Discriminant Variables

Several fundamental properties of discriminant variables are developed. In addition, the proportionality of the discriminant variables, canonical variables and RAO principal components is demonstrated.     

New Procedure for Selection of Variables in Location Model for Mixed Variable Discrimination

A new method for the choice of variables with the greatest discriminatory power in the location model for mixed variable discriminant analysis is presented in the paper. The procedure based on the multivariate discriminatory measure enables a simultaneous reduction of the number of discrete and continuous variables. The introduced criterion can be used for both optimal or step-wise selection of variable subset. As an example the results of the stepwise variable selection for some medical data are presented in the paper.     

On the Use of Various Methods of Discriminant Analysis

The use of discriminant analysis for normal distributed populations with common or differing variances, and for populations with distributions of unknown type is discussed and illustrated by an example. Existing programs are mentioned. The results of the various methods of discriminant analysis are compared with each other.     

Application of Discriminant Analysis to the Family Planning Data

The main strategy of family planning program in many over populated countries like India, China etc. is to bring down fertility by propagating various family planning devices like Tubectomy, IUD, Vasectomy, conventional contraceptives etc. Data was collected on various socio-economic and demographic characteristics of the users of these devices. Based on it we have developed a discriminant function for these devices using the methodology given by Kumar (1983).     

Discriminant Analysis of Biological Shape Profile for Hybridization

Role of hybridization on growth, nomenclature, speciation, genetics and wildlife management is widely recognised. New situations of hybridization are being discovered and studied yearly (SHORT, 1965). Changes of size make changes of shape and proportions necessary (AlEXANDER, 1971) and for constant efficiency of many body functions (e.g., the locomotory, respiratory and the digestive) systematic size-correlated alteration of physical shape is an adaptive necessity for many organic relationships (GOULD, 1966). Need for analysing shape for hybridization is therefore obvious. Often an objective of studying hybridization is to estimate the degree of suspected hybrids and thereby specify the distribution of the hybrids in relation to the two parental species, A study of hybridization must recognise the effects of the additive genetic (A) as well as the nonadditive genetic sources (see, e.g., MISRA, 1975a). Discriminant analysis offers a powerful tool for studies of hybrid zones or zones of abrupt phenetic transition, as it is based on the maximisation of differences between biologically meaningful reference samples (ROHWER, 1972). This paper presents a discriminant analysis of biological shape profiles for hybridization based on A and NA sources.     

Some Further Remarks on Robust Selection of Variables in Discriminant Analysis

A robust method of selecting variables with the greatest discriminatory power is presented in the paper. It is based on the robustified Wilks A statistic and can be applied in a multi-group discrimination problem. An application to some respiratory disease data together with a comparison of the classical procedure is also given.     

Using Adaptive Methods to Select Variables in Case‐Control Studies

A variables selection method for case‐control studies is proposed that uses an adaptive weighting scheme along with a permutation method to determine if a variable is useful in differentiating the cases from the controls. This adaptive method is used to select exposure variables for the analysis of data from a bladder cancer case‐control study. An extensive simulation study shows that the adaptive method is nearly as effective at finding those variables that are related to case‐control status when normally distributed variables are used. The simulation also shows that the proposed variable selection procedure is much more effective than the stepwise discriminant analysis method when the variables are not normally distributed. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effect of Sample Design in the Discriminant Analysis for Two Groups

This paper shows the effect of sample design on the Discriminant Analysis for two groups by means of a simulation study involving stratified design. Four criteria of discrimination are used and compared. Also, the equivalency between the Multiple Linear Regression using the Generalized Estimating Equations and the Discriminant Analysis for two normal populations from a Complex Design is proved. The results are applied to an epidemiological problem.     

Variable Selection in Canonical Discriminant Analysis for Family Studies

Summary In family studies, canonical discriminant analysis can be used to find linear combinations of phenotypes that exhibit high ratios of between‐family to within‐family variabilities. But with large numbers of phenotypes, canonical discriminant analysis may overfit. To estimate the predicted ratios associated with the coefficients obtained from canonical discriminant analysis, two methods are developed; one is based on bias correction and the other based on cross‐validation. Because the cross‐validation is computationally intensive, an approximation to the cross‐validation is also developed. Furthermore, these methods can be applied to perform variable selection in canonical discriminant analysis. The proposed methods are illustrated with simulation studies and applications to two real examples.     

