scholarly journals Separation of Chromatographic Co-Eluted Compounds by Clustering and by Functional Data Analysis

Metabolites ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 214
Author(s):  
Aneta Sawikowska ◽  
Anna Piasecka ◽  
Piotr Kachlicki ◽  
Paweł Krajewski
Keyword(s):  
Simulated Data ◽  
Principal Component ◽  
Real Data ◽  
Functional Principal Component Analysis ◽  
Additional Advantage ◽  
Time Alignment ◽  
Peak Separation ◽  
Biological Mixtures ◽  
Overlapping Peaks ◽  
Retention Time Alignment

Peak overlapping is a common problem in chromatography, mainly in the case of complex biological mixtures, i.e., metabolites. Due to the existence of the phenomenon of co-elution of different compounds with similar chromatographic properties, peak separation becomes challenging. In this paper, two computational methods of separating peaks, applied, for the first time, to large chromatographic datasets, are described, compared, and experimentally validated. The methods lead from raw observations to data that can form inputs for statistical analysis. First, in both methods, data are normalized by the mass of sample, the baseline is removed, retention time alignment is conducted, and detection of peaks is performed. Then, in the first method, clustering is used to separate overlapping peaks, whereas in the second method, functional principal component analysis (FPCA) is applied for the same purpose. Simulated data and experimental results are used as examples to present both methods and to compare them. Real data were obtained in a study of metabolomic changes in barley (Hordeum vulgare) leaves under drought stress. The results suggest that both methods are suitable for separation of overlapping peaks, but the additional advantage of the FPCA is the possibility to assess the variability of individual compounds present within the same peaks of different chromatograms.

scholarly journals Tailored multivariate analysis for modulated enhanced diffraction

2015 ◽  
Vol 48 (6) ◽  
pp. 1679-1691 ◽  
Author(s):  
Rocco Caliandro ◽  
Pietro Guccione ◽  
Giovanni Nico ◽  
Goknur Tutuncu ◽  
Jonathan C. Hanson
Keyword(s):  
Multivariate Analysis ◽  
Simulated Data ◽  
Principal Component ◽  
Real Data ◽  
System Response ◽  
Structural Variations ◽  
Structural Investigations ◽  
Decomposition Approach ◽  
Figures Of Merit ◽  
Decomposition Procedure

Modulated enhanced diffraction (MED) is a technique allowing the dynamic structural characterization of crystalline materials subjected to an external stimulus, which is particularly suited forin situandoperandostructural investigations at synchrotron sources. Contributions from the (active) part of the crystal system that varies synchronously with the stimulus can be extracted by an offline analysis, which can only be applied in the case of periodic stimuli and linear system responses. In this paper a new decomposition approach based on multivariate analysis is proposed. The standard principal component analysis (PCA) is adapted to treat MED data: specific figures of merit based on their scores and loadings are found, and the directions of the principal components obtained by PCA are modified to maximize such figures of merit. As a result, a general method to decompose MED data, called optimum constrained components rotation (OCCR), is developed, which produces very precise results on simulated data, even in the case of nonperiodic stimuli and/or nonlinear responses. The multivariate analysis approach is able to supply in one shot both the diffraction pattern related to the active atoms (through the OCCR loadings) and the time dependence of the system response (through the OCCR scores). When applied to real data, OCCR was able to supply only the latter information, as the former was hindered by changes in abundances of different crystal phases, which occurred besides structural variations in the specific case considered. To develop a decomposition procedure able to cope with this combined effect represents the next challenge in MED analysis.

scholarly journals Detecting Inversions with PCA in the Presence of Population Structure

2019 ◽  
Author(s):  
Ronald J. Nowling ◽  
Krystal R. Manke ◽  
Scott J. Emrich
Keyword(s):  
Simulated Data ◽  
Principal Component ◽  
Real Data ◽  
Malaria Vectors ◽  
Anopheles Coluzzii ◽  
Nucleotide Polymorphisms ◽  
Data Set ◽  
Single Nucleotide ◽  
Closely Related Species ◽  
Proper Analysis

ABSTRACTChromosomal inversions are associated with reproductive isolation and adaptation in insects such as Drosophila melanogaster and the malaria vectors Anopheles gambiae and Anopheles coluzzii. While methods based on read alignment have been useful in humans for detecting inversions, these methods are less successful in insects due to long repeated sequences at the breakpoints. Alternatively, inversions can be detected using principal component analysis (PCA) of single nucleotide polymorphisms (SNPs). We apply PCA-based inversion detection to a simulated data set and real data from multiple insect species, which vary in complexity from a single inversion in samples drawn from a single population to analyzing multiple overlapping inversions occurring in closely-related species, samples of which that were generated from multiple geographic locations. We show empirically that proper analysis of these data can be challenging when multiple inversions or populations are present, and that our alternative framework is more robust in these more difficult scenarios.

