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Roy S, Singh J, Ray SS. Weighted Combination of Łukasiewicz implication and Fuzzy Jaccard similarity in Hybrid Ensemble Framework (WCLFJHEF) for Gene Selection. Comput Biol Med 2024; 170:107981. [PMID: 38262204 DOI: 10.1016/j.compbiomed.2024.107981] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Revised: 01/02/2024] [Accepted: 01/12/2024] [Indexed: 01/25/2024]
Abstract
A framework is developed for gene expression analysis by introducing fuzzy Jaccard similarity (FJS) and combining Łukasiewicz implication with it through weights in hybrid ensemble framework (WCLFJHEF) for gene selection in cancer. The method is called weighted combination of Łukasiewicz implication and fuzzy Jaccard similarity in hybrid ensemble framework (WCLFJHEF). While the fuzziness in Jaccard similarity is incorporated by using the existing Gödel fuzzy logic, the weights are obtained by maximizing the average F-score of selected genes in classifying the cancer patients. The patients are first divided into different clusters, based on the number of patient groups, using average linkage agglomerative clustering and a new score, called WCLFJ (weighted combination of Łukasiewicz implication and fuzzy Jaccard similarity). The genes are then selected from each cluster separately using filter based Relief-F and wrapper based SVMRFE (Support Vector Machine with Recursive Feature Elimination). A gene (feature) pool is created by considering the union of selected features for all the clusters. A set of informative genes is selected from the pool using sequential backward floating search (SBFS) algorithm. Patients are then classified using Naïve Bayes'(NB) and Support Vector Machine (SVM) separately, using the selected genes and the related F-scores are calculated. The weights in WCLFJ are then updated iteratively to maximize the average F-score obtained from the results of the classifier. The effectiveness of WCLFJHEF is demonstrated on six gene expression datasets. The average values of accuracy, F-score, recall, precision and MCC over all the datasets, are 95%, 94%, 94%, 94%, and 90%, respectively. The explainability of the selected genes is shown using SHapley Additive exPlanations (SHAP) values and this information is further used to rank them. The relevance of the selected gene set are biologically validated using the KEGG Pathway, Gene Ontology (GO), and existing literatures. It is seen that the genes that are selected by WCLFJHEF are candidates for genomic alterations in the various cancer types. The source code of WCLFJHEF is available at http://www.isical.ac.in/~shubhra/WCLFJHEF.html.
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Affiliation(s)
- Sukriti Roy
- Machine Intelligence Unit, Indian Statistical Institute, Kolkata 700108, India.
| | - Joginder Singh
- Center for Soft Computing Research, Indian Statistical Institute, Kolkata 700108, India.
| | - Shubhra Sankar Ray
- Machine Intelligence Unit, Indian Statistical Institute, Kolkata 700108, India; Center for Soft Computing Research, Indian Statistical Institute, Kolkata 700108, India.
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Odaka M, Magnin M, Inoue K. Gene network inference from single-cell omics data and domain knowledge for constructing COVID-19-specific ICAM1-associated pathways. Front Genet 2023; 14:1250545. [PMID: 37719701 PMCID: PMC10501835 DOI: 10.3389/fgene.2023.1250545] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 08/16/2023] [Indexed: 09/19/2023] Open
Abstract
Introduction: Intercellular adhesion molecule 1 (ICAM-1) is a critical molecule responsible for interactions between cells. Previous studies have suggested that ICAM-1 triggers cell-to-cell transmission of HIV-1 or HTLV-1, that SARS-CoV-2 shares several features with these viruses via interactions between cells, and that SARS-CoV-2 cell-to-cell transmission is associated with COVID-19 severity. From these previous arguments, it is assumed that ICAM-1 can be related to SARS-CoV-2 cell-to-cell transmission in COVID-19 patients. Indeed, the time-dependent change of the ICAM-1 expression level has been detected in COVID-19 patients. However, signaling pathways that consist of ICAM-1 and other molecules interacting with ICAM-1 are not identified in COVID-19. For example, the current COVID-19 Disease Map has no entry for those pathways. Therefore, discovering unknown ICAM1-associated pathways will be indispensable for clarifying the mechanism of COVID-19. Materials and methods: This study builds ICAM1-associated pathways by gene network inference from single-cell omics data and multiple knowledge bases. First, single-cell omics data analysis extracts coexpressed genes with significant differences in expression levels with spurious correlations removed. Second, knowledge bases validate the models. Finally, mapping the models onto existing pathways identifies new ICAM1-associated pathways. Results: Comparison of the obtained pathways between different cell types and time points reproduces the known pathways and indicates the following two unknown pathways: (1) upstream pathway that includes proteins in the non-canonical NF-κB pathway and (2) downstream pathway that contains integrins and cytoskeleton or motor proteins for cell transformation. Discussion: In this way, data-driven and knowledge-based approaches are integrated into gene network inference for ICAM1-associated pathway construction. The results can contribute to repairing and completing the COVID-19 Disease Map, thereby improving our understanding of the mechanism of COVID-19.
