{"title":"Functional principal component analysis for incomplete space–time data","authors":"","doi":"10.1007/s10651-024-00598-7","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>Environmental signals, acquired, e.g., by remote sensing, often present large gaps of missing observations in space and time. In this work, we present an innovative approach to identify the main variability patterns, in space–time data, when data may be affected by complex missing data structures. We formalize the problem in the framework of functional data analysis, proposing an innovative method of functional principal component analysis (fPCA) for incomplete space–time data. The functional nature of the proposed method permits to borrow information from measurements observed at nearby spatio-temporal locations. The resulting functional principal components are smooth fields over the considered spatio-temporal domain, and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. Moreover, they can be used to provide a reconstruction of the missing entries, also under severe missing data patterns. The proposed model combines a weighted rank-one approximation of the data matrix with a roughness penalty. We show that the estimation problem can be solved using a majorize–minimization approach, and provide a numerically efficient algorithm for its solution. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can handle multidimensional spatial domains with complex shapes, such as water bodies with complicated shorelines, or curved spatial regions with complex orography. As shown by simulation studies, the proposed space–time fPCA is superior to alternative techniques for Principal Component Analysis with missing data. We further highlight the potentiality of the proposed method for environmental problems, by applying space–time fPCA to the study of the lake water surface temperature (LWST) of Lake Victoria, in Central Africa, starting from satellite measurements with large gaps. LWST is considered one of the fundamental indicators of how climate change is affecting the environment, and is recognized as an essential climate variable.</p>","PeriodicalId":50519,"journal":{"name":"Environmental and Ecological Statistics","volume":"84 1","pages":""},"PeriodicalIF":3.0000,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Environmental and Ecological Statistics","FirstCategoryId":"93","ListUrlMain":"https://doi.org/10.1007/s10651-024-00598-7","RegionNum":4,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENVIRONMENTAL SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
Environmental signals, acquired, e.g., by remote sensing, often present large gaps of missing observations in space and time. In this work, we present an innovative approach to identify the main variability patterns, in space–time data, when data may be affected by complex missing data structures. We formalize the problem in the framework of functional data analysis, proposing an innovative method of functional principal component analysis (fPCA) for incomplete space–time data. The functional nature of the proposed method permits to borrow information from measurements observed at nearby spatio-temporal locations. The resulting functional principal components are smooth fields over the considered spatio-temporal domain, and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. Moreover, they can be used to provide a reconstruction of the missing entries, also under severe missing data patterns. The proposed model combines a weighted rank-one approximation of the data matrix with a roughness penalty. We show that the estimation problem can be solved using a majorize–minimization approach, and provide a numerically efficient algorithm for its solution. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can handle multidimensional spatial domains with complex shapes, such as water bodies with complicated shorelines, or curved spatial regions with complex orography. As shown by simulation studies, the proposed space–time fPCA is superior to alternative techniques for Principal Component Analysis with missing data. We further highlight the potentiality of the proposed method for environmental problems, by applying space–time fPCA to the study of the lake water surface temperature (LWST) of Lake Victoria, in Central Africa, starting from satellite measurements with large gaps. LWST is considered one of the fundamental indicators of how climate change is affecting the environment, and is recognized as an essential climate variable.
期刊介绍：
Environmental and Ecological Statistics publishes papers on practical applications of statistics and related quantitative methods to environmental science addressing contemporary issues.
Emphasis is on applied mathematical statistics, statistical methodology, and data interpretation and improvement for future use, with a view to advance statistics for environment, ecology and environmental health, and to advance environmental theory and practice using valid statistics.
Besides clarity of exposition, a single most important criterion for publication is the appropriateness of the statistical method to the particular environmental problem. The Journal covers all aspects of the collection, analysis, presentation and interpretation of environmental data for research, policy and regulation. The Journal is cross-disciplinary within the context of contemporary environmental issues and the associated statistical tools, concepts and methods. The Journal broadly covers theory and methods, case studies and applications, environmental change and statistical ecology, environmental health statistics and stochastics, and related areas. Special features include invited discussion papers; research communications; technical notes and consultation corner; mini-reviews; letters to the Editor; news, views and announcements; hardware and software reviews; data management etc.
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