STEPWISE CANONICAL DISCRIMINANT ANALYSIS OF CONTINUOUS DIGITALIZED SIGNALS:APPLICATION TO CHROMATOGRAMS OF WHEAT PROTEINS

Continuous digitalized signals such as spectra,electrophoregrams or chromatograms generally have alarge number of data points and contain redundant information.It is therefore troublesome performingdiscriminant analysis without any preliminary selection of variables.A procedure for the application ofcanonical discriminant analysis(CDA)on this kind of data is studied.CDA can be presented as asuccession of two principal component analyses(PCAs).The first is performed directly on the raw dataand gives PC scores.The second is applied on the gravity centres of each qualitative group assessed onthe normalized PC scores.A stepwise procedure for selection of the relevant PC scores is presented.Themethod has been tested on an illustrative collection of 165 size-exclusion high-performance(SE-HPLC)chromatograms of proteins of wheat belonging to 55 genotypes and grown in three locations.Thediscrimination of the growing locations was performed using seven to nine PC scores and gave more than86% accurate classifications of the samples both in the training sets and the verification sets.Thegenotypes were also rather well identified,with more than 85% of the samples correctly classified.Thestudied method gives a way of assessing relevant mathematical distances between digitalized signalsaccording to qualitative knowledge of the samples.     

基于形态学及傅里叶分析对两种南极冰鱼耳石外型的研究

根据2014年3—4月以及2015年4—9月在南设得兰群岛以及南乔治亚群岛周边水域采集的裘氏鳄头冰鱼(Champsocephalus gunnari)及雪冰(Chionobathyscus dewitti)样本,对其耳石进行5种基础形态参数测量并转换为7种形态学参数,比较分析了两种冰鱼间的耳石形态学差异,再利用傅里叶分析法选取两种耳石的77个傅里叶系数进行判别。结果表明,两种冰鱼耳石长、高、周长、面积及质量均与体长呈显著的幂指数关系(P0.01)。由形态指标分析可知,裘氏鳄头冰鱼较雪冰耳石环率更低,即更趋近于圆,更为规则,且耳石厚度上略薄。两者各项形态参数间均存在显著性差异(P0.01)。对耳石77个傅里叶谐值进行主成分分析,其中前20个主成分解释总变异的82.491%,两种冰鱼的因子分布图上重叠量较少,可见区分度较好,判别分析选取了其中的6个傅里叶值建立了判别函数,总体判别率为96.15%。总体而言,可利用耳石外型对两种冰鱼进行种类判别,傅里叶分析更为直观清晰且较为准确。本研究可为南极冰鱼耳石形态学研究提供基础数据,并就其种类鉴别提供备选方法。     

Cluster analysis of seismic moment tensor orientations

This paper demonstrates that well-known methods of cluster analysis and multivariate data analysis are useful for geodynamic interpretation of seismic moment tensors. To use these methods, moment tensors are expressed as vectors in a 6-D space. These are vectors in a rigorous sense, rather than an arbitrary set of ordered numbers, because a dot product can be defined that is independent of the coordinate system. In this vector space, non-isotropic moment tensors are a 5-D linear subspace and normalized moment tensors are unit vectors, or points on a unit sphere. Distance along a great circle of the unit sphere satisfies reasonable requirements for any measure of the difference between normalized moment tensors. In regions with a few isolated sets of orientations, cluster analysis based on the great circle distance identifies the same groups of earthquakes that a seismologist would. Figures based on principal component analysis and discriminant analysis illustrate orientation clustering better than equal area projections of moment tensor principal axes. In one case where clusters have been claimed to exist, orientations appear to be continuously distributed and no evidence is found for separate populations of moment tensors.     

呼伦贝尔沙地沙丘砂来源的定量分析— 逐步判别分析(SDA)在粒度分析方面的应用

以呼伦贝尔沙地砂物质的粒度分析资料为基础,利用两组间的逐步判别分析(SDA) 来筛选决定不同沉积物间差异的主导因子,根据主导因子的个数、Mahalanobis距离D2、通过统计学检验的信度琢等3个因素,来定量地确定两个总体间的相似性大小。分析结果表明:呼伦贝尔沙地的风成沙丘砂主要来源于海拉尔组砂(Q3),但河流冲积砂和古土壤也有不可忽视的作用;在嵯岗镇附近及其以西的海拉尔河下游宽阔河谷中,自然条件下河流冲积砂也可以成为风成沙丘砂的主要沙源。     