A generalization of functional clustering for discrete multivariate longitudinal data

2020 ◽  
Vol 29 (11) ◽  
pp. 3205-3217
Author(s):  
Yaeji Lim ◽  
Ying Kuen Cheung ◽  
Hee-Seok Oh
Keyword(s):  
Longitudinal Data ◽  
Gaussian Process ◽  
Clustering Algorithm ◽  
Principal Component ◽  
Real Data ◽  
Functional Principal Component Analysis ◽  
Functional Clustering ◽  
Multivariate Gaussian ◽  
Discrete Longitudinal Data ◽  
Multivariate Gaussian Process

This paper presents a new model-based generalized functional clustering method for discrete longitudinal data, such as multivariate binomial and Poisson distributed data. For this purpose, we propose a multivariate functional principal component analysis (MFPCA)-based clustering procedure for a latent multivariate Gaussian process instead of the original functional data directly. The main contribution of this study is two-fold: modeling of discrete longitudinal data with the latent multivariate Gaussian process and developing of a clustering algorithm based on MFPCA coupled with the latent multivariate Gaussian process. Numerical experiments, including real data analysis and a simulation study, demonstrate the promising empirical properties of the proposed approach.

scholarly journals G-Tric: generating three-way synthetic datasets with triclustering solutions

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
João Lobo ◽  
Rui Henriques ◽  
Sara C. Madeira
Keyword(s):  
State Of The Art ◽  
Synthetic Data ◽  
Ground Truth ◽  
Real Data ◽  
Three Dimensions ◽  
Additional Advantage ◽  
Urban Dynamics ◽  
Data Generator ◽  
Real World Datasets ◽  
Synthetic Datasets

Abstract Background Three-way data started to gain popularity due to their increasing capacity to describe inherently multivariate and temporal events, such as biological responses, social interactions along time, urban dynamics, or complex geophysical phenomena. Triclustering, subspace clustering of three-way data, enables the discovery of patterns corresponding to data subspaces (triclusters) with values correlated across the three dimensions (observations $$\times$$ × features $$\times$$ × contexts). With increasing number of algorithms being proposed, effectively comparing them with state-of-the-art algorithms is paramount. These comparisons are usually performed using real data, without a known ground-truth, thus limiting the assessments. In this context, we propose a synthetic data generator, G-Tric, allowing the creation of synthetic datasets with configurable properties and the possibility to plant triclusters. The generator is prepared to create datasets resembling real 3-way data from biomedical and social data domains, with the additional advantage of further providing the ground truth (triclustering solution) as output. Results G-Tric can replicate real-world datasets and create new ones that match researchers needs across several properties, including data type (numeric or symbolic), dimensions, and background distribution. Users can tune the patterns and structure that characterize the planted triclusters (subspaces) and how they interact (overlapping). Data quality can also be controlled, by defining the amount of missing, noise or errors. Furthermore, a benchmark of datasets resembling real data is made available, together with the corresponding triclustering solutions (planted triclusters) and generating parameters. Conclusions Triclustering evaluation using G-Tric provides the possibility to combine both intrinsic and extrinsic metrics to compare solutions that produce more reliable analyses. A set of predefined datasets, mimicking widely used three-way data and exploring crucial properties was generated and made available, highlighting G-Tric’s potential to advance triclustering state-of-the-art by easing the process of evaluating the quality of new triclustering approaches.