基于SOFM神经网络与判别分析的肝硬化识别方法的研究

将SOFM神经网络与医师诊断相结合对腹部MRI进行样本分类，并利用判别分析方法对肝硬化进行图像识别．应用此方法对随机抽取的40枚腹部MRI图像进行处理，以7．5％的误判率结果说明了本方法的有效性．     

Goodness of Fit of Discriminant Functions from the Vector Space of Fixed Variates

Alternative proofs of some of KSHIRSAGAR's (1971) results on testing discriminant functions or canonical variables in the vector space of fixed variates are given. These results are derived in terms of the original variates unlike KSHIRSAGAR (1971) who derives the results by using random orthogonal transformations and triangular decompositions of the original matrix variates.     

On Estimating Missing Values in Linear Discriminant Analysis – Part I

The application of discriminant analysis like other multivariate procedures is essentially complicated with incomplete data. Therefore several methods for handling missing observations occuring in initial samples were compared with each other. Recommendations are given for selecting a suitable method depending on underlying parameters.     

Linear Discriminant Functions and Problems of Hybridization

A discriminant analysis method for frequency data for hybridization based on weighted multivariate analysis of variance is given for allotting an individual to one of groups.     

一种基于特征筛选的原核生物启动子判别分析方法

启动子识别是研究基因转录调控的重要环节,但目前方法的识别正确率偏低。在深入分析原核启动子特征的基础上,提出了一种基于特征筛选的原核启动子判别分析方法,首先在启动子序列的组成特征、信号特征和结构特征中选取备选特征,为每个特征建立适当的描述模型,并对主要的保守模式采用复合模式模型;再通过模型计算对备选特征进行逐步筛选,优化特征集,将序列表示为组合特征向量;最终利用二次判别分析实现识别。对大肠杆菌和枯草杆菌实际启动子数据进行的刀切法测试验证了方法的有效性和通用性。对于大肠杆菌非编码区(70启动子,识别的平均正确率达到了85.8%,优于其它几种典型识别方法;对于大肠杆菌编码区内部)70启动子和其它几种原核启动子,平均正确率也都超过了80%。方法框架还具有良好的可扩展性,能够方便地容纳新特征,使识别性能不断提高。     

鳓形态指标体系分析及雌雄鉴别模型

对鳓的形态指标体系进行了主成分分析和R-聚类分析．鳓的形态指标大体可归纳为“大小因子”、“形态因子”和“头型因子”;关于“肥瘦”方面、“长度”方面和“头部”的指标各自的相关较为密切,而这三类指标间的相关较小．在此分析基础上,构建了48个相对指标,并用逐步判别建立了雌雄判别模型,此模型回判的错判率为8．9％．     

Nearest Neighbor Classification Rule for Mixtures of Discrete and Continuous Random Variables

In this paper very simple nonparametric classification rule for mixtures of discrete and continuous random variables is described. It is based on the method of nearest neighbor proposed by Cover and Hart (1967). The bounds on the limit of the nearest neighbor rule risks are given. Both lower and upper bound depend on the Bayes risk and the loss function. Finally the method is compared with other existing methods on some practical data set.     

Optimal Representation of Supplementary Variables in Biplots from Principal Component Analysis and Correspondence Analysis

This paper treats the topic of representing supplementary variables in biplots obtained by principal component analysis (PCA) and correspondence analysis (CA). We follow a geometrical approach where we minimize errors that are obtained when the scores of the PCA or CA solution are projected onto a vector that represents a supplementary variable. This paper shows that optimal directions for supplementary variables can be found by solving a regression problem, and justifies that earlier formulae from Gabriel are optimal in the least squares sense. We derive new results regarding the geometrical properties, goodness of fit statistics and the interpretation of supplementary variables. It is shown that supplementary variables can be represented by plotting their correlation coefficients with the axes of the biplot only when the proper type of scaling is used. We discuss supplementary variables in an ecological context and give illustrations with data from an environmental monitoring survey.     

Application of Discriminant Analysis in Distinguishing Plant Photosynthetic Types-A Case Study in Northeast China Transect (NECT) Area

Discriminant analysis is an important method in multivariate statistic analysis to distinguish whatever type an individual should belong to. Based on the field actual photosynthetic data obtained from the research platform--Northeast China Transect (NECT), the concept and principle of discriminant analysis were used to distinguish the different plant photosynthetic types. A number of indices related to plant photosynthetic rate measured by a LCA4 photosynthesis system were selected to build the discriminant model. In this case study, 15 plant species from C4 plant functional groups and 51 from C3 plant functional groups were selected to build a discriminant model. The rate of accuracy, of returned classification using methods of squared Mahalanobis distances from group centroids and posterior probabilities, reached to 98.48 %. With the help of this model, any plants' photosynthetic types could be distinguished simply by using their four related parameters, viz., photosynthetic rate, transpiration, stomatal conductance and the temperature difference between leaf surface and atmosphere.