概率神经网络在判别分析中的比较优势

判别分析是多元统计分析的三大支柱之一。传统的判别分析方法,如距离判别法、贝叶斯判别法、费希尔判别法等在判别分析中误判率较高,因此有必要引入概率神经网络(PNN)进行判别分析。文章对传统判别方法的基本思想与假设条件及PNN的建模机制与判别原理进行了介绍;用两个案例比较了常用判别分析与PNN判别分析的效率。     

使用评估模型的判别分析

一、回归与判别分析 所谓判别分析,就是要判别一个样品究竞属于哪一类比较合适.这样做的前提是对总体已有一个分类.为了对总体分类,一般应该有训练样本,它的分类和统计指标都是已知的,然后从训练样本计算出判别规则,再根据判别规则去判别那个样品究竟属于哪一类.判别分析主要方法有距离判别、Bayes判别、Fisher判别等.     

SPSS中判别分析方法的正确使用

判别分析是多元统计中判别样品所属类型的一种常用方法.它的研究对象是训练样本,也就是说原始数据的具体分类是事先已知的,然后根据原始数据求出判别函数,将待判样本的数据代入判别函数中,判断其类型.常用的判别分析方法主要有:距离判别、Fisher判别、Bayes判别、逐步判别.在SPSS中直接给出了Fisher和Bayes两种方法的判别,但是SPSS对于这两种判别方式的命名和我们一般教科书里的命名不尽相同,再加之这两种方法本身的复杂性,使用起来要特别小心.     

基于球极投影变换核估计Bayes判别方法的上市公司ST预测

特别处理(Special Treatment,缩写为“ST”)是股票市场为了保护投资者利益提出的一项政策。文章介绍了两种非参数判别分析方法,判别一家上市公司是否被特殊处理:第一种是基于普通多元核密度估计Bayes判别分析方法;第二种是基于球极投影变换的核密度估计Bayes判别方法,并结合沪深股市数据进行了实证分析。结果显示:对于适中的样本容量,后者的预测能力要优于前者。显示出球极投影变换核密度估计判别方法的优良性,为使用者提供良好的依据。     

距离判别分析的应用

判别分析是一种在各种领域都有广泛应用的统计判别与分组的技术方法,文章对距离判别分析进行了具体的介绍,然后应用其解决实际问题。     

Fisher多类判别分析法在期货价格预测中的应用

基于期货价格变化趋势的可预测性,利用判别分析中的Fisher多类判别模型,运用MATLAB程序语言编程,对期货交易中三月铜的数据进行分析,得到了判别函数,给出了预测判别准则,进一步讨论了其在期货价格预测中的应用。     

Bayes判别信用评价模型及其应用研究

本文在简要综述了上市公司信用评级的研究现状,特别是基于判别分析方法的信用评价模型的研究与应用的基础上,引入Bayes判别法则(最小ECM法则),在总体协方差相等和不等的不同假设下建立两类模式分类的信用评价模型;并运用该模型对我国2000年106家上市公司进行模式识别训练及分类的实证,计算其明显误判率(APER)和期望真实误判率(E(AER)),最后讨论了的该评价模型的性能.     

多元统计方法在判别贷款企业是否具有还款能力中的应用

在发放贷款前怎样判别企业是否具有还款能力，一直作为金融系统信贷部门工作的重点。目前信贷部门在实际操作巾一般采用t性分析入法，若能采用一种量化方法来判别贷款企业是否能归还贷款，将对金融部门的贷款审查、投放．防止产生新的不良资产带来极大的便利。据此，笔者做了一次调查分析，采用多元统计方法，叶以在贷前对贷款企业进行判别、归类，从而评价贷款企儿的还款能力。一、费歇判别分析方法的基本思想费歇判别的思想是投影，将K级P维数据投影到某一方向，使得它们的投影组与组之间尽可能地分开。在分析过程中，它借用一元方差分析…     

有关距离判别理论方法的补充和讨论

距离判别理论中，通常采用重心距离来定义类与类之间的距离对待判样品进行判别。对新样品实行判别，将其归入系统聚类形成的分类，如果仍采用重心距离判别法，会由于没有与原有聚类时所用的类与类之间的距离相一致而产生误判。提出对基于系统聚类分类结果的距离判别理论方法的补充，把系统聚类中的八种类与类之间距离的概念引入到距离判别方法中。从而使距离判别中类与类距离的定义与系统聚类中相一致，通过实例分析，证明增强了距离判别的可靠性。     

