Using geovisual analytics to compare the performance of geographically weighted discriminant analysis versus its global counterpart,linear discriminant analysis

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.     

Evaluation and comparison of landslide susceptibility mapping methods: a case study for the Ulus district,Bartın,northern Turkey

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.     

逐步判别分析法在筛选泥石流评价因子中的应用

运用逐步判别分析原理,在多个评价因子中按其对泥石流沟判别能力贡献的大小进行筛选,从而确定泥石流沟的评价因子。应用改进的层次分析法对筛选后的评价因子进行赋权,使求得的判断矩阵满足一致性要求,避免了层次分析法后期检验过程中多次调整判断矩阵带来的过于主观性的问题。在评价因子的筛选和赋权的基础上进行了单沟泥石流危险度评价的实例验证,结果表明,运用逐步判别分析法筛选后的评价因子客观、准确地反映了当地泥石流危险度的影响因素,与传统方法所得危险度结果相比更符合泥石流危险度实际情况,可靠性更强。     

基于逐步判别分析的砂土液化预测研究

为高效地进行砂土液化的预测,运用逐步判别法,从8个液化影响因子中选择平均粒径、烈度、震中距等3个判别能力显著的影响因子,建立判别函数,并利用工程实例进行验证。研究结果表明：逐步判别分析模型预测性能良好,且能有效地选择对砂土液化起主导作用的因子。相比距离判别分析,逐步判别分析建立的判别函数更加稳定,且所需测试因子较少,节省了因试验和现场调查所耗费的大量人力、物力和时间,因此逐步判别分析是一种值得推广的砂土液化预测方法。     

临涣矿区突水水源标型微量元素及其判别模型

利用示踪不同含水层水文地球化学特征的标型微量元素捕捉突水预兆期内的水文地球化学信息,建立判别模型分析煤矿重大突水水源,具有重要的理论与实践意义。本课题利用任楼井田及所在临涣矿区其他生产矿井的长观孔、矿井出水点从上而下分别取第四系第四含水层、二叠系煤系砂岩含水层、石炭系太原组岩溶含水层及奥陶系岩溶含水层24个水样,测试了24种微量元素含量。通过分析4类主要突水含水层微量元素含量与聚类规律,得到了Be、Zn、Ga、Sr、U、Zr、Cs、Ba8种主要突水含水层的标型微量元素,建立了以标型微量元素作为解释变量的突水水源Bayes线性判别模型。以24个水样为训练样本,得到模型判别正确率达到了80%,并分析了区域水循环与水文地球化学演化对判别模型效果具有一定程度的控制作用。     

矿井涌水水源判别的GRA-SDA耦合模型

选取矿井涌水水源判别中常用的灰色关联分析和逐步判别分析作为基础模型,分析了两者的优缺点及单独使用中存在的问题,提出耦合判别思路,设计了GRA-SDA耦合式水源判别模型。利用某矿区实际样本数据,选取Na++K+、Ca2+、Mg2+、Cl-、SO42-、HCO3-共6组离子以及矿化度作为判别因子,对该模型进行实例验证。分析表明,该模型判别结果与实际情况吻合较好,与单独使用一种分析方法相比较,有效地提高了水源判别正确率。     

Sediment distribution patterns and related depositional environments in the Atchafalaya Bay,Louisiana

Abstract

Three sets of bottom sediment samples, totalling 563, were collected in the Atchafalaya Bay, Louisiana. Cluster analysis was applied to each set of data based on grain‐size distribution. Comparison between resulting clusters and depositional environments indicates that the results of cluster analysis are sedimentologically meaningful and environmentally significant. A follow‐up discriminant analysis shows the stability of the classification system. The system then, in turn, can be used to classify sediments from unknown sources in the study area.     

矿井底板破碎带温度场模型推导及模拟分析

为了研究矿井底板破碎带温度场对地下水的响应机制,运用热传导理论,结合数学物理方法,建立了垂向水流作用下岩体温度场模型和地下水、空气等多热源作用下岩体过余温度分布模型,并求出了相应模型的温度、温度梯度及过余温度解析解。结果表明：沿着地下水径流方向,起始段的岩体温度梯度值一般较小,而终止段的温度梯度值则一般较大;当温度梯度与地下水流动方向相反时,岩体温度梯度变化幅度较小;回采工作面接近含导水构造时,距离导水构造越近,同一时刻岩体过余温度增大越迅速,体现在温度曲线的曲率相应增大。在一定范围内,地下水对矿井岩体温度梯度及过余温度影响显著。     

竹亚科植硅体形态学研究及其生态学意义

选择我国常见的竹亚科19属64种进行系统的植硅体形态学研究,对竹亚科特有的长鞍型植硅体的长度、宽度、高度(侧面宽)和硅质颗粒数目等参数进行了测量。研究发现,合轴散生竹长鞍型植硅体个体最大(长度20.6±0.2m,宽度12.8±0.5m,高度12.4±0.1m,颗粒数2.8±0.5),单轴散生竹次之(长度18.8±0.8m,宽度11.7±0.4m,高度11.8±0.3m,颗粒数1.9±0.1),复轴混生竹再次(长度18.3±1.5m,宽度11.2±1.5m,高度11.4±1.7m,颗粒数1.8±0.4),合轴丛生竹最小(长度18.0±1.8m,宽度9.7±0.5m,侧面宽10.1±1.4m,颗粒数2.6±0.3)。经判别分析显示以长鞍型植硅体三维形态参数和硅质颗粒数目为变量可以区分竹亚科植物各生态型,并初步明确了长鞍型植硅体形态与竹亚科生态型的对应关系,探讨了其与竹亚科植物生境条件之间的对应关系,以及在竹亚科植物演化序列中的意义,为利用竹亚科长鞍型植硅体形态进行古环境分析提供了基础性资料。