农田面积（不含病虫害）、有效灌溉耕地面积、耕地面积;第二主成分方差贡献率为0.25,是影响粮食生产的重要因素和农业生产的生命补给。包括农业用电量、化肥、农用机械等生产资料投入和主要粮食作物稳产面积、劳动力投入因素指标;第三主成分为农药应用量,方差贡献率为0.068,影响较小。主成分累计方差贡献为0.872。通过对关中地区农业粮食生产变化的影响因素分析,可以为政府部门提出数据支撑和相关性的建议。     

沙拐枣属植物果实性状的数值分类研究

筛选出我国沙拐枣属(calligonum L.)植物15种,测定了果实刺/翅毛排数、刺/翅毛质地、扭曲方向、扭曲程度等11项指标。应用主成分分析法对15种沙拐枣属植物果实性状的各项指标进行了分析,结果表明,第一主成分贡献率为29.704%,其中沟槽深度、肋棱突起程度、刺毛稀疏度是影响沙拐枣果实性状的主要因素;第二主成分贡献率为25.598%,主要包括了基部加宽度、果组。对沙拐枣果实性状指标进行PCA排序可将其划分为4类:第一类包括翅/刺毛排数、刺毛稀疏度、肋棱宽度;第二类包括果组、果实扭曲方向、扭曲程度;第三类包括刺毛/翅质地、刺毛/翅粗硬、沟槽深度、肋棱突起程度;第四类包括果实基部是否加宽。通过第一、第二和第三主成分分析体现了沙拐枣果实趋向于沟槽浅、肋棱浅,而果实刺毛密度趋向于增加。     

Detecting ethnic residential clusters using an optimisation clustering method

To understand residential clustering of contemporary immigrants and other ethnic minorities in urban areas, it is important to first identify where they are clustered. In recent years, increasing attention has been given to the use of local statistics as a tool for finding the location of racial/ethnic residential clusters. However, since many existing local statistics are primarily developed for epidemiological studies where clustering is associated with relatively rare events, its application in studies of residential segregation may not always yield satisfactory results. This article proposes an optimisation clustering method for delineating the boundaries of ethnic residential clusters. The proposed approach uses a modified greedy algorithm to find the most likely extent of clusters and employs total within-group absolute deviations as a clustering criterion. To demonstrate the effectiveness of the method, we applied it to a set of synthetic landscapes and to two empirical data sets in Auckland, New Zealand. The results show that the proposed method can detect ethnic residential clusters effectively and that it has potential for use in other disciplines as it offers an ability to detect large, arbitrarily shaped clusters.     

Data-driven approach to characterize urban vitality: how spatiotemporal context dynamically defines Seoul’s nighttime

ABSTRACT

This study takes a data-driven approach to define urban nighttime by examining the spatiotemporal dynamics of urban vitality. Using micro-scale spatiotemporal analysis, this paper empirically provides a comprehensive, yet granular, picture of collective human behaviors in cities. Using Seoul, South Korea as a case study site, it prioritizes the spatiotemporal context in order to mitigate uncertain contextual effects inherent in such forms of data-driven analysis. Instead of leaving the data re-grouping up to researcher’s arbitrary decision, this paper employs a functional principal component analysis (FPCA) to systematically transform a set of discrete data to a continuous functional form. This paper applies FPCA on 24-hour-based dataset of pedestrian traffic in Seoul in order to make a data-driven extraction of principal components that characterize the city’s unique patterns of urban vitality. Extracting principal components allows for less statistically obvious phenomena to be measured that would have otherwise been hidden within the data. This approach proved successful in capturing nighttime vitality patterns that are eclipsed by the overwhelming trend of daytime patterns. Additionally, this paper compares differences between regions and seasons to examine what the differences can tell about the definition of nighttime.     

On covariance propagation of eigenparameters of symmetric n-D tensors

Symmetric tensors are typically encountered during investigations associated with stress and strain analysis and, thus, they are of particular interest to geophysicists and geodesists. Furthermore, symmetric tensors are studied using eigentheory analysis which provides the decomposition of the tensor on its principal components (n independent eigenvalues and the corresponding eigenvectors). In this paper, an analytical expression of the covariance matrix of the eigenvalues and eigenvectors of an n-D symmetric tensor is derived based on the principles of linear algebra and differential calculus. Through numerical tests, the proposed formulation is proven to give realistic uncertainty estimates of the determined eigenparameters. The methodology also reveals the significant impact on uncertainty assessments when the parameter dependencies between principal components are neglected.     

区域旅游产业化测度体系研究

旅游产业化水平是区域综合竞争力的重要组成部分。阐述旅游产业化的内涵,从效度、效率和效益3个维度分析影响区域旅游产业化水平的关键因素,建立了7个项目指标和24个因子指标的评价体系,采用基于主成分分析法的综合评价模型对国内31个省级行政区2004年的旅游产业化水平进行综合评价。     

A Synoptic Climatology of Severe Storms in Virginia*

A synoptic climatology is developed for Virginia using 21 years of late spring and summer surface and upper air observations. The climatology is produced by applying a combination of principal components analysis and cluster analysis such that each day is classified into one of a distinct number of synoptic situations. Days on which at least one severe storm occurred in Virginia are merged with the synoptic climatology. A majority of severe storms are associated with one synoptic situation distinguished by moderate instability and a high moisture content.     

MULTIVARIATE RESPONSE SURFACE MODELLING BY PRINCIPAL COMPONENTS ANALYSIS

Analysis of multivariate response data by modelling the principal components of the response has beenapplied to two sets of data. In both cases principal components analysis revealed the relationships amongthe response variables and exploited them to simplify the problem of modelling and optimizing themultivariate response. The models and optima obtained from the principal components comparedfavourably with the individual models and simultaneous optima.     

Positional uncertainty in manually digitized map data

Digital map coordinates represent the locations of real world entities. As such, differences can exist between the ‘tru’ and digital database coordinates of those entities. This paper reports on a statistical characterization of positional error in manually-digitized and map-registered point data, the relative contribution of point type and operator to digitization error, and the effects of map media type on the positional uncertainty associated with registration.

Manually-digitized point data were collected by four operators from mylar and paper maps. Point locations for a number of different feature types were sampled from United States Geological Survey (USGS) 1:24 000 scale maps. Linear models were used to estimate the variance components due to among-operator, map media, point type and registration effects. The statistical distribution of signed distance deviations for manually-digitized data was leptokurtic relative to a random normal variate. Unsigned deviations averaged 0-054 mm. Squared distance deviations were not different from a Chi-square random variate. Variance components indicate that among-operator differences in positional uncertainty were large and statistically significant, while differences among point type were small and non-significant. Signed distance deviations associated with a first-order afhne followed a normal distribution. Unsigned distance deviations associated with a first-order affinc transformation averaged 0068mm, and squared distance deviations were distributed as a Chi-square. Differences in transformation accuracy were not related to type of map media.     

COMMENTS ON THE NIPALS ALGORITHM

The Non-linear lterative Partial Least Squares(NIPALS)algorithm is used in principal componentanalysis to decompose a data matrix into score vectors and eigenvectors(loading vectors)plus a residualmatrix.N1PALS starts with some guessed starting vector.The principal components obtained by NIPALSdepends on the starting vector;the first principal component could not always be computed.Wold hassuggested a starting vector for NIPALS,but we have found that even if this starting vector is used,thefirst principal component cannot be obtained in all cases.The reason why such a situation occurs isexplained by the power method.A simple modification of the original NIPALS procedure to avoid gettingsmaller eigenvalues is presented.