Canonical Correlation Analysis of Formulation Optimization Experiments

Formulation optimization experiments are primarily composed of two groups of variables, a set of independent variables and a set of dependent variables. Simultaneous consideration of all the variables in a single analysis is desirable since it provides an opportunity to study the interrelationships of all variables, independent as well as dependent at the same time and imparts an in-depth insight into the entire system as a whole. A multivariate statistical analysis, known as canonical correlation analysis, has indeed this capability. In addition, the analysis has the capacity of extracting the maximum possible correlation, called canonical correlation, between the variables of the two sets. The larger the value of the canonical correlation (0.90 or above), the higher is the predictability of one set from the other set. The analysis produces two composite canonical functions, one for each set. They can be used to streamline the subsequent search process associated with the full-fledged optimization analysis. The analysis also has the cardinal property to rank-order the variables in each set according to their relative contributions to the canonical prediction function, and to delineate the most important variable in each set. This information can be useful in monitoring the future performance of the formulation in a time-and-cost effective manner and in selecting variables for future experiments. All the relevant features of the analysis have been depicted in this paper in the context of a mobile phase composition optimization experiment.     

On the free energy of liquid-metal plasma

The free energy of simple liquid metal in the approximation of the integral smallness of the electron–ion interaction has been found on the basis of the model of single-component plasma as the initial system. The result obtained holds at the equivalency of correlation functions determined within Gibbs canonical and large canonical distributions.     

多彩色空间相关分析的人脸识别算法

人脸识别是当前人工智能和模式识别的研究热点,得到了广泛的关注.基于对不同色彩空间数据的分析,论文提出了多彩色空间典型相关分析的人脸识别方法.文中对2维的Contourlet变换特性进行了分析和讨论,利用Contourlet的多尺度,方向性和各向异性等特点,提出了一种基于Contourlet变换的彩色人脸识别算法.算法对原图进行Contourlet分解,对分解得到的低频和高频图像进行cca分析.典型相关分析是一种有效的分析方法,其实际应用十分广泛.低频系数反映图像的轮廓信息,高频系数反映图像的细节信息,使用cca充分利用不同频率的信息,使不同色彩空间的不同分辨率图形的相关性达到最大,得到投影系数,最后,采用决策级最近邻分类器完成人脸识别.在对彩色人脸数据库AR的识别实验中,该算法识别率达到98％以上,与传统算法相比,该算法不仅既有良好的识别结果,而且具有很快的运算速度.     

Sure screening by ranking the canonical correlations

The sure independence screening procedure by ranking the marginal Pearson correlation is well documented in literatures and works satisfactorily in the ultra-high dimensional case. However, this marginal Person correlation learning would easily miss the variable that is marginally uncorrelated with the response but correlated with the response jointly with some other variables. This failure in missing an important variable is due to the fact that the marginal Pearson correlation does not use the joint information of the response and a set of covariates. In this paper, we introduce a new screening method which leaves a variable into the active set if it jointly with some other variables has a high canonical correlation with the response. This is accomplished via ranking canonical correlations between the response and all possible sets of k variables. Our results show that the procedure has the sure screening property and substantially reduces the dimensionality to a moderate size against the sample size. Extensive simulations demonstrate that our new method performs substantially better than the existing sure independence screening approaches based on the marginal Pearson correlation or Kental’s tau rank correlation. A real data set is also analyzed by implementing our approach.     

Researching the Link Between the Geometric and Rènyi Discord for Special Canonical Initial States Based on Neural Network Method

Quantum correlation which is different to the entanglement and classical correlation plays important role in quantum information field. In our setup, neural network method is adopted to simulate the link between the Rènyi discord (α = 2) and the geometric discord (Bures distance) for special canonical initial states in order to show the consistency of physical results for different quantification methods. Our results are useful for studying the differences and commonalities of different quantizing methods of quantum correlation.     

