Variables In Multivariate Data Research Articles

Netgwas: An R Package for Network-Based Genome Wide Association Studies

Graphical models are powerful tools for modeling and making statistical inferences regarding complex associations among variables in multivariate data. In this paper we introduce the R package netgwas, which is designed based on undirected graphical models to accomplish three important and interrelated goals in genetics: constructing linkage map, reconstructing linkage disequilibrium (LD) networks from multi-loci genotype data, and detecting high-dimensional genotype-phenotype networks. The netgwas package deals with species with any chromosome copy number in a unified way, unlike other software. It implements recent improvements in both linkage map construction (Behrouzi and Wit, 2018), and reconstructing conditional independence network for non-Gaussian continuous data, discrete data, and mixed discrete-and-continuous data (Behrouzi and Wit, 2017). Such datasets routinely occur in genetics and genomics such as genotype data, and genotype-phenotype data. We demonstrate the value of our package functionality by applying it to various multivariate example datasets taken from the literature. We show, in particular, that our package allows a more realistic analysis of data, as it adjusts for the effect of all other variables while performing pairwise associations. This feature controls for spurious associations between variables that can arise from classical multiple testing approach. This paper includes a brief overview of the statistical methods which have been implemented in the package. The main body of the paper explains how to use the package. The package uses a parallelization strategy on multi-core processors to speed-up computations for large datasets. In addition, it contains several functions for simulation and visualization. The netgwas package is freely available at this https URL

확률적 비유사성 벡터를 활용한 변수선택기법

Pupose: Unnecessary variables in multivariate data degrade the performance of models while building or implementing a machine learning classification model. Therefore, it is important to build a model by selecting appropriate variables that can enhance its accuracy. This paper proposes a new feature selection method overcoming the parametric limitation inherent in false discovery rate (FDR) method one of the popular feature selection algorithms.<BR>Methods: We calculated the rank of variables in order of importance by randomly extracting the samples of each class and compared the absolute dissimilarity between classes. We performed various simulations to compare the classification performance of stochastically selected dissimilarity vectors.<BR>Results: The proposed algorithm is reliable when the data distribution has a nonparametric characteristics.<BR>Conclusion: The proposed idea can be adequately used to select appropriate variables in case of multivariate data having variables whose mean values cannot be representative or its distribution is unknown.

Dietary Intakes of Vegetable Protein, Folate,and Vitamins B-6 and B-12 Are Partially Correlated with Physical Functioning of Dutch Older Adults Using Copula Graphical Models

Background:In nutritional epidemiology, dealing with confounding and complex internutrient relations are major challenges. An often-used approach is dietary pattern analyses, such as principal component analysis, to deal with internutrient correlations, and to more closely resemble the true way nutrients are consumed. However, despite these improvements, these approaches still require subjective decisions in the preselection of food groups. Moreover, they do not make efficient use of multivariate dietary data, because they detect only marginal associations. We propose the use of copula graphical models (CGMs) to model and make statistical inferences regarding complex associations among variables in multivariate data, where associations between all variables can be learned simultaneously. Objectives:We aimed to reconstruct nutritional intake and physical functioning networks in Dutch older adults by applying a CGM. Methods:We addressed this issue by uncovering the pairwise associations between variables while correcting for the effect of remaining variables. More specifically, we used a CGM to infer the precision matrix, which contains all the conditional independence relations between nodes in the graph. The nonzero elements of the precision matrix indicate the presence of a direct association. We applied this method to reconstruct nutrient–physical functioning networks from the combined data of 4 studies (Nu-Age, ProMuscle, ProMO, and V-Fit, total n = 662, mean ± SD age = 75 ± 7 y). The method was implemented in the R package nutriNetwork which is freely available at https://cran.r-project.org/web/packages/nutriNetwork. Results:Greater intakes of vegetable protein and vitamin B-6 were partially correlated with higher scores on the total Short Physical Performance Battery (SPPB) and the chair rise test. Greater intakes of vitamin B-12 and folate were partially correlated with higher scores on the chair rise test and the total SPPB, respectively. Conclusions:We determined that vegetable protein, vitamin B-6, folate, and vitamin B-12 intakes are partially correlated with improved functional outcome measurements in Dutch older adults.

