Identification of Block-Structured Covariance Matrix on an Example of Metabolomic Data
Modern investigation techniques (e.g., metabolomic, proteomic, lipidomic, genomic, transcriptomic, phenotypic), allow to collect high-dimensional data, where the number of observations is smaller than the number of features. In such cases, for statistical analyzing, standard methods cannot be applie...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Online Access: | https://www.mdpi.com/2297-8739/8/11/205 |
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| author | Adam Mieldzioc Monika Mokrzycka Aneta Sawikowska |
| author_facet | Adam Mieldzioc Monika Mokrzycka Aneta Sawikowska |
| author_sort | Adam Mieldzioc |
| collection | DOAJ |
| description | Modern investigation techniques (e.g., metabolomic, proteomic, lipidomic, genomic, transcriptomic, phenotypic), allow to collect high-dimensional data, where the number of observations is smaller than the number of features. In such cases, for statistical analyzing, standard methods cannot be applied or lead to ill-conditioned estimators of the covariance matrix. To analyze the data, we need an estimator of the covariance matrix with good properties (e.g., positive definiteness), and therefore covariance matrix identification is crucial. The paper presents an approach to determine the block-structured estimator of the covariance matrix based on an example of metabolomic data on the drought resistance of barley. This method can be used in many fields of science, e.g., in agriculture, medicine, food and nutritional sciences, toxicology, functional genomics and nutrigenomics. |
| first_indexed | 2024-03-10T05:04:10Z |
| format | Article |
| id | doaj.art-73c315c0f9af43f1b48a7627fe433471 |
| institution | Directory Open Access Journal |
| issn | 2297-8739 |
| language | English |
| last_indexed | 2024-03-10T05:04:10Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Separations |
| spelling | doaj.art-73c315c0f9af43f1b48a7627fe4334712023-11-23T01:29:50ZengMDPI AGSeparations2297-87392021-11-0181120510.3390/separations8110205Identification of Block-Structured Covariance Matrix on an Example of Metabolomic DataAdam Mieldzioc0Monika Mokrzycka1Aneta Sawikowska2Department of Mathematical and Statistical Methods, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, PolandInstitute of Plant Genetics, Polish Academy of Sciences, Strzeszyńska 34, 60-479 Poznań, PolandDepartment of Mathematical and Statistical Methods, Poznań University of Life Sciences, Wojska Polskiego 28, 60-637 Poznań, PolandModern investigation techniques (e.g., metabolomic, proteomic, lipidomic, genomic, transcriptomic, phenotypic), allow to collect high-dimensional data, where the number of observations is smaller than the number of features. In such cases, for statistical analyzing, standard methods cannot be applied or lead to ill-conditioned estimators of the covariance matrix. To analyze the data, we need an estimator of the covariance matrix with good properties (e.g., positive definiteness), and therefore covariance matrix identification is crucial. The paper presents an approach to determine the block-structured estimator of the covariance matrix based on an example of metabolomic data on the drought resistance of barley. This method can be used in many fields of science, e.g., in agriculture, medicine, food and nutritional sciences, toxicology, functional genomics and nutrigenomics.https://www.mdpi.com/2297-8739/8/11/205covariance structurecompound symmetry matrixfirst-order autoregression matrixToeplitz matrixestimationstructure identification |
| spellingShingle | Adam Mieldzioc Monika Mokrzycka Aneta Sawikowska Identification of Block-Structured Covariance Matrix on an Example of Metabolomic Data Separations covariance structure compound symmetry matrix first-order autoregression matrix Toeplitz matrix estimation structure identification |
| title | Identification of Block-Structured Covariance Matrix on an Example of Metabolomic Data |
| title_full | Identification of Block-Structured Covariance Matrix on an Example of Metabolomic Data |
| title_fullStr | Identification of Block-Structured Covariance Matrix on an Example of Metabolomic Data |
| title_full_unstemmed | Identification of Block-Structured Covariance Matrix on an Example of Metabolomic Data |
| title_short | Identification of Block-Structured Covariance Matrix on an Example of Metabolomic Data |
| title_sort | identification of block structured covariance matrix on an example of metabolomic data |
| topic | covariance structure compound symmetry matrix first-order autoregression matrix Toeplitz matrix estimation structure identification |
| url | https://www.mdpi.com/2297-8739/8/11/205 |
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