呼伦贝尔沙地沙丘砂来源的定量分析--逐步判别分析(SDA)在粒度分析方面的应用

Quantltatively determining the sources of dune sand uis one of the problems necessarily and urgently to be solved in aeolian landforms and desertification research. Based on the granulometric data of sand materials from the Hulun Buir Sandy Land, the paper employs the stepwise discriminant analysis technique (SDA) for two groups to select the principal factors determining the differences between surface loose sediments. The extent of similarity between two statistical populations can be described quantitatively by three factors such as the number of principal variables, Mahalanobis distance D^2 and confidence level α for F-test. Results reveal that: 1) Aeolian dune sand in the region mainly derives from Hailar Formation (Q3), while fluvial sand and palaeosol also supply partially source sand for dunes; and 2) in the vicinity of Cuogang Town and west of the broad valley of the lower reaches of Hailar River, fluvial sand can naturally become principal supplier for dune sand.     

METHODOLOGY: DISCRIMINANT FUNCTION ANALYSIS OF COMPOSITIONAL DATA: AN EXAMPLE FROM HYDRAULIC GEOMETRY

Many of the data sets analyzed by physical geographers are compositional in nature: they have row vectors that add to one (or 100%). These unit-sum constrained data sets should not be analyzed by standard multivariate statistical methods. Significant differences were found in the log-ratio mean vectors of the hydraulic exponents (which are unit-sum constrained) for two classes of streams: those with cohesive, non-vertical banks, and those with one firm and one loose bank. Compositional discriminant function analysis of bank stability on the basis of hydraulic geometry had a success rate of 88%, making routinely archived measurements of stream width, cross-sectional area, mean velocity, and discharge a readily available data base for predicting the stability of stream reaches. [Key words: geomorphology, hydraulic geometry, discriminant function, statistics.]     

荒漠-过渡带-绿洲界定——以石羊河流域为例

中国西北干旱区发源于山地的河流为中下游地区带来了丰富的水土资源,在荒漠中孕育出绿洲,过渡带位于其间,构成荒漠-过渡带-绿洲地理景观单元。界定荒漠、过渡带、绿洲的空间分布,可为干旱区生态系统格局、过程和服务方面的精确认知评价提供空间参考。以石羊河流域为例,选取训练样本,利用常用遥感指标和景观格局指数,通过判别分析方法,对荒漠、过渡带和绿洲空间范围进行界定。结果表明:采用通过逐步判别分析筛选出的6项遥感指标和2项景观指数构建的判别函数,与单独利用遥感指标或景观指数构建的判别函数,计算出训练样本的判别准确率分别为92.4%、84.0%、70.2%。采用遥感指标结合景观指数的综合判别分析,比单独利用遥感指标或景观指数判别准确率分别提高了8.4%\,22.2%。经综合指标判别分析,得出除主要山地外的石羊河流域荒漠、过渡带和绿洲面积分别为133万、49万、58万hm²。     

主成分分析方法在区域经济研究中的应用--以新疆为例

主成分分析方法（PCA）及采用此法做综合评价的原理和步骤，并用两个方面的实例具体阐述了主成分分析方法在区域经济研究中的应用，最后对这种方法的特点及应用中须注意的问题进行了初步总结。     

STANDARD ERRORS IN THE EIGENVALUES OF A CROSS-PRODUCT MATRIX:THEORY AND APPLICATIONS

New expressions are derived for the standard errors in the eigenvalues of a cross-product matrix by themethod of error propagation.Cross-product matrices frequently arise in multivariate data analysis,especially in principal component analysis (PCA).The derived standard errors account for the variabilityin the data as a result of measurement noise and are therefore essentially different from the standarderrors developed in multivariate statistics.Those standard errors were derived in order to account for thefinite number of observations on a fixed number of variables,the so-called sampling error.They can beused for making inferences about the population eigenvalues.Making inferences about the populationeigenvalues is often not the purposes of PCA in physical sciences,This is particularly true if themeasurements are performed on an analytical instrument that produces two-dimensional arrays for onechemical sample:the rows and columns of such a data matrix cannot be identified with observations onvariables at all.However,PCA can still be used as a general data reduction technique,but now the effectof measurement noise on the standard errors in the eigenvalues has to be considered.The consequencesfor significance testing of the eigenvalues as well as the usefulness for error estimates for scores andloadings of PCA,multiple linear regression (MLR) and the generalized rank annihilation method(GRAM) are discussed.The adequacy of the derived expressions is tested by Monte Carlo simulations.     