Constrained nonmetric principal component analysis

Constrained principal component analysis (CPCA) is a useful tool for comprehending the distinctive features of the classes of both subjects and variables in multivariate data. For example, given the class information of variables and subjects as external information, CPCA provides the principal components for the external information of both the variables and subjects. In addition to that, in CPCA, the fit results can be evaluated easily. In this study, we extend CPCA to categorical data via incorporating the notion of optimal scaling. We call our method constrained nonmetric principal component analysis (CNPCA). The advantage of this method is that it can consider the nonlinear relations between categories and estimate the components so that the fit is better than that in CPCA.

Bayesian Modelling of Dupuytren Disease by Using Gaussian Copula Graphical Models

SummaryDupuytren disease is a fibroproliferative disorder with unknown aetiology that often progresses and eventually can cause permanent contractures of the fingers affected. We provide a computationally efficient Bayesian framework to discover potential risk factors and investigate which fingers are jointly affected. Our Bayesian approach is based on Gaussian copula graphical models, which provide a way to discover the underlying conditional independence structure of variables in multivariate data of mixed types. In particular, we combine the semiparametric Gaussian copula with extended rank likelihood to analyse multivariate data of mixed types with arbitrary marginal distributions. For structural learning, we construct a computationally efficient search algorithm by using a transdimensional Markov chain Monte Carlo algorithm based on a birth–death process. In addition, to make our statistical method easily accessible to other researchers, we have implemented our method in C++ and provide an interface with R software as an R package BDgraph, which is freely available from http://CRAN.R-project.org/package=BDgraph.

Computed ABC Analysis for Rational Selection of Most Informative Variables in Multivariate Data.

ObjectiveMultivariate data sets often differ in several factors or derived statistical parameters, which have to be selected for a valid interpretation. Basing this selection on traditional statistical limits leads occasionally to the perception of losing information from a data set. This paper proposes a novel method for calculating precise limits for the selection of parameter sets.MethodsThe algorithm is based on an ABC analysis and calculates these limits on the basis of the mathematical properties of the distribution of the analyzed items. The limits im-plement the aim of any ABC analysis, i.e., comparing the increase in yield to the required additional effort. In particular, the limit for set A, the “important few”, is optimized in a way that both, the effort and the yield for the other sets (B and C), are minimized and the additional gain is optimized.ResultsAs a typical example from biomedical research, the feasibility of the ABC analysis as an objective replacement for classical subjective limits to select highly relevant variance components of pain thresholds is presented. The proposed method improved the biological inter-pretation of the results and increased the fraction of valid information that was obtained from the experimental data.ConclusionsThe method is applicable to many further biomedical problems in-cluding the creation of diagnostic complex biomarkers or short screening tests from comprehensive test batteries. Thus, the ABC analysis can be proposed as a mathematically valid replacement for traditional limits to maximize the information obtained from multivariate research data.

Visual Correlation Analysis of Numerical and Categorical Data on the Correlation Map.

Correlation analysis can reveal the complex relationships that often exist among the variables in multivariate data. However, as the number of variables grows, it can be difficult to gain a good understanding of the correlation landscape and important intricate relationships might be missed. We previously introduced a technique that arranged the variables into a 2D layout, encoding their pairwise correlations. We then used this layout as a network for the interactive ordering of axes in parallel coordinate displays. Our current work expresses the layout as a correlation map and employs it for visual correlation analysis. In contrast to matrix displays where correlations are indicated at intersections of rows and columns, our map conveys correlations by spatial proximity which is more direct and more focused on the variables in play. We make the following new contributions, some unique to our map: (1) we devise mechanisms that handle both categorical and numerical variables within a unified framework, (2) we achieve scalability for large numbers of variables via a multi-scale semantic zooming approach, (3) we provide interactive techniques for exploring the impact of value bracketing on correlations, and (4) we visualize data relations within the sub-spaces spanned by correlated variables by projecting the data into a corresponding tessellation of the map.