数量化Ⅱ类弓形效应修正方法及应用

对应分析在对定性数据进行数量化处理过程中出现了“弓形效应”，关于对应分析的“弓形效应”的修正方法已经有了丰富的研究成果，避免了可能错误的分析结果，对理论界和应用领域都有重要意义。数量化Ⅱ类是关于定性数据的一种判别分析方法，在国内外已被广泛应用。本文通过大量模拟数据研究发现，数量化Ⅱ类在对定性数据进行数量化过程中出现了“弓形效应”，降低了正判别率，同时不能正确再现原始数据信息，得出与原始数据信息不符的错误分析结果，为修正“弓形效应”，提出了二阶段判别分析法，并从正判别率和对原始数据再现程度两个方面对数量化Ⅱ类与二阶段判别分析法进行了比较，同时将二阶段判别分析法运用到个人信用评级中，发现二阶段判别分析法的判别性能优于数量化Ⅱ类。     

A NEW APPROACH TO DISCRIMINATION AND CLASSIFICATION USING A HAUSDORFF TYPE DISTANCE

A new method of discrimination and classification based on a Hausdorff type distance is proposed. In two groups, the Hausdorff distance is defined as the sum of the furthest distance of the nearest elements of one set to another. This distance has some useful properties and is exploited in developing a discriminant criterion between individual objects belonging to two groups based on a finite number of classification variables. The discrimination criterion is generalized to more than two groups in a couple of ways. Several data sets are analysed and their classification accuracy is compared to that obtained from linear discriminant function and the results are encouraging. The method in simple, lends itself to parallel computation and imposes less stringent conditions on the data.     

Kernel naive Bayes discrimination for high‐dimensional pattern recognition

Kernel discriminant analysis translates the original classification problem into feature space and solves the problem with dimension and sample size interchanged. In high‐dimension low sample size (HDLSS) settings, this reduces the ‘dimension’ to that of the sample size. For HDLSS two‐class problems we modify Mika's kernel Fisher discriminant function which – in general – remains ill‐posed even in a kernel setting; see Mika et al. (1999). We propose a kernel naive Bayes discriminant function and its smoothed version, using first‐ and second‐degree polynomial kernels. For fixed sample size and increasing dimension, we present asymptotic expressions for the kernel discriminant functions, discriminant directions and for the error probability of our kernel discriminant functions. The theoretical calculations are complemented by simulations which show the convergence of the estimators to the population quantities as the dimension grows. We illustrate the performance of the new discriminant rules, which are easy to implement, on real HDLSS data. For such data, our results clearly demonstrate the superior performance of the new discriminant rules, and especially their smoothed versions, over Mika's kernel Fisher version, and typically also over the commonly used naive Bayes discriminant rule.     

A comparison of regularization methods applied to the linear discriminant function with high-dimensional microarray data

Classification of gene expression microarray data is important in the diagnosis of diseases such as cancer, but often the analysis of microarray data presents difficult challenges because the gene expression dimension is typically much larger than the sample size. Consequently, classification methods for microarray data often rely on regularization techniques to stabilize the classifier for improved classification performance. In particular, numerous regularization techniques, such as covariance-matrix regularization, are available, which, in practice, lead to a difficult choice of regularization methods. In this paper, we compare the classification performance of five covariance-matrix regularization methods applied to the linear discriminant function using two simulated high-dimensional data sets and five well-known, high-dimensional microarray data sets. In our simulation study, we found the minimum distance empirical Bayes method reported in Srivastava and Kubokawa [Comparison of discrimination methods for high dimensional data, J. Japan Statist. Soc. 37(1) (2007), pp. 123–134], and the new linear discriminant analysis reported in Thomaz, Kitani, and Gillies [A Maximum Uncertainty LDA-based approach for Limited Sample Size problems – with application to Face Recognition, J. Braz. Comput. Soc. 12(1) (2006), pp. 1–12], to perform consistently well and often outperform three other prominent regularization methods. Finally, we conclude with some recommendations for practitioners.     

The rank transformation as a method of discrimination with some examples

The procedure of statistical discrimination Is simple in theory but so simple in practice. An observation x₀possibly uiultivariate, is to be classified into one of several populations π₁,…,π_k which have respectively, the density functions f₁(x), ? ? ? , f_k(x). The decision procedure is to evaluate each density function at X₀ to see which function gives the largest value f_i(X₀) , and then to declare that X₀ belongs to the population corresponding to the largest value. If these den-sities can be assumed to be normal with equal covariance matricesthen the decision procedure is known as Fisher’s linear discrimi-nant function (LDF) method. In the case of unequal covariance matrices the procedure is called the quadratic discriminant func-tion (QDF) method. If the densities cannot be assumed to be nor-mal then the LDF and QDF might not perform well. Several different procedures have appeared in the literature which offer discriminant procedures for nonnormal data. However, these pro-cedures are generally difficult to use and are not readily available as canned statistical programs.