CLASSIFICATION:OLDTIMERS AND NEWCOMERS

Classification and regression techniques are among the most used tools by chemometricians.Withclassification,the two classic methods are discriminant analysis and SIMCA.In this paper we discuss theconnection between these two methods and introduce two new ones of the same family:DASCO(discriminantanalysis with shrunken covariances)and RDA(regularized discriminant analysis).We demonstrate on bothsimulated and real data sets that their performance is superior to the old favorites.This is especially truein small-sample/high-dimension settings typical in chemistry.     

Discriminant analysis of the geomorphic characteristics and stability of landslide dams

Landslides can cause the formation of dams, but these dams often fail soon after lake formation. Thus, rapidly evaluating the stability of a landslide dam is crucial for effective hazard mitigation. This study utilizes discriminant analysis based on a Japanese dataset consisting of 43 well documented landslide dams to determine the significant variables, including log-transformed peak flow (or catchment area), and log-transformed dam height, width and length in hierarchical order, which affect the stability of a landslide dam. The high overall prediction power (88.4% of the 43 training cases are correctly classified) and the high cross-validation accuracy (86%) demonstrate the robustness of the proposed discriminant models PHWL (with variables including log-transformed peak flow, and log-transformed dam height, width and length) and AHWL (with variables including log-transformed catchment area, and log-transformed dam height, width and length). Compared to a previously proposed “DBI” index-based graphic approach, the discriminant model AHV – which uses the log-transformed catchment area, dam height, and dam volume as relevant variables – shows better ability to evaluate the stability of landslide dams. Although these discriminant models are established using a Japanese dataset only, the present multivariate statistical approach can be applied for an expanded dataset without any difficulty when more completely documented worldwide landslide-dam data are available.     

三江平原沼泽的生态分类

本文根据生态学原则,采用主成分、聚类制别分析相结合的方法,对三江平原沼泽进行生态分类。将该区沼泽划分为二个沼泽类、四个沼泽亚类和八个沼泽体。并给出了衡量沼泽类型之间差异的数量尺度和对未知类型归类的判别数学模型,并论证了沼泽生态分类应采用的重要指标。     

主成分分析法在新疆兵团经济可持续发展能力评价中的应用

采用多元统计主成分分析方法对新疆兵团13个师1991～2006年的各师农场职工家庭人均纯收入、人均农业增加值、人均工业增加值、人均第二产业增加值、人均GDP等11个经济指标进行分析计算并且对各师的综合经济可持续能力进行比较。结果表明：从原始数据中提出占总方差86．6％的4个因子来反映各师的经济可持续发展程度,经分析发现影响各师的4个主成分因子：（1）人均GDP、人均工业增加值（包括第二产业、第三产业的增加值）的因子控制;（2）人均新增固定资产、人均固定资产投资等反映人均资产投入的综合指标;（3）反映人均耕地面积、人均利润、人均社会消费品零售总额的综合指标。（4）反映人均农业增加值、人均固定资产投入及人均社会消费品零售总额的综合指标。然后将各主成分得分结合主成分权重进行计算得出各师经济可持续能力值,其中农一师排在第一。从总体上看1992～2006年各师经济可持续发展的综合指标趋势是逐渐上升的,发展具有可持续性。,     

An approach to differentiate informal settlements using spectral,texture, geomorphology and road accessibility metrics

This research distinguishes informal from formal neighborhoods in developing countries by analyzing shape (form), terrain geomorphology, texture, road networks and dominant settlement materials (vegetation, soil, asphalt) to produce a multivariate, spatially explicit evaluation of settlement structure. The principal datasets require only high resolution imagery and elevation data which are both widely available. Ancillary data, field surveys, and dwelling outlines, which are difficult to obtain from developing countries in general, are not required. Twenty-four variables derived from a review of informal settlement and suburban sprawl research describing settlement characteristics were identified and tested for significance. From both discriminant function analysis and regression trees, seven variables were identified to be significant in distinguishing informal and formal settlements using data from Guatemala. Results show promise in using limited data to identify informal settlements in Latin American countries or other less developed nations.     