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Affiliation(s)
- Mitsuhiro Odaka
- The Graduate University for Advanced Studies, SOKENDAI, Tokyo, Japan
- Principles of Informatics Research Division, National Institute of Informatics, Tokyo, Japan
- Laboratoire des Sciences du Numérique de Nantes, École Centrale de Nantes, Nantes Université, UMR 6004, Nantes, France
- Japan Society for the Promotion of Science, Tokyo, Japan
| | - Morgan Magnin
- Principles of Informatics Research Division, National Institute of Informatics, Tokyo, Japan
- Laboratoire des Sciences du Numérique de Nantes, École Centrale de Nantes, Nantes Université, UMR 6004, Nantes, France
| | - Katsumi Inoue
- The Graduate University for Advanced Studies, SOKENDAI, Tokyo, Japan
- Principles of Informatics Research Division, National Institute of Informatics, Tokyo, Japan
- Laboratoire des Sciences du Numérique de Nantes, École Centrale de Nantes, Nantes Université, UMR 6004, Nantes, France
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Watts J, Allen E, Mitoubsi A, Khojandi A, Eales J, Papamarkou T. Towards Faster Gene Expression Prediction via Dimensionality Reduction and Feature Selection. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2023; 2023:1-4. [PMID: 38083578 DOI: 10.1109/embc40787.2023.10340962] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2023]
Abstract
The majority of genes have a genetic component to their expression. Elastic nets have been shown effective at predicting tissue-specific, individual-level gene expression from genotype data. We apply principal component analysis (PCA), linkage disequilibrium pruning, or the combination of the two to reduce, or generate, a lower-dimensional representation of the genetic variants used as inputs to the elastic net models for the prediction of gene expression. Our results show that, in general, elastic nets attain their best performance when all genetic variants are included as inputs; however, a relatively low number of principal components can effectively summarize the majority of genetic variation while reducing the overall computation time. Specifically, 100 principal components reduce the computational time of the models by over 80% with only an 8% loss in R2. Finally, linkage disequilibrium pruning does not effectively reduce the genetic variants for predicting gene expression. As predictive models are commonly made for over 27,000 genes for more than 50 tissues, PCA may provide an effective method for reducing the computational burden of gene expression analysis.
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Min J, Tu J, Xu C, Lukas H, Shin S, Yang Y, Solomon SA, Mukasa D, Gao W. Skin-Interfaced Wearable Sweat Sensors for Precision Medicine. Chem Rev 2023; 123:5049-5138. [PMID: 36971504 PMCID: PMC10406569 DOI: 10.1021/acs.chemrev.2c00823] [Citation(s) in RCA: 82] [Impact Index Per Article: 82.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
Abstract
Wearable sensors hold great potential in empowering personalized health monitoring, predictive analytics, and timely intervention toward personalized healthcare. Advances in flexible electronics, materials science, and electrochemistry have spurred the development of wearable sweat sensors that enable the continuous and noninvasive screening of analytes indicative of health status. Existing major challenges in wearable sensors include: improving the sweat extraction and sweat sensing capabilities, improving the form factor of the wearable device for minimal discomfort and reliable measurements when worn, and understanding the clinical value of sweat analytes toward biomarker discovery. This review provides a comprehensive review of wearable sweat sensors and outlines state-of-the-art technologies and research that strive to bridge these gaps. The physiology of sweat, materials, biosensing mechanisms and advances, and approaches for sweat induction and sampling are introduced. Additionally, design considerations for the system-level development of wearable sweat sensing devices, spanning from strategies for prolonged sweat extraction to efficient powering of wearables, are discussed. Furthermore, the applications, data analytics, commercialization efforts, challenges, and prospects of wearable sweat sensors for precision medicine are discussed.
