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1.
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. 相似文献
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Peter Foley 《International journal of geographical information science》2013,27(4):633-661
Geographically weighted spatial statistical methods are a family of spatial statistical methods developed to address the presence of non-stationarity in geographical processes, the so-called spatial heterogeneity. While these methods have recently become popular for analysis of spatial data, one of their characteristics is that they produce outputs that in themselves form complex multi-dimensional spatial data sets. Interpretation of these outputs is therefore not easy, but is of high importance, since spatial and non-spatial patterns in the results of these methods contain clues to causes of underlying non-stationarity. In this article, we focus on one of the geographically weighted methods, the geographically weighted discriminant analysis (GWDA), which is a method for prediction and analysis of categorical spatial data. It is an extension of linear discriminant analysis (LDA) that allows the relationship between the predictor variables and the categories to vary spatially. This produces a very complex data set of GWDA results, which include on top of the already complex discriminant analysis outputs (e.g. classifications and posterior probabilities) also spatially varying outputs (e.g. classification function parameters). In this article, we suggest using geovisual analytics to visualise results from LDA and GWDA to facilitate comparison between the global and local method results. For this, we develop a bespoke visual methodology that allows us to examine the performance of global and local classification method in terms of quality of classification. Furthermore, we are also interested in identifying the presence (or absence) of non-stationarity through comparison of the outputs of both methods. We do this in two ways. First, we visually explore spatial autocorrelation in both LDA and GWDA misclassifications. Second, we focus on relationships between the classification result and the independent variables and how they vary over space. We describe our visual analytic system for exploration of LDA and GWDA outputs and demonstrate our approach on a case study using a data set linking election results with a selection of socio-economic variables. 相似文献
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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.] 相似文献
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Regularized discriminant analysis has proven to be a most effective classifier for problems wheretraditional classifiers fail because of a lack of sufficient training samples,as is often the case in high-dimensional settings.However,it has been shown that the model selection procedure of regularizeddiscriminant analysis,determining the degree of regularization,has some deficiencies associated with it.We propose a modified model selection procedure based on a new appreciation function.By means ofan extensive simulation it was shown that the new model selection procedure performs better than theoriginal one.We also propose that one of the control parameters of regularized discriminant analysis beallowed to take on negative values.This extension leads to an improved performance in certain situations.The results are confirmed using two chemical data sets. 相似文献
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《Urban geography》2013,34(1):49-67
This study examines one gentrifying neighborhood, Ohio City, in Cleveland, Ohio. It utilizes block group-level data and discriminant analysis to identify key variables associated with the gentrification process. Two discriminant functions resulted from the analysis. One function is highly associated with the percentage of college-educated residents and the other associated with a high proportion of white population, aged 25 to 40, with high median incomes. The discriminant power accounted for by the two discriminant functions is 89%. The results of this study argue for increased use of block group data to examine gentrification, since these data allow more accurate analysis of gentrification borders, neighborhood change, and gentrification modeling. 相似文献
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Arif Mert Eker Mehmet Dikmen Selim Cambazoğlu Şebnem H.B. Düzgün 《International journal of geographical information science》2013,27(1):132-158
The purpose of this study was to investigate the capabilities of different landslide susceptibility methods by comparing their results statistically and spatially to select the best method that portrays the susceptibility zones for the Ulus district of the Bart?n province (northern Turkey). Susceptibility maps based on spatial regression (SR), linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), logistic regression (LR) method, and artificial neural network method (ANN) were generated, and the effect of each geomorphological parameter was determined. The landslide inventory map digitized from previous studies was used as a base map for landslide occurrence. All of the analyses were implemented with respect to landslides classified as rotational, active, and deeper than 5 m. Three different sets of data were used to produce nine explanatory variables (layers). The study area was divided into grids of 90 m × 90 m, and the ‘seed cell’ technique was applied to obtain statistically balanced population distribution over landslide inventory area. The constructed dataset was divided into two datasets as training and test. The initial assessment consisted of multicollinearity of explanatory variables. Empirical information entropy analysis was implemented to quantify the spatial distribution of the outcomes of these methods. Results of the analyses were validated by using success rate curve (SRC) and prediction rate curve (PRC) methods. Additionally, statistical and spatial comparisons of the results were performed to determine the most suitable susceptibility zonation method in this large-scale study area. In accordance with all these comparisons, it is concluded that ANN was the best method to represent landslide susceptibility throughout the study area with an acceptable processing time. 相似文献