Comparing models of debris-flow susceptibility in the alpine environment

Debris-flows are widespread in Val di Fassa (Trento Province, Eastern Italian Alps) where they constitute one of the most dangerous gravity-induced surface processes. From a large set of environmental characteristics and a detailed inventory of debris flows, we developed five models to predict location of debris-flow source areas. The models differ in approach (statistical vs. physically-based) and type of terrain unit of reference (slope unit vs. grid cell). In the statistical models, a mix of several environmental factors classified areas with different debris-flow susceptibility; however, the factors that exert a strong discriminant power reduce to conditions of high slope-gradient, pasture or no vegetation cover, availability of detrital material, and active erosional processes. Since slope and land use are also used in the physically-based approach, all model results are largely controlled by the same leading variables.Overlaying susceptibility maps produced by the different methods (statistical vs. physically-based) for the same terrain unit of reference (grid cell) reveals a large difference, nearly 25% spatial mismatch. The spatial discrepancy exceeds 30% for susceptibility maps generated by the same method (discriminant analysis) but different terrain units (slope unit vs. grid cell). The size of the terrain unit also led to different susceptibility maps (almost 20% spatial mismatch). Maps based on different statistical tools (discriminant analysis vs. logistic regression) differed least (less than 10%). Hence, method and terrain unit proved to be equally important in mapping susceptibility.Model performance was evaluated from the percentages of terrain units that each model correctly classifies, the number of debris-flow falling within the area classified as unstable by each model, and through the metric of ROC curves. Although all techniques implemented yielded results essentially comparable; the discriminant model based on the partition of the study area into small slope units may constitute the most suitable approach to regional debris-flow assessment in the Alpine environment.     

地理环境因子对肌酸激酶同工酶参考值的影响

研究目的旨在探讨三种常用的变量筛选回归方法对中国健康成年人肌酸激酶同工酶（CK-MB）参考值在地理空间上的分布规律特征,应用于制定不同地区CK-MB参考值标准,为临床医学研究做出贡献。方法通过阅读大量文献搜集全国137个市县级单位共8697例健康成年人CK-MB参考值,并选择了地理位置、气候、土壤三大类共24项地理因子。使用相关分析方法检验CK-MB参考值和地理因子之间的显著性,提取到9项相关性地理因子。基于R语言评估模型多重共线性的严重程度,建立CK-MB参考值岭回归（Ridge）模型、拉索回归（Lasso）模型、主成分分析模型。对比得到最优预测模型,拟合全国2322个市县级单位健康成年人CK-MB预测参考值,再结合地统计分析,运用析取克里金法进行趋势分析,得到CK-MB预测参考值地理分布规律特征。结果表明全国2322个市县级单位的健康成年人CK-MB参考值具有空间自相关性,模型测试表明,主成分分析法具有更好的模拟和预测能力。研究表明健康成年人CK-MB参考值分别与纬度、年日照时数、年平均相对湿度、年降水量、气温年较差、年平均气温、表土石砾含量、表土（粘土）阳离子交换量、表土（粉土）阳离子交换量具有显著的相关性。由地理空间分布图显示,整体上呈北高南低,从东南沿海向西北内陆逐渐升高的趋势。通过搜集到的任一地区地理因子,结合主成分分析预测模型或已得的地理分布图可确定该地区健康人CK-MB参考值范围,为在临床诊断中考虑地域差异提供参考。     

An automated approach to the classification of the slope units using digital data

Digital elevation and remote sensing data sets contain different, yet complementary, information related to geomorphological features. Digital elevation models (DEMs) represent the topography, or land form, whereas remote sensing data record the reflectance/emittance, or spectral, characteristics of surfaces. Computer analysis of integrated digital data sets can be exploited for geomorphological classification using automated methods developed in the remote sensing community. In the present study, geomorphological classification in a moderate- to high-relief area dominated by slope processes in southwest Yukon Territory, Canada, is performed with a combined set of geomorphometric and spectral variables in a linear discriminant analysis. An automated method was developed to find the boundaries of geomorphological objects and to extract the objects as groups of aggregated pixels. The geomorphological objects selected are slope units, with the boundaries being breaks of slope on two-dimensional downslope profiles. Each slope unit is described by variables summarizing the shape, topographic, and spectral characteristics of the aggregated group of pixels. Overall discrimination accuracy of 90% is achieved for the aggregated slope units in ten classes.     

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.     

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。