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Affiliation(s)
- Jihong Min
- Andrew and Peggy Cherng Department of Medical Engineering, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, 91125, USA
| | - Jiaobing Tu
- Andrew and Peggy Cherng Department of Medical Engineering, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, 91125, USA
| | - Changhao Xu
- Andrew and Peggy Cherng Department of Medical Engineering, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, 91125, USA
| | - Heather Lukas
- Andrew and Peggy Cherng Department of Medical Engineering, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, 91125, USA
| | - Soyoung Shin
- Andrew and Peggy Cherng Department of Medical Engineering, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, 91125, USA
| | - Yiran Yang
- Andrew and Peggy Cherng Department of Medical Engineering, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, 91125, USA
| | - Samuel A. Solomon
- Andrew and Peggy Cherng Department of Medical Engineering, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, 91125, USA
| | - Daniel Mukasa
- Andrew and Peggy Cherng Department of Medical Engineering, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, 91125, USA
| | - Wei Gao
- Andrew and Peggy Cherng Department of Medical Engineering, Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California, 91125, USA
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A systematic review of artificial intelligence-based COVID-19 modeling on multimodal genetic information. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2023; 179:1-9. [PMID: 36809830 PMCID: PMC9938959 DOI: 10.1016/j.pbiomolbio.2023.02.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Revised: 02/07/2023] [Accepted: 02/12/2023] [Indexed: 02/21/2023]
Abstract
This study systematically reviews the Artificial Intelligence (AI) methods developed to resolve the critical process of COVID-19 gene data analysis, including diagnosis, prognosis, biomarker discovery, drug responsiveness, and vaccine efficacy. This systematic review follows the guidelines of Preferred Reporting for Systematic Reviews and Meta-Analyses (PRISMA). We searched PubMed, Embase, Web of Science, and Scopus databases to identify the relevant articles from January 2020 to June 2022. It includes the published studies of AI-based COVID-19 gene modeling extracted through relevant keyword searches in academic databases. This study included 48 articles discussing AI-based genetic studies for several objectives. Ten articles confer about the COVID-19 gene modeling with computational tools, and five articles evaluated ML-based diagnosis with observed accuracy of 97% on SARS-CoV-2 classification. Gene-based prognosis study reviewed three articles and found host biomarkers detecting COVID-19 progression with 90% accuracy. Twelve manuscripts reviewed the prediction models with various genome analysis studies, nine articles examined the gene-based in silico drug discovery, and another nine investigated the AI-based vaccine development models. This study compiled the novel coronavirus gene biomarkers and targeted drugs identified through ML approaches from published clinical studies. This review provided sufficient evidence to delineate the potential of AI in analyzing complex gene information for COVID-19 modeling on multiple aspects like diagnosis, drug discovery, and disease dynamics. AI models entrenched a substantial positive impact by enhancing the efficiency of the healthcare system during the COVID-19 pandemic.
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Hasan MM, Islam MU, Sadeq MJ, Fung WK, Uddin J. Review on the Evaluation and Development of Artificial Intelligence for COVID-19 Containment. SENSORS (BASEL, SWITZERLAND) 2023; 23:527. [PMID: 36617124 PMCID: PMC9824505 DOI: 10.3390/s23010527] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Revised: 12/23/2022] [Accepted: 12/29/2022] [Indexed: 06/17/2023]
Abstract
Artificial intelligence has significantly enhanced the research paradigm and spectrum with a substantiated promise of continuous applicability in the real world domain. Artificial intelligence, the driving force of the current technological revolution, has been used in many frontiers, including education, security, gaming, finance, robotics, autonomous systems, entertainment, and most importantly the healthcare sector. With the rise of the COVID-19 pandemic, several prediction and detection methods using artificial intelligence have been employed to understand, forecast, handle, and curtail the ensuing threats. In this study, the most recent related publications, methodologies and medical reports were investigated with the purpose of studying artificial intelligence's role in the pandemic. This study presents a comprehensive review of artificial intelligence with specific attention to machine learning, deep learning, image processing, object detection, image segmentation, and few-shot learning studies that were utilized in several tasks related to COVID-19. In particular, genetic analysis, medical image analysis, clinical data analysis, sound analysis, biomedical data classification, socio-demographic data analysis, anomaly detection, health monitoring, personal protective equipment (PPE) observation, social control, and COVID-19 patients' mortality risk approaches were used in this study to forecast the threatening factors of COVID-19. This study demonstrates that artificial-intelligence-based algorithms integrated into Internet of Things wearable devices were quite effective and efficient in COVID-19 detection and forecasting insights which were actionable through wide usage. The results produced by the study prove that artificial intelligence is a promising arena of research that can be applied for disease prognosis, disease forecasting, drug discovery, and to the development of the healthcare sector on a global scale. We prove that artificial intelligence indeed played a significantly important role in helping to fight against COVID-19, and the insightful knowledge provided here could be extremely beneficial for practitioners and research experts in the healthcare domain to implement the artificial-intelligence-based systems in curbing the next pandemic or healthcare disaster.