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基于人格特质这一视角,结合旅游消费者购买决策程序理论,探讨和研究城市居民的出游行为偏好。首先,运用5因素人格特质量表测量了武汉市居民的人格特质,在此基础上运用聚类分析和判别分析,将潜在旅游者细分成不同人格特质类型的人群,其次,运用卡方检验、交叉分析等方法具体分析了不同人格类型的武汉市居民在出游行为偏好上的差异性,得出的研究结论是:基于人格特质这一心理变量,可以把武汉市居民细分成外向随和型、严谨含蓄型、开放时尚型3种不同人格类型的人群;不同人格类型的潜在旅游消费者在出游行为偏好上也具有一定的差异性。 相似文献
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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. 相似文献
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荒漠-过渡带-绿洲界定——以石羊河流域为例 总被引：1，自引：1，他引：0
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。 相似文献
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ZHAONIAN CHENG ERYI ZHU NIANYI CHEN Shanghai Institute of Metallurgy Academia Sini Shanghai China 《地理学报(英文版)》1993,(4)
In this paper we discuss the orthogonal expansion of data matrices and its application to mapping andmodelling. Two new methods, modified optimal discriminant plane (MODP) for mapping and orderGram-Schmidt orthogonalization (OGSO) for modelling, are proposed and examples are given. 相似文献
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Owen J. Furuseth 《The Professional geographer》1985,37(4):443-451
County-level policies and programs to conserve farmland in California are examined through discriminant analysis. Based on 1981 state planning data, four degrees of farmland protection effort are established. A two-function discriminant analysis using 17 agricultural, socioeconomic, and political-ideological variables correctly predicts the fourfold classification of 88 percent of the counties. The propensity to enact protective actions is associated with the intensity of agricultural development, local government spending and taxing practices, demographic characteristics, ideological and political party voting traditions. 相似文献
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Cluster analysis of seismic moment tensor orientations 总被引：1，自引：0，他引：1
Raymond J. Willemann 《Geophysical Journal International》1993,115(3):617-634
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. 相似文献
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Onuoha Iheanyichukwu Joachim Norhaya Kamarudin Godwin Uche Aliagha Miswan Abdul Hakim Mohammed Hishmuddin Mohd Ali 《Geographical review》2017,107(3):496-515
The aim of this study is to identify the predictive factors and variables that motivate decisions to supply sustainable or green commercial properties, and to apply discriminant analysis technique to assess if there are significant differences in perception between real estate developers in Malaysia and Nigeria based on the identified variables. The result revealed a significant discriminant function differentiating the two countries based on their perception of the variables. The motivational components and attributes were found to be in favor of Malaysia. The Wilks' lambda F‐test and the standardized discriminant function coefficients, showed that there were significant differences between developers in both countries as assessed by the life‐cycle cost motivations, green policies and certification, market strategy, developers expected rate of return, green tax incentive, and available green skills. However, the variables with the most predictive power in accounting for the differences were found to be within the measures of life‐cycle, cost‐saving motivations. 相似文献
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自然界中沉积物的组成和成因具有多样性。应用粒度方法可以区分、提取和判别沉积物中的各个组分。粒度方法主要有频率曲线和累积曲线分布法、数学函数组分提取法(包括Weibull分布函数拟合法、端元模型分析法、标准偏差法、粒度分维法等)和粒度参数判别公式法。综合应用上述方法可有效地判别出单一沉积物的物质来源或者复杂沉积物中的各个组分,而这些方法被前人广泛地应用于湖泊研究中,提取了过去的环境变化信息,也指导了作者在盐湖沉积中的研究工作。 相似文献
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《Urban geography》2013,34(3):246-257
This study identifies generational divisions among urban areas, investigates traditional regional divisions of Frostbelt/Sunbelt, and formally tests whether these divisions can be identified using contemporary socioeconomic variables. Contemporary urban areas are influenced by initial technological and cultural patterns. Cities formed in the 19th century are different than those formed in the 20th century. Urban generations, therefore, are defined as periods in history when particular urban areas first experienced substantial growth. Technological and cultural patterns also vary from region to region. The urban areas, therefore, also are classified regionally based on Gober's (1984) definition of Frostbelt and Sunbelt. The various classifications are all examined using analysis of covariance and discriminant analysis. The analysis of covariance demonstrates that generation and region significantly affected the study variables individually. In turn, the results of the discriminant analysis demonstrate that it is possible to discriminate generationally and regionally based on the study variables as a group. 相似文献
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An application of polynomial curve fitting to sediment cumulative frequency distributions is presented to delineate the foreshore depositional patterns along the barrier beaches of the Rhode Island southshore. The analysis is based on 92 sampled stations where data for beach geometry, tidal stage, and sediment size were collected. Using the size-frequency classes obtained from sieving the foreshore sediment samples at 0.25 O intervals and fitting third-degree polynomial equations to these data, over 94% of the variation within the sediment cumulative frequency distributions is explained. The four curve coefficients (a, b, c, d) derived from the predicted third-degree equation are used in a discriminant function analysis to test the relationship between the curve shape and sediment source. Comparison of the discriminant scores with the respective station locations suggests that a series of Pleistocene headlands which occur as discrete points along the beach are serving as independent sources of sediment for the system. 相似文献
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Discriminant analysis of the geomorphic characteristics and stability of landslide dams 总被引：1，自引：0，他引：1
Jia-Jyun Dong Yu-Hsiang Tung Chien-Chih Chen Jyh-Jong Liao Yii-Wen Pan 《Geomorphology》2009,110(3-4):162-171
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. 相似文献
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DOMINIQUE BERTRAND PHILIPPE COURCOUX JEAN-CLAUDE AUTRAN REGIS MERITAN PAUL ROBERT 《地理学报(英文版)》1990,(6)
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. 相似文献