Another approach to discriminant analysis is to use some sortof mathematical trans format ion on the samples so that their distribution function is approximately normal, and then use the convenient LDF and QDF methods. One transformation that:applies to all distributions equally well is the rank transformation. The result of this transformation is that a very simple and easy to use procedure is made available. This procedure is quite robust as is evidenced by comparisons of the rank transform results with several published simulation studies.     

A study on discriminant analysis techniques applied to multivariate lognormal data

The purpose of this paper is to examine the multiple group (>2) discrimination problem in which the group sizes are unequal and the variables used in the classification are correlated with skewed distributions. Using statistical simulation based on data from a clinical study, we compare the performances, in terms of misclassification rates, of nine statistical discrimination methods. These methods are linear and quadratic discriminant analysis applied to untransformed data, rank transformed data, and inverse normal scores data, as well as fixed kernel discriminant analysis, variable kernel discriminant analysis, and variable kernel discriminant analysis applied to inverse normal scores data. It is found that the parametric methods with transformed data generally outperform the other methods, and the parametric methods applied to inverse normal scores usually outperform the parametric methods applied to rank transformed data. Although the kernel methods often have very biased estimates, the variable kernel method applied to inverse normal scores data provides considerable improvement in terms of total nonerror rate.     

A Simulation Study of the Performance of Five Discriminant Analysis Methods for Mixtures of Continuous and Binary Variables

The present study investigates the performance of fice discrimination methods for data consisting of a mixture of continuous and binary variables. The methods are Fisher’s linear discrimination, logistic discrimination, quadratic discrimination, a kernal model and an independence model. Six-dimensional data, consisting of three binary and three continuous variables, are simulated according to a location model. The results show an almost identical performance for Fisher’s linear discrimination and logistic discrimination. Only in situations with independently distributed variables the independence model does have a reasonable discriminatory ability for the dimensionality considered. If the log likelihood ratio is non-linear ratio is non-linear with respect to its continuous and binary part, the quadratic discrimination method is substantial better than linear and logistic discrimination, followed by the kernel method. A very good performance is obtained when in every situation the better one of linear and quardratic discrimination is used.     

我国粮食单产保险纯费率厘定的实证研究

粮食保险属于政策性农业保险,其费率厘定应以风险区划为基础,准确的费率厘定将有助于政府制订出科学的保险支农政策。本文从以产量变化测度自然风险对粮食安全的影响这一新的视角建立了粮食安全自然风险影响的评价指标体系。利用系统聚类法、K-均值聚类法和模糊聚类法对我国粮食生产进行了省级保险风险区划,并以Fisher判别法、Bayes判别法和逐步判别法进行了回判验证。在对各省（市、区）粮食单产分布进行检验的基础上,选取经验费率法厘定了单产保险的纯费率,并结合风险区划结果和政策取向对纯费率进行了调整。进一步的研究需要实施较小基本单位的风险区划和费率厘定,基本单位越小,费率厘定越符合实际,但工作量越大。     

Logistic Discrimination with Total Variation Regularization

This article introduces a regularized logistic discrimination method that is especially suited for discretized stochastic processes (such as periodograms, spectrograms, EEG curves, etc.). The proposed method penalizes the total variation of the discriminant directions, giving smaller misclassification errors than alternative methods, and smoother and more easily interpretable discriminant directions. The properties of the new method are studied by simulation and by a real-data example involving classification of phonemes.     

Default Bayesian analysis of the Behrens–Fisher problem

In the Bayesian approach, the Behrens–Fisher problem has been posed as one of estimation for the difference of two means. No Bayesian solution to the Behrens–Fisher testing problem has yet been given due, perhaps, to the fact that the conventional priors used are improper. While default Bayesian analysis can be carried out for estimation purposes, it poses difficulties for testing problems. This paper generates sensible intrinsic and fractional prior distributions for the Behrens–Fisher testing problem from the improper priors commonly used for estimation. It allows us to compute the Bayes factor to compare the null and the alternative hypotheses. This default procedure of model selection is compared with a frequentist test and the Bayesian information criterion. We find discrepancy in the sense that frequentist and Bayesian information criterion reject the null hypothesis for data, that the Bayes factor for intrinsic or fractional priors do not.     

Variational discriminant analysis with variable selection

A fast Bayesian method that seamlessly fuses classification and hypothesis testing via discriminant analysis is developed. Building upon the original discriminant analysis classifier, modelling components are added to identify discriminative variables. A combination of cake priors and a novel form of variational Bayes we call reverse collapsed variational Bayes gives rise to variable selection that can be directly posed as a multiple hypothesis testing approach using likelihood ratio statistics. Some theoretical arguments are presented showing that Chernoff-consistency (asymptotically zero type I and type II error) is maintained across all hypotheses. We apply our method on some publicly available genomics datasets and show that our method performs well in practice for its computational cost. An R package VaDA has also been made available on Github.