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Affiliation(s)
- Md. Mahadi Hasan
- Department of Computer Science and Engineering, Asian University of Bangladesh, Ashulia 1349, Bangladesh
| | - Muhammad Usama Islam
- School of Computing and Informatics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
| | - Muhammad Jafar Sadeq
- Department of Computer Science and Engineering, Asian University of Bangladesh, Ashulia 1349, Bangladesh
| | - Wai-Keung Fung
- Department of Applied Computing and Engineering, Cardiff School of Technologies, Cardiff Metropolitan University, Cardiff CF5 2YB, UK
| | - Jasim Uddin
- Department of Applied Computing and Engineering, Cardiff School of Technologies, Cardiff Metropolitan University, Cardiff CF5 2YB, UK
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Barbosa-Silva A, Magalhães M, da Silva GF, da Silva FAB, Carneiro FRG, Carels N. A Data Science Approach for the Identification of Molecular Signatures of Aggressive Cancers. Cancers (Basel) 2022; 14:2325. [PMID: 35565454 PMCID: PMC9103663 DOI: 10.3390/cancers14092325] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2022] [Revised: 03/04/2022] [Accepted: 03/12/2022] [Indexed: 02/05/2023] Open
Abstract
The main hallmarks of cancer include sustaining proliferative signaling and resisting cell death. We analyzed the genes of the WNT pathway and seven cross-linked pathways that may explain the differences in aggressiveness among cancer types. We divided six cancer types (liver, lung, stomach, kidney, prostate, and thyroid) into classes of high (H) and low (L) aggressiveness considering the TCGA data, and their correlations between Shannon entropy and 5-year overall survival (OS). Then, we used principal component analysis (PCA), a random forest classifier (RFC), and protein-protein interactions (PPI) to find the genes that correlated with aggressiveness. Using PCA, we found GRB2, CTNNB1, SKP1, CSNK2A1, PRKDC, HDAC1, YWHAZ, YWHAB, and PSMD2. Except for PSMD2, the RFC analysis showed a different list, which was CAD, PSMD14, APH1A, PSMD2, SHC1, TMEFF2, PSMD11, H2AFZ, PSMB5, and NOTCH1. Both methods use different algorithmic approaches and have different purposes, which explains the discrepancy between the two gene lists. The key genes of aggressiveness found by PCA were those that maximized the separation of H and L classes according to its third component, which represented 19% of the total variance. By contrast, RFC classified whether the RNA-seq of a tumor sample was of the H or L type. Interestingly, PPIs showed that the genes of PCA and RFC lists were connected neighbors in the PPI signaling network of WNT and cross-linked pathways.
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Affiliation(s)
- Adriano Barbosa-Silva
- Center for Medical Statistics, Informatics and Intelligent Systems, Institute for Artificial Intelligence, Medical University of Vienna, 1090 Vienna, Austria;
- Centre for Translational Bioinformatics, William Harvey Research Institute, Queen Mary University of London, London E14NS, UK
- ITTM S.A.—Information Technology for Translational Medicine, Esch-sur-Alzette, 4354 Luxembourg, Luxembourg
| | - Milena Magalhães
- Plataforma de Modelagem de Sistemas Biológicos, Center for Technology Development in Health (CDTS), Oswaldo Cruz Foundation (FIOCRUZ), Rio de Janeiro 21040900, Brazil; (M.M.); (G.F.d.S.)
| | - Gilberto Ferreira da Silva
- Plataforma de Modelagem de Sistemas Biológicos, Center for Technology Development in Health (CDTS), Oswaldo Cruz Foundation (FIOCRUZ), Rio de Janeiro 21040900, Brazil; (M.M.); (G.F.d.S.)
| | - Fabricio Alves Barbosa da Silva
- Laboratório de Modelagem Computacional de Sistemas Biológicos, Scientific Computing Program, Oswaldo Cruz Foundation (FIOCRUZ), Rio de Janeiro 21040900, Brazil;
| | - Flávia Raquel Gonçalves Carneiro
- Center for Technology Development in Health (CDTS), Oswaldo Cruz Foundation (FIOCRUZ), Rio de Janeiro 21040900, Brazil
- Laboratório Interdisciplinar de Pesquisas Médicas, Instituto Oswaldo Cruz, Oswaldo Cruz Foundation (FIOCRUZ), Rio de Janeiro 21040900, Brazil
- Program of Immunology and Tumor Biology, Brazilian National Cancer Institute (INCA), Rio de Janeiro 20231050, Brazil
| | - Nicolas Carels
- Plataforma de Modelagem de Sistemas Biológicos, Center for Technology Development in Health (CDTS), Oswaldo Cruz Foundation (FIOCRUZ), Rio de Janeiro 21040900, Brazil; (M.M.); (G.F.d.S.)
