Large correlation analysis

In this paper, a novel supervised dimensionality reduction method is developed based on both the correlation analysis and the idea of large margin learning. The method aims to maximize the minimal correlation between each dimensionality-reduced instance and its class label, thus named as large correlation analysis (LCA). Unlike most existing correlation analysis methods such as CCA, CCAs and CDA, which all maximize the total or ensemble correlation over all training instances, LCA devotes to maximizing the individual correlations between given instances and its associated labels and is established by solving a relaxed quadratic programming with box-constraints. Experimental results on real-world datasets from both UCI and USPS show its effectiveness compared to the existing canonical correlation analysis methods.     

Model selection for canonical correlation analysis

1. IntroductionLet X and Y be p x 1 and q x 1 random vectors, respectively, and let p 5 q. PutCanonica1 correlation analysis focuses on the relationship between the two sets of randomvariables, X.. 1 and Yax 1' We ca1l EFllZl,Zdz Z2l the canonical correlation matrix (CCM).Let pf,',p; (l > Pf 2.' 2 p; 2 0) be the eigenvalues of CCM. Their positive squareroots pl )', pp are the population canonical correlation coefficients. Letbe the sample covaxiance matrix, where U'1,' 5 Wi. ar…     

Canonical correlations in multi-way layout

In this paper, some formulas are proposed, which concern the numbers of unit canonical correlations in a multi-way layout. Different types of canonical correlations are considered and their connection with connectedness and orthogonality are examined.     

上市公司经营绩效评价方法的典型相关分析

本文介绍了上市公司经营绩效的传统评价方法和EVA、MVA方法,并对几种方法进行了比较,采用典型相关分析方法,以沪市180指标股的相关数据进行了实证研究。我们发现EVA类指标与传统财务评价指标的结论是相一致的,都是公司经营绩效的有效反映。     

Assessing Local Influence in Canonical Correlation Analysis

The first order local influence approach is adopted in this paper to assess the local influence of observations to canonical correlation coefficients, canonical vectors and several relevant test statistics in canonical correlation analysis. This approach can detect different aspects of influence due to different perturbation schemes. In this paper, we consider two different kinds, namely, the additive perturbation scheme and the case-weights perturbation scheme. It is found that, under the additive perturbation scheme, the influence analysis of any canonical correlation coefficient can be simplified to just observing two predicted residuals. To do the influence analysis for canonical vectors, a scale invariant norm is proposed. Furthermore, by choosing proper perturbation scales on different variables, we can compare the different influential effects of perturbations on different variables under the additive perturbation scheme. An example is presented to illustrate the effectiveness of the first order local influence approach.     

Classification accuracy and correlation: LDA in failure prediction

The relationship between canonical correlation and classification accuracy in linear discriminant analysis is explored mathematically. The discriminant score is assumed to conform to a uniform distribution on the interval (0, 1]. This distribution is used as a reference distribution to extract a minimum correlation for certain classification accuracy. Four different cases are analyzed. First, a case for equal group size is considered for an overall accuracy of 100%. Second, the results are generalized for unequal group size. Third, existence of discordant observations is allowed. Fourth, the effect of concentration is analyzed for the first case. The results are demonstrated by numerical examples. In addition, a sample of 2092 default and 63,072 non-default Finnish firms are used to empirically illustrate the results in the context of failure prediction. The results show that group size of default firms, number of discordant observations, and bipolar concentration of observations strongly affect both canonical correlation and classification accuracy.     

Use of the multinomial jack-knife and bootstrap in generalized non-linear canonical correlation analysis

In this paper we discuss the estimation of mean and standard errors of the eigenvalues and category quantifications in generalized non-linear canonical correlation analysis (OVERALS). Starting points are the delta method equations, but the jack-knife and bootstrap are used to provide finite difference approximations to the derivatives.     

统计相关性分析方法的进展

系统综述了自19世纪开始且至今常用统计相关性的方法,例如Pearson和Spearman相关系数,CorGc和CovGc 相关性及距离相关性方法。重点介绍了2011年提出的MIC方法以及由此引发的毁誉参半的大量评述,旨在揭示这一热点领域研究面貌。该领域不仅受到统计学家的关注,而且受到了分析大样本和异质数据的应用研究领域的学者们的追捧,例如基因组生物学家和网络信息研究者。这些研究者期望在众多已有方法的理解和剖析中更恰当地付诸应用,并提出新的应用问题来推动新的分析方法的创造。     

Functional estimation incorporating prior correlation information

This paper deals with the problem of estimating functional data from a functional noise model, i.e., on the basis of the observations of a discrete-time stochastic process in additive white noise which can be correlated with the process. Assuming prior information on the correlation functions involved and using principal component analysis for stochastic processes, a general suboptimum estimation procedure is derived. The proposed solution is valid for smoothing, filtering and prediction problems, can be applied to estimate any operation of the process, such as derivatives, and constitutes a computationally efficient algorithm.     

Asymptotic distributions in the projection pursuit based canonical correlation analysis

In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and weighting vectors are derived.     

典型相关分析在医学上的一个应用

本文将典型相关分析应用于女童多源性假性性早熟 ,推导出其性征程度与雌激素水平只有中等程度正相关的结论     

Canonical Metrics on Generalized Cartan-Hartogs Domains

In this paper, the author considers a class of bounded pseudoconvex domains,i.e., the generalized Cartan-Hartogs domains Ω(μ, m). The first result is that the natural Khler metric g~(Ω(μ,m)) of Ω(μ, m) is extremal if and only if its scalar curvature is a constant. The second result is that the Bergman metric, the Ka¨hler-Einstein metric, the Carathéodary metric, and the Koboyashi metric are equivalent for Ω(μ, m).     

