Thesis (Ph.D.)--University of Melbourne, Dept. of Mathematics and Statistics, 2007. / Typescript. Includes bibliographical references.

Recently there has been a renewed interest in formative measurement and its role in properly specified models. Formative measurement models are difficult to identify, and hence to estimate and test. Existing solutions to the identification problem are shown to not adequately represent the formative constructs of interest. We propose a new two-step approach to operationalize a formatively measured construct that allows a closely matched common factor equivalent to be included in any structural equation model. We provide an artificial example and an original empirical study of privacy to illustrate our approach. Detailed proofs are given in an appendix.

archives@tulane.edu / Modern biomedical studies often collect multiple types of high-dimensional data on a common set of objects. A representative model for the integrative analysis of multiple data types is to decompose each data matrix into a low-rank common-source matrix generated by latent factors shared across all data types, a low-rank distinctive-source matrix corresponding to each data type, and an additive noise matrix. We propose a novel decomposition method, called the decomposition-based generalized canonical correlation analysis, which appropriately defines those matrices by imposing a desirable orthogonality constraint on distinctive latent factors that aims to sufficiently capture the common latent factors. To further delineate the common and distinctive patterns between two data types, we propose another new decomposition method, called the common and distinctive pattern analysis. This method takes into account the common and distinctive information between the coefficient matrices of the common latent factors. We develop consistent estimation approaches for both proposed decompositions under high-dimensional settings, and demonstrate their finite-sample performance via extensive simulations. We illustrate the superiority of proposed methods over the state of the arts by real-world data examples obtained from The Cancer Genome Atlas and Human Connectome Project. / 1 / Zhe Qu

Understanding how communication between brain areas evolves to support dynamic function remains a fundamental challenge in neuroscience. One approach to this question is functional connectivity analysis, in which statistical coupling measures are employed to detect signatures of interactions between brain regions. Because the brain uses multiple communication mechanisms at different temporal and spatial scales, and because the neuronal signatures of communication are often weak, powerful connectivity inference methodologies require continued development specific to these challenges. Here we address the challenge of inferring task-related functional connectivity in brain voltage recordings. We first develop a framework for detecting changes in statistical coupling that occur reliably in a task relative to a baseline period. The framework characterizes the dynamics of connectivity changes, allows inference on multiple spatial scales, and assesses statistical uncertainty. This general framework is modular and applicable to a wide range of tasks and research questions. We demonstrate the flexibility of the framework in the second part of this thesis, in which we refine the coupling statistics and hypothesis tests to improve statistical power and test different proposed connectivity mechanisms. In particular, we introduce frequency domain coupling measures and define test statistics that exploit theoretical properties and capture known sampling variability. The resulting test statistics use correlation, coherence, canonical correlation, and canonical coherence to infer task-related changes in coupling. Because canonical correlation and canonical coherence are not commonly used in functional connectivity analyses, we derive the theoretical values and statistical estimators for these measures. In the third part of this thesis, we present a sample application of these techniques to electrocorticography data collected during an overt reading task. We discuss the challenges that arise with task-related human data, which is often noisy and underpowered, and present functional connectivity results in the context of traditional and contemporary within-electrode analytics. In two of nine subjects we observe time-domain and frequency-domain network changes that accord with theoretical models of information routing during motor processing. Taken together, this work contributes a methodological framework for inferring task-related functional connectivity across spatial and temporal scales, and supports insight into the rapid, dynamic functional coupling of human speech.

This article reports on the results of a survey which investigated the nature of relationships between hospital and multihospital organization-centered factors and background characteristics, and multihospital organization effectiveness. Canonical correlation is employed in analyzing the data. Results and their implications are discussed.