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Jeong J, Kim T, Lee BJ, Lee J. PCA-based sub-surface structure and defect analysis for germanium-on-nothing using nanoscale surface topography. Sci Rep 2022; 12:7205. [PMID: 35504973 PMCID: PMC9065006 DOI: 10.1038/s41598-022-11185-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Accepted: 04/19/2022] [Indexed: 11/09/2022] Open
Abstract
Empty space in germanium (ESG) or germanium-on-nothing (GON) are unique self-assembled germanium structures with multiscale cavities of various morphologies. Due to their simple fabrication process and high-quality crystallinity after self-assembly, they can be applied in various fields including micro-/nanoelectronics, optoelectronics, and precision sensors, to name a few. In contrast to their simple fabrication, inspection is intrinsically difficult due to buried structures. Today, ultrasonic atomic force microscopy and interferometry are some prevalent non-destructive 3-D imaging methods that are used to inspect the underlying ESG structures. However, these non-destructive characterization methods suffer from low throughput due to slow measurement speed and limited measurable thickness. To overcome these limitations, this work proposes a new methodology to construct a principal-component-analysis based database that correlates surface images with empirically determined sub-surface structures. Then, from this database, the morphology of buried sub-surface structure is determined only using surface topography. Since the acquisition rate of a single nanoscale surface micrograph is up to a few orders faster than a thorough 3-D sub-surface analysis, the proposed methodology benefits from improved throughput compared to current inspection methods. Also, an empirical destructive test essentially resolves the measurable thickness limitation. We also demonstrate the practicality of the proposed methodology by applying it to GON devices to selectively detect and quantitatively analyze surface defects. Compared to state-of-the-art deep learning-based defect detection schemes, our method is much effortlessly finetunable for specific applications. In terms of sub-surface analysis, this work proposes a fast, robust, and high-resolution methodology which could potentially replace the conventional exhaustive sub-surface inspection schemes.
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Affiliation(s)
- Jaewoo Jeong
- Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 34141, South Korea.,Center for Extreme Thermal Physics and Manufacturing, Korea Advanced Institute of Science and Technology, Daejeon, 34141, South Korea
| | - Taeyeong Kim
- Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 34141, South Korea.,Center for Extreme Thermal Physics and Manufacturing, Korea Advanced Institute of Science and Technology, Daejeon, 34141, South Korea
| | - Bong Jae Lee
- Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 34141, South Korea.,Center for Extreme Thermal Physics and Manufacturing, Korea Advanced Institute of Science and Technology, Daejeon, 34141, South Korea
| | - Jungchul Lee
- Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 34141, South Korea. .,Center for Extreme Thermal Physics and Manufacturing, Korea Advanced Institute of Science and Technology, Daejeon, 34141, South Korea.
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Application of principal component analysis on temporal evolution of COVID-19. PLoS One 2021; 16:e0260899. [PMID: 34855909 PMCID: PMC8638895 DOI: 10.1371/journal.pone.0260899] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2021] [Accepted: 11/18/2021] [Indexed: 11/20/2022] Open
Abstract
The COVID-19 is one of the worst pandemics in modern history. We applied principal component analysis (PCA) to the daily time series of the COVID-19 death cases and confirmed cases for the top 25 countries from April of 2020 to February of 2021. We calculated the eigenvalues and eigenvectors of the cross-correlation matrix of the changes in daily accumulated data over monthly time windows. The largest eigenvalue describes the overall evolution dynamics of the COVID-19 and indicates that evolution was faster in April of 2020 than in any other period. By using the first two PC coefficients, we can identify the group dynamics of the COVID-19 evolution. We observed groups under critical states in the loading plot and found that American and European countries are represented by strong clusters in the loading plot. The first PC plays an important role and the correlations (C1) between the normalized logarithmic changes in deaths or confirmed cases and the first PCs may be used as indicators of different phases of the COVID-19. By varying C1 over time, we identified different phases of the COVID-19 in the analyzed countries over the target time period.
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