Main inorganic component measurement of seawater using near-infrared spectroscopy

The potential of near-infrared (NIR) spectroscopy to measure the main inorganic components of seawater as salt-manufacturing materials was investigated. A total of 72 seawater samples collected from six locations was used, and spectra (1100-1800 nm) were acquired by a NIR spectrophotometer with a 1-mm path length. Principal component analysis (PCA), canonical correlation analysis (CCA), and partial least-squares (PLS) regression were performed based on the reference inorganic components. As a result, the principal component analysis and canonical correlation analysis showed that the near-infrared spectra could be related to the inorganic components of seawater. The partial least-squares regression analysis showed that the inorganic components (ion concentration of Cl, Na+, K+, SO4(2-), and Ca2+) could be predicted with good accuracy using NIR spectra and their second derivatives. For Cl ion and K+ ion concentrations, the accuracy was high.     

一类线性矩阵方程的最佳逼近解

本文利用投影定理、广义奇异值分解和标准相关分解技巧给出了一种求矩阵方程AXB=C的最小二乘反对称解的方法,得到了通解表达式。进而利用此表达式,导出了通解集做为一个矩阵集与任意给定矩阵的最小距离元素。     

A Test Statistic in Canonical Correlation Analysis for Categorical Variables

In canonical correlation analysis (CCA), it is important to estimate the number of nonzero canonical correlations in the population. One way to estimate the number is to consider the dimensionality testing problem. In CCA for continuous variables, some test statistics for the problem have been derived under the normality assumption. However, there are only a few papers on test statistics in CCA for categorical variables.

In this article, a test statistic in CCA for categorical variables is suggested. The test statistic is derived from the rational used for continuous variables. Some properties of the test statistic are examined through mathematical investigations and numerical simulations.

     

Polarized Electrons

The frequency up-conversion process with a (classical) stochastic coupling is studied on the basis of canonical equations. Exact results for the number operators and the correlation functions (with zero time-lag) are extracted from the equations by the use of Ito-McShane calculus. The results indicate the absence of antibunching, at least for zero time-delay.     

Coherent state path integral approach to multi-time correlation functions and photon emission in a semiconductor microcavity

In this paper by using the coherent state path integral field theory approach, we calculate the grand canonical partition function of an interacting combined system in the presence of the relevant source terms. It allows us to calculate multi-time correlation functions of interacting systems without using the quantum regression theorem. Then, we investigate the power spectrum and the second-order correlation function of the emitted photons from a microcavity in the presence of excitations of a semiconductor quantum well. By using the Hubbard–Stratonovich transformation, we investigate the effects of reservoir, detuning, the Coulomb interaction and the phase space filling on the power spectrum and the second-order correlation function of the emitted photons.     

广义特征值问题与两线性流形之间夹角的计算

高维欧氏空间中的两线性流形的夹角可用带二次等式约束的二次规划(QP-QEC)刻画。这样的夹角计算在统计学和数据分析中有许多重要应用,比如,两组随机变量的典型相关分析和核典型相关分析。本文用KKT条件探讨了更一般的QP-QEC与其对应的一般特征值问题之间的关系。在此基础上,借助一般特征值问题的解法,给出了这种夹角的算法。     

空间相关噪声下信源个数的聚类检测算法

针对空间相关噪声情况,利用两个独立阵列之间噪声不相关的特性,采用联合协方差矩阵的规范相关系数作为聚类特征,提出了一种基于模糊c均值聚类的信源个数检测方法.并详细分析了应用Fuzzy-c-Means(FCM)聚类算法进行信源个数检测的3个问题: 聚类的趋势、有效性和聚类中心的初始化.与经典算法相比,本文算法有较好的角度分辨力和检测性能.仿真结果证明了该方法的有效性和鲁棒性.     

Correlation Analysis for Simultaneously Controlling Reliability and Validity

The purpose of the present study is to propose a procedure for correlation analysis of several (especially two) sets of variables, which includes canonical correlation analysis, principal component analysis, and multiple regression analysis as a special case. The proposed method derives components from each set of variables which maximize the weighted geometric mean of two types of indicators: one is the contribution rate of the components for their original variables, the other is the squared correlation between the components. In terms of the test theory, the former are indicators of reliability and the latter are indicators of concurrent validity. Through the numerical examples applying this method to the data of two Japanese language personality inventory, the method is shown to be particularly useful when determining the weights for test items.