This study was to explore the relationships between personal exposure to 10 volatile organic compounds (VOCs) and biochemical liver tests with the application of canonical correlation analysis. Data from a subsample of the 1999-2000 National Health and Nutrition Examination Survey were used. Serum albumin, total bilirubin (TB), alanine aminotransferase (ALT), aspartate aminotransferase (AST), lactate dehydrogenase (LDH), alkaline phosphatase (ALP), and γ-glutamyl transferase (GGT) served as the outcome variables. Personal exposures to benzene, chloroform, ethylbenzene, tetrachloroethene, toluene, trichloroethene, o-xylene, m-,p-xylene, 1,4-dichlorobenzene, and methyl tert-butyl ether (MTBE) were assessed through the use of passive exposure monitors worn by study participants. The first two canonical correlations were 0.3218 and 0.2575, suggesting a positive correlation mainly between the six VOCs (benzene, ethylbenzene, toluene, o-xylene, m-,p-xylene, and MTBE) and the three biochemical liver tests (albumin, ALP, and GGT) and a positive correlation mainly between the two VOCs (1,4-dichlorobenzene and tetrachloroethene) and the two biochemical liver tests (LDH and TB). Subsequent multiple linear regressions show that exposure to benzene, toluene, or MTBE was associated with serum albumin, while exposure to tetrachloroethene was associated with LDH and total bilirubin. In conclusion, exposure to certain VOCs as a group or individually may influence certain biochemical liver test results in the general population.

<p> The theory of canonical correlation analysis has been combined with that of trend surface analysis in order to construct a multivariate trend surface which is called a canonical trend surface. </p> <p> A canonical trend surface is a parsimonious summarization of areal variations of a set of geological variates. This trend has a property of maximum correlation between variates and geographic coordinates. It does not show the absolute value of each variate, but it shows the nature of the variation of a linear combination of the variates. The Permian system in western Kansas and eastern Colorado was studied as a numerical example to illustrate the general procedures in solving practical problems and also to demonstrate the validity of this technique. By use of this type of trend it is possible to reveal the underlying pattern of geographic variation common to a set of variates. </p> <p> Other applications of canonical correlation analysis in geology have been explained with illustrative geological examples, namely: the relationships between two sets of variates, matching two factor patterns, Q-technique canonical correlation, and discriminatory analysis. </p> <p> Comparison of canonical correlation analysis and principal factor solution in factor analysis suggests that factor analysis may be more appropriate for suggesting interrelationships among variables, while canonical correlation analysis may be a suitable tool for prediction problems. </p> <p> FORTRAN IV programs for these computations are listed in appendices with instructions for using them. </p> / Thesis / Doctor of Philosophy (PhD)

This dissertation is concerned with the problem of the exact pole-placement by minimum control effort using state and output feedback for linear multivariable systems. The novelty of the design lies in obtaining a direct transformation of the system matrices into a modified controllable canonical form. Two realizations are identified, and the algorithms to obtain them are derived. In both cases, the transformation matrix has some degrees of freedom by tuning a scalar or a set of scalars within the matrix. These degrees of freedom are utilized in the solution to reduce further the norm of the state feedback matrix. Then the pole-placement problem is solved by minimizing a certain functional, subject to a set of specified constraints. A non-canonical form approach to the problem is also proposed, where it was only necessary to transform the input matrix to a special form. The transformation matrix, in this method, has larger degrees of freedom which can be utilized in the solution. Moreover, a new pole-placement method based on the non-canonical approach is derived. The solution, in this method, was made possible by solving the Lyapunov matrix equation. Finally, an iterative algorithm for pole-placement by output feedback is extended so as to obtain an output feedback matrix with a small norm. The extension has been accomplished by applying the successive pole shifting method. Two schemes for the pole shifting are proposed. The first is to successively shift the poles through straight paths starting from the open loop poles and ending at the desired poles, whereas the second scheme shifts the poles according to a successive change of their characteristic polynomial coefficients. / Ph. D. / incomplete_metadata