Canonical factorization of continuous functions on the -torus

In this article we study the canonical factorization of continuous complex-valued functions on the -dimensional torus belonging to a weighted Wiener algebra with respect to a linear order on the -tuples of integers. It is proved that a function has a canonical factorization in this algebra if and only if it has a logarithm belonging to this algebra. A second characterization is given in terms of winding numbers. Moreover, the maximal ideal spaces of the relevant Banach algebras are identified.

     

Regularized generalized canonical correlation analysis for multiblock or multigroup data analysis

This paper presents an overview of methods for the analysis of data structured in blocks of variables or in groups of individuals. More specifically, regularized generalized canonical correlation analysis (RGCCA), which is a unifying approach for multiblock data analysis, is extended to be also a unifying tool for multigroup data analysis. The versatility and usefulness of our approach is illustrated on two real datasets.     

Riemannian Trust-Region Method for the Maximal Correlation Problem

The maximal correlation problem (MCP) arising in the canonical correlation analysis is very important to assess the relationship between sets of random variables. Efficient and fast methods for solving MCP are desired in broad statistical and nonstatistical applications. Some early proposed algorithms are based on the first-order information of MCP, and fast convergence could not be expected. In this article, we turn the generic Riemannian trust-region method of Absil et al. [2 P.-A. Absil , C. G. Baker , and K. A. Gallivan ( 2007 ). Trust-region methods on Riemannian manifolds . Found. Comput. Math. 7 : 303 – 330 . [Google Scholar]] into a practical algorithm for MCP, which enjoys the global convergence and local superlinear convergence rate. The structure-exploiting preconditioning technique is also discussed in solving the trust-region subproblem. Numerical empirical evaluation and a comparison against other methods are reported, which shows that the method is efficient in solving MCPs.     

An algebraic theory for statistical information based on the theory of hints

Statistical problems were at the origin of the mathematical theory of evidence, or Dempster–Shafer theory. It was also one of the major concerns of Philippe Smets, starting with his PhD dissertation. This subject is reconsidered here, starting with functional models, describing how data is generated in statistical experiments. Inference is based on these models, using probabilistic assumption-based reasoning. It results in posterior belief functions on the unknown parameters. Formally, the information used in the process of inference can be represented by hints. Basic operations on hints are combination, corresponding to Dempster’s rule, and focussing. This leads to an algebra of hints. Applied to functional models, this introduces an algebraic flavor into statistical inference. It emphasizes the view that in statistical inference different pieces of information have to be combined and then focussed onto the question of interest. This theory covers Bayesian and Fisher type inference as two extreme cases of a more general theory of inference.     

The analysis of correlation integrals in terms of extremal value theory

In this paper we first give an overview of the methods of analysis of time series in terms of correlation integrals, which were developed for time series generated by deterministic systems. From the extremal value theory one obtains asymptotic information on the behaviour of the correlation integrals of time series generated by non-deterministic (mixing) systems. This leads to an analysis in terms of correlation integrals which is complementary to the estimation of dimension and entropy.Dedicated to the memory of Ricardo Mañé     

Data envelopment analysis of mutual funds based on second-order stochastic dominance

Although data envelopment analysis (DEA) has been extensively used to assess the performance of mutual funds (MF), most of the approaches overestimate the risk associated to the endogenous benchmark portfolio. This is because in the conventional DEA technology the risk of the target portfolio is computed as a linear combination of the risk of the assessed MF. This neglects the important effects of portfolio diversification. Other approaches based on mean–variance or mean–variance–skewness are non-linear. We propose to combine DEA with stochastic dominance criteria. Thus, in this paper, six distinct DEA-like linear programming (LP) models are proposed for computing relative efficiency scores consistent (in the sense of necessity) with second-order stochastic dominance (SSD). The aim is that, being SSD efficient, the obtained target portfolio should be an optimal benchmark for any rational risk-averse investor. The proposed models are compared with several related approaches from the literature.     

关于解极大相关问题P-SOR算法的收敛性

对求解极大相关问题的P-SOR方法的收敛性做了进一步研究.得到了一些新的收敛条件.为了提高收敛到全局最大解的可能性,提出了一种新的初始向量选择策略.给出了P-SOR算法的对称形式(P-SSOR).还给出了一种算法精化策略.最后,用数值例子说明新方法的有效性.     

Generating random correlation matrices based on partial correlations

A d-dimensional positive definite correlation matrix R=(ρ_ij) can be parametrized in terms of the correlations ρ_i,i+1 for i=1,…,d-1, and the partial correlations ρ_{ij|i+1,…j-1} for j-i2. These parameters can independently take values in the interval (-1,1). Hence we can generate a random positive definite correlation matrix by choosing independent distributions F_ij, 1i<jd, for these parameters. We obtain conditions on the F_ij so that the joint density of (ρ_ij) is proportional to a power of det(R) and hence independent of the order of indices defining the sequence of partial correlations. As a special case, we have a simple construction for generating R that is uniform over the space of positive definite correlation matrices. As a byproduct, we determine the volume of the set of correlation matrices in -dimensional space. To prove our results, we obtain a simple remarkable identity which expresses det(R) as a function of ρ_i,i+1 for i=1,…,d-1, and ρ_{ij|i+1,…j-1} for j-i2.