     

Constrained Principal Component Analysis: A Comprehensive Theory

Constrained principal component analysis (CPCA) incorporates external information into principal component analysis (PCA) of a data matrix. CPCA first decomposes the data matrix according to the external information (external analysis), and then applies PCA to decomposed matrices (internal analysis). The external analysis amounts to projections of the data matrix onto the spaces spanned by matrices of external information, while the internal analysis involves the generalized singular value decomposition (GSVD). Since its original proposal, CPCA has evolved both conceptually and methodologically; it is now founded on firmer mathematical ground, allows a greater variety of decompositions, and includes a wider range of interesting special cases. In this paper we present a comprehensive theory and various extensions of CPCA, which were not fully envisioned in the original paper. The new developments we discuss include least squares (LS) estimation under possibly singular metric matrices, two useful theorems concerning GSVD, decompositions of data matrices into finer components, and fitting higher-order structures. We also discuss four special cases of CPCA; 1) CCA (canonical correspondence analysis) and CALC (canonical analysis with linear constraints), 2) GMANOVA (generalized MANOVA), 3) Lagrange's theorem, and 4) CANO (canonical correlation analysis) and related methods. We conclude with brief remarks on advantages and disadvantages of CPCA relative to other competitors. Received: June 23, 2000; revised version: July 9, 2001     

Pulse-mode study of the quantum correlation of photons in an N-photon Dicke model

Abstract

We find the N-photon state emitted by an N-step Dicke model and provide a method to construct the field coherence functions based on it. Our effort is concentrated on the second order coherence, or the one-photon density matrix. When expressed in its canonical representation, this matrix gives the photon number occupying each ‘pulse eigenmode’. This number serves as an indicator of the correlation between photons. By studying the evolution of the one-photon density matrix we can trace the creation of such correlation during the emission. From the asymptotic solution we are able to find approximate scaling law relations between the photon degeneracy in the eigenmodes and the total number of photons involved.     

Data modeling and method analysis for brain imaging genetics

Brain imaging genetics is a popular research topic on evaluating the association between genetic variations and neuroimaging quantitative traits (QTs). As a bi‐multivariate analysis method, sparse canonical correlation analysis (CCA) is a useful technique which identifies efficiently genetic diseases on the brain with modeling dependencies between the variables of genotype data and phenotype data. The initial efforts on evaluating several space CCA methods are made for brain imaging genetics. A linear model is proposed to generate realistic imaging genomic data with selected genotype‐phenotype associations from real data and effectively capture the sparsity underlying projects. Three space CCA algorithms are applied to the synthetic data, and show better or comparable performance on the synthetic data in terms of the estimated canonical correlations. They have successfully identified an important association between genotype and phenotype. Experiments on simulated and real imaging genetic data show that approximating covariance structure using an identity or diagonal matrix and the approach used in these space CCA algorithms could limit the space CCA capability in identifying the underlying imaging genetics associations. Further development depends largely on enhanced space CCA methods that effectively pay attention to the covariance structures in simulated and real imaging genetics data.     

An empirical examination of sourcing's role in developing manufacturing flexibilities

Past research on manufacturing flexibility has emphasized technology and its contributions to flexibility. This study examines the role of sourcing practices in achieving manufacturing flexibilities. Manufacturing flexibility is conceptualized as a multi-dimensional construct and a taxonomy of existing research is developed. An exploratory empirical examination of the sourcing practices-flexibility linkage using canonical correlation and regression analysis suggests significant relationships between sourcing practice and manufacturing flexibilities. The results support the need for treating manufacturing flexibility as a multi-dimensional construct. The results also suggest that a firm could deploy specific sourcing practices to target specific manufacturing flexibilities in pursuit of agilitybased competitive advantages.     

Metrology and the linear canonical transform

It is shown experimentally that both surface tilt and in-plane translation motion can be independently estimated using the speckle photographic correlation technique by capturing consecutive images in two linear canonical transform domains (using two different quadratic phase systems). A geometric interpretation, based on use of the Wigner distribution function is presented to describe the method and a simple matrix approach, based on the ABCD matrix, is used to quantify it. It is shown that the sensitivity and dynamic range of measurement of both tilt and translation are both variable and depend on the parameters of the ABCD matrix.     

Canonical-covariant Wigner function in polar form

The two-dimensional Wigner function is examined in polar canonical coordinates, and covariance properties under the action of affine canonical transformations are derived.