The Experts below are selected from a list of 393663 Experts worldwide ranked by ideXlab platform
Antoine Godichon-baggioni - One of the best experts on this subject based on the ideXlab platform.
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Fast estimation of the median covariation matrix with application to online robust Principal Components Analysis
TEST, 2017Co-Authors: Hervé Cardot, Antoine Godichon-baggioniAbstract:The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended to infinite dimensional spaces. We define estimators, based on recursive algorithms, that can be simply updated at each new observation and are able to deal rapidly with large samples of high-dimensional data without being obliged to store all the data in memory. Asymptotic convergence properties of the recursive algorithms are studied under weak conditions in general separable Hilbert spaces. The computation of the Principal Components can also be performed online and this approach can be useful for online outlier detection. A simulation study clearly shows that this robust indicator is a competitive alternative to minimum covariance determinant when the dimension of the data is small and robust Principal Components Analysis based on projection pursuit and spherical projections for high-dimension data. An illustration on a large sample and high-dimensional dataset consisting of individual TV audiences measured at a minute scale over a period of 24 h confirms the interest of considering the robust Principal Components Analysis based on the median covariation matrix. All studied algorithms are available in the R package Gmedian on CRAN.
Thomas Lengauer - One of the best experts on this subject based on the ideXlab platform.
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relative Principal Components Analysis application to analyzing biomolecular conformational changes
Journal of Chemical Theory and Computation, 2019Co-Authors: Mazen Ahmad, Volkhard Helms, Olga V Kalinina, Thomas LengauerAbstract:A new method termed “Relative Principal Components Analysis” (RPCA) is introduced that extracts optimal relevant Principal Components to describe the change between two data samples representing two macroscopic states. The method is widely applicable in data-driven science. Calculating the Components is based on a physical framework that introduces the objective function (the Kullback–Leibler divergence) appropriate for quantifying the change of the macroscopic state affected by the changes in the microscopic features. To demonstrate the applicability of RPCA, we analyze the thermodynamically relevant conformational changes of the protein HIV-1 protease upon binding to different drug molecules. In this case, the RPCA method provides a sound thermodynamic foundation for analyzing the binding process and thus characterizing both the collective and the locally relevant conformational changes. Moreover, the relevant collective conformational changes can be reconstructed from the informative latent variables t...
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relative Principal Components Analysis application to analyzing biomolecular conformational changes
bioRxiv, 2018Co-Authors: Mazen Ahmad, Volkhard Helms, Olga V Kalinina, Thomas LengauerAbstract:A new method termed Relative Principal Components Analysis (RPCA) is introduced that extracts optimal relevant Principal Components to describe the change between two data samples representing two macroscopic states. The method is applicable in all areas of data-driven science. Mining of the Components is based on a unified physical framework which introduces the objective function, namely the Kullback-Leibler divergence, appropriate for quantifying the change of the macroscopic state as it is effected by the microscopic features. Moreover, we provide a proof of existence of a low-dimensional space for latent informative features of the change. To demonstrate the applicability of RPCA, we analyze the thermodynamically relevant conformational changes of the protein HIV-1 protease upon binding to different drug molecules. In this case, the RPCA method provides a sound thermodynamic foundation for the Analysis of the binding process. The relevant collective (global) conformational changes can be reconstructed from the informative latent variables to exhibit both the enhanced and the restricted conformational fluctuations upon ligand association. Moreover, RPCA characterizes the locally relevant conformational changes which can be presented on the structure of the protein.
Marielle Linting - One of the best experts on this subject based on the ideXlab platform.
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nonlinear Principal Components Analysis with catpca a tutorial
Journal of Personality Assessment, 2012Co-Authors: Marielle Linting, Anita J Van Der KooijAbstract:This article is set up as a tutorial for nonlinear Principal Components Analysis (NLPCA), systematically guiding the reader through the process of analyzing actual data on personality assessment by the Rorschach Inkblot Test. NLPCA is a more flexible alternative to linear PCA that can handle the Analysis of possibly nonlinearly related variables with different types of measurement level. The method is particularly suited to analyze nominal (qualitative) and ordinal (e.g., Likert-type) data, possibly combined with numeric data. The program CATPCA from the Categories module in SPSS is used in the analyses, but the method description can easily be generalized to other software packages.
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nonlinear Principal Components Analysis introduction and application
Psychological Methods, 2007Co-Authors: Marielle Linting, Jacqueline J Meulman, Patrick J F Groenen, Anita J Van Der KoojjAbstract:The authors provide a didactic treatment of nonlinear (categorical) Principal Components Analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated Principal Components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover nonlinear relationships between variables. Also, nonlinear PCA can deal with variables at their appropriate measurement level; for example, it can treat Likert-type scales ordinally instead of numerically. Every observed value of a variable can be referred to as a category. While performing PCA, nonlinear PCA converts every category to a numeric value, in accordance with the variable's Analysis level, using optimal quantification. The authors discuss how optimal quantification is carried out, what Analysis levels are, which decisions have to be made when applying nonlinear PCA, and how the results can be interpreted. The strengths and limitations of the method are discussed. An example applying nonlinear PCA to empirical data using the program CATPCA (J. J. Meulman, W. J. Heiser, & SPSS, 2004) is provided.
Hervé Cardot - One of the best experts on this subject based on the ideXlab platform.
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Fast estimation of the median covariation matrix with application to online robust Principal Components Analysis
TEST, 2017Co-Authors: Hervé Cardot, Antoine Godichon-baggioniAbstract:The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended to infinite dimensional spaces. We define estimators, based on recursive algorithms, that can be simply updated at each new observation and are able to deal rapidly with large samples of high-dimensional data without being obliged to store all the data in memory. Asymptotic convergence properties of the recursive algorithms are studied under weak conditions in general separable Hilbert spaces. The computation of the Principal Components can also be performed online and this approach can be useful for online outlier detection. A simulation study clearly shows that this robust indicator is a competitive alternative to minimum covariance determinant when the dimension of the data is small and robust Principal Components Analysis based on projection pursuit and spherical projections for high-dimension data. An illustration on a large sample and high-dimensional dataset consisting of individual TV audiences measured at a minute scale over a period of 24 h confirms the interest of considering the robust Principal Components Analysis based on the median covariation matrix. All studied algorithms are available in the R package Gmedian on CRAN.
Anita J Van Der Koojj - One of the best experts on this subject based on the ideXlab platform.
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nonlinear Principal Components Analysis introduction and application
Psychological Methods, 2007Co-Authors: Marielle Linting, Jacqueline J Meulman, Patrick J F Groenen, Anita J Van Der KoojjAbstract:The authors provide a didactic treatment of nonlinear (categorical) Principal Components Analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated Principal Components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover nonlinear relationships between variables. Also, nonlinear PCA can deal with variables at their appropriate measurement level; for example, it can treat Likert-type scales ordinally instead of numerically. Every observed value of a variable can be referred to as a category. While performing PCA, nonlinear PCA converts every category to a numeric value, in accordance with the variable's Analysis level, using optimal quantification. The authors discuss how optimal quantification is carried out, what Analysis levels are, which decisions have to be made when applying nonlinear PCA, and how the results can be interpreted. The strengths and limitations of the method are discussed. An example applying nonlinear PCA to empirical data using the program CATPCA (J. J. Meulman, W. J. Heiser, & SPSS, 2004) is provided.