Multi-view datasets arise naturally in statistical genetics when the genetic and trait profile of an individual is portrayed by two feature vectors. A motivating problem concerning the Skin Intrinsic Fluorescence (SIF) study on the Diabetes Control and Complications Trial (DCCT) subjects is presented. A widely applied quantitative method to explore the correlation structure between two domains of a multi-view dataset is the Canonical Correlation Analysis (CCA), which seeks the canonical loading vectors such that the transformed canonical covariates are maximally correlated. In the high dimensional case, regularization of the dataset is required before CCA can be applied. Furthermore, the nature of genetic research suggests that sparse output is more desirable. In this thesis, two regularized CCA (rCCA) methods and a sparse CCA (sCCA) method are presented. When correlation sub-structure exists, stand-alone CCA method will not perform well. To tackle this limitation, a mixture of local CCA models can be employed. In this thesis, I review a correlation clustering algorithm proposed by Fern, Brodley and Friedl (2005), which seeks to group subjects into clusters such that features are identically correlated within each cluster. An evaluation study is performed to assess the effectiveness of CCA and correlation clustering algorithms using artificial multi-view datasets. Both sCCA and sCCA-based correlation clustering exhibited superior performance compare to the rCCA and rCCA-based correlation clustering. The sCCA and the sCCA-clustering are applied to the multi-view dataset consisted of PrediXcan imputed gene expression and SIF measurements of DCCT subjects. The stand-alone sparse CCA method identified 193 among 11538 genes being correlated with SIF#7. Further investigation of these 193 genes with simple linear regression and t-test revealed that only two genes, ENSG00000100281.9 and ENSG00000112787.8, were significance in association with SIF#7. No plausible clustering scheme was detected by the sCCA based correlation clustering method. / Thesis / Master of Science (MSc)

Orientador: Carlos Roberto Padovani / Banca: Teresa Cristina Martins Dias / Banca: Sandra Fiorelli de P. Simeão / Banca: Marie Oshiiwa / Banca: Antonio Carlos Simões Pião / Resumo: A necessidade de entender o relacionamento entre variáveis biológicas faz da análise multivariada uma metodologia com grande potencial de aplicação em várias áreas do conhecimento. Na agricultura, sua utilização vem auxiliando a compreensão e a obtenção de respostas altamente interessantes e práticas, que permitem optar pelo seu emprego, tanto pela eficiência como pela acurácia do método na interpretação dos resultados. A partir da utilização de técnicas multivariadas pautadas em procedimentos quantitativos mais robustos e sensíveis, buscou-se caracterizar o perfil produtivo e climático das microrregiões do Sudeste do estado de Mato Grosso e construir modelos para quantificar e aprofundar a interrelação entre produtividade e variáveis climáticas nas respectivas regiões. Para classificar microrregiões semelhantes segundo suas características, quando nenhuma suposição foi feita concernente ao número de grupos ou a estrutura do grupo, utilizou-se a análise de agrupamento. Buscando variáveis agrícolas e de produtividade e a incorporação de novos procedimentos multivariados na interrelação desses indicadores, utilizou-se a análise de correlação canônica. Para a operacionalização desses procedimentos multivariados foram estabelecidas técnicas para estimar os componentes climáticos não disponíveis em algumas das microrregiões estudadas. A análise de agrupamento permitiu desenhar um mosaico de heterogeneidade espacial e estabelecer diferentes perfis na composição dos grupos de microrregião, reunindo as mais tradicionais no cultivo de uma espécie, ou mais produtivas, ou aquelas mais propícias ao desenvolvimento de determinada cultura. A análise fatorial estabeleceu dois eixos canônicos para as interrelações entre as culturas, sendo o primeiro fator explicando 42,22% da variância total correlacionado com as culturas anuais, podendo... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The knowledge of the relationship between biological variables makes the multivariate analysis a potential tool for applications in several science fields. In agriculture, this technique has enabled the understanding and obtaining responses very real, which show the possibility of use by both the efficiency and the accuracy of the method in the interpretation of results. The purpose of this research is to use of multivariate techniques based on quantitative procedures to improve the knowledge about the climatic variables of the southeast of Mato Grosso state, which helps to solve problems in the agricultural sector. Also, the grouping analysis classified the micro regions in similar groups. The factorial analysis showed the dimensions of the variation structure of data, enabling the determination of the extent of each variable in each dimension. The smaller regions were defined from interpreting of the interrelationship between the products grown in the region. The correlation canonic analysis was used to describe the association between the number of variables and agricultural productivity. Thus, new procedures were incorporated in multivariate interrelationship of these indicators. Some climatic components, not available in a few micro regions, were estimated through multivariate techniques. Cluster analysis allowed the design of a mosaic of spatial heterogeneity regions. It established different profiles in the composition of groups, joining the more traditional in the culture of a species, or more productive, or those for the development of a particular culture. The factorial analysis established two canonical axes for the interrelationships between cultures. The first factor explaining 42.22% of total variance associated with annual crops (called "annual crops factor "). The second factor explained 16, 11% ("semi perennial crop factor")... (Complete abstract click electronic access below) / Doutor