On the usability of three-dimensional display in parallel coordinates: Evaluating the efficiency of identifying two-dimensional relationships

In recent years, several different attempts have been made to extend the well-known technique of parallel coordinates using a three-dimensional display. This article presents an evaluation that investigates the performance of the three-dimensional parallel coordinates technique and compares it with standard, two-dimensional parallel coordinates for analysis of two-dimensional relationships. Three-dimensional parallel coordinates, based on parallel planes instead of parallel axes, have been used for many years within the information visualization community for a variety of applications. Despite its quite common use, no formal evaluation detailing its usefulness for different tasks has been conducted. The evaluation presented in this article is the first step towards determining the usefulness of this type of three-dimensional parallel coordinates. The study compared three-dimensional parallel coordinates, using two different axis configurations commonly seen in the literature, with standard two-dimensional parallel coordinates for identification of two-dimensional relationships between variables in multivariate data. This type of task and the relationships to be judged are known to be well supported by two-dimensional parallel coordinates and multi-relational three-dimensional parallel coordinates. The results show that for identification of two-dimensional relationships, two-dimensional parallel coordinates are superior to the three-dimensional extensions, in terms of both response time and accuracy. Subjective opinions were also in favour of two-dimensional parallel coordinates. This study adds to the much-needed body of work examining the usability of three-dimensional representations in information visualization and for what tasks and data a proposed method is or is not appropriate.

Effect of Interfacially Active Fractions of Some Egyptian Crude Oils on Their Emulsion Stability

Four samples from different crude oils were used for this study: light and heavy crude oils from Iran and two crude oils from Egypt, namely, Ras Gharb and Suez mix. The asphaltenes were separated from these crude oils and then the maltene (non‐asphaltenic fraction) was fractionated into waxes, aromatics, and resins. All fractions were characterized using FTIR and UV spectroscopic analyses in addition to gel permeation chromatograph (GPC). These fractions were tested for their emulsion stability. For chemometric analysis different parameters (variables) have been used to study the effect of different fractions (objects) on the emulsion stability. Such variables included the integrated areas under the stretching absorption peaks of CH in the range of 3000–2800 cm−1, C˭O in the range of 1750–1650 cm−1, and the aromatic C˭C in the range of 1650–1550 cm−1, as well as UV absorption value at 235 nm and average molecular weight (MW). Principal component analysis (PCA) and multiple linear regression (MLR) were conducted for examining the relationship between multiple variables and the stability of water‐in‐crude oil emulsions. The results of PCA explain the interrelationships between the observations and variables in multivariate data. The correlation coefficients between different parameters derived from PCA reveals that the UV absorption value and MW are strongly correlated with emulsion stability. It also reveals that the resins, asphaltenes, and maltene have better emulsion stability than waxes and lower molecular weight aromatics. The linear relationship between the parameters and the stability of water‐in‐crude oil emulsions using MLR was modeled according to the better statistical results. The obtained mathematical model can be used to predict the stability of water‐in‐crude oil emulsions from the chemical groups and functionalities in each crude oil fraction.

Two-dimensional correlation analysis

This tutorial reviews the recent computational advances in two-dimensional (2D) correlation spectroscopy, presents the theory, and provides examples applying 2D correlation analysis. Two-dimensional correlation analysis is a method for visualizing the relationships among the variables in multivariate data and their temporal behavior by applying the complex cross-correlation function. This function measures correlations that occur at the same rate or frequency with respect to the data acquisition time. The complex cross-correlation function yields real and imaginary components that contain information about the phase behavior of the variables. The real component provides information about mutually dependent in-phase variations. Variations that occur out-of-phase (with time lags or leads) are given by the imaginary component. Two-dimensional correlation analysis is a general analysis method that can be used for the treatment of data from a variety of applications including image, distribution, environmental, and kinetic analysis.