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

scholarly journals Penalized partial least squares for pleiotropy

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Camilo Broc ◽  
Therese Truong ◽  
Benoit Liquet
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Association Studies ◽  
A Priori ◽  
Simulated Data ◽  
Real Data ◽  
Genome Wide Association Studies ◽  
Genetic Associations ◽  
Multiple Traits ◽  
Application Fields

Abstract Background The increasing number of genome-wide association studies (GWAS) has revealed several loci that are associated to multiple distinct phenotypes, suggesting the existence of pleiotropic effects. Highlighting these cross-phenotype genetic associations could help to identify and understand common biological mechanisms underlying some diseases. Common approaches test the association between genetic variants and multiple traits at the SNP level. In this paper, we propose a novel gene- and a pathway-level approach in the case where several independent GWAS on independent traits are available. The method is based on a generalization of the sparse group Partial Least Squares (sgPLS) to take into account groups of variables, and a Lasso penalization that links all independent data sets. This method, called joint-sgPLS, is able to convincingly detect signal at the variable level and at the group level. Results Our method has the advantage to propose a global readable model while coping with the architecture of data. It can outperform traditional methods and provides a wider insight in terms of a priori information. We compared the performance of the proposed method to other benchmark methods on simulated data and gave an example of application on real data with the aim to highlight common susceptibility variants to breast and thyroid cancers. Conclusion The joint-sgPLS shows interesting properties for detecting a signal. As an extension of the PLS, the method is suited for data with a large number of variables. The choice of Lasso penalization copes with architectures of groups of variables and observations sets. Furthermore, although the method has been applied to a genetic study, its formulation is adapted to any data with high number of variables and an exposed a priori architecture in other application fields.

scholarly journals Calibration of Camera and Flash LiDAR System with a Triangular Pyramid Target

2021 ◽  
Vol 11 (2) ◽  
pp. 582
Author(s):  
Zean Bu ◽  
Changku Sun ◽  
Peng Wang ◽  
Hang Dong
Keyword(s):  
Simulated Data ◽  
Real Data ◽  
Calibration Method ◽  
Multiple Sensors ◽  
Triangular Pyramid ◽  
World Coordinate System ◽  
Flash Lidar ◽  
Novel Method ◽  
3D Information ◽  
Incremental Validation

Calibration between multiple sensors is a fundamental procedure for data fusion. To address the problems of large errors and tedious operation, we present a novel method to conduct the calibration between light detection and ranging (LiDAR) and camera. We invent a calibration target, which is an arbitrary triangular pyramid with three chessboard patterns on its three planes. The target contains both 3D information and 2D information, which can be utilized to obtain intrinsic parameters of the camera and extrinsic parameters of the system. In the proposed method, the world coordinate system is established through the triangular pyramid. We extract the equations of triangular pyramid planes to find the relative transformation between two sensors. One capture of camera and LiDAR is sufficient for calibration, and errors are reduced by minimizing the distance between points and planes. Furthermore, the accuracy can be increased by more captures. We carried out experiments on simulated data with varying degrees of noise and numbers of frames. Finally, the calibration results were verified by real data through incremental validation and analyzing the root mean square error (RMSE), demonstrating that our calibration method is robust and provides state-of-the-art performance.

scholarly journals Prediction of Fuel Poverty Potential Risk Index Using Six Regression Algorithms: A Case-Study of Chilean Social Dwellings

2021 ◽  
Vol 13 (5) ◽  
pp. 2426
Author(s):  
David Bienvenido-Huertas ◽  
Jesús A. Pulido-Arcas ◽  
Carlos Rubio-Bellido ◽  
Alexis Pérez-Fargallo
Keyword(s):  
Low Income ◽  
Potential Risk ◽  
Energy Use ◽  
Risk Index ◽  
Computing Time ◽  
Simulated Data ◽  
Real Data ◽  
Support Vector ◽  
Energy Poverty ◽  
Regression Algorithms

In recent times, studies about the accuracy of algorithms to predict different aspects of energy use in the building sector have flourished, being energy poverty one of the issues that has received considerable critical attention. Previous studies in this field have characterized it using different indicators, but they have failed to develop instruments to predict the risk of low-income households falling into energy poverty. This research explores the way in which six regression algorithms can accurately forecast the risk of energy poverty by means of the fuel poverty potential risk index. Using data from the national survey of socioeconomic conditions of Chilean households and generating data for different typologies of social dwellings (e.g., form ratio or roof surface area), this study simulated 38,880 cases and compared the accuracy of six algorithms. Multilayer perceptron, M5P and support vector regression delivered the best accuracy, with correlation coefficients over 99.5%. In terms of computing time, M5P outperforms the rest. Although these results suggest that energy poverty can be accurately predicted using simulated data, it remains necessary to test the algorithms against real data. These results can be useful in devising policies to tackle energy poverty in advance.

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