Exploratory functional data analysis

Zhuo Qu (), Wenlin Dai (), Carolina Euan (), Ying Sun () and Marc G. Genton ()
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Zhuo Qu: King Abdullah University of Science and Technology
Wenlin Dai: Institute of Statistics and Big Data, Renmin University of China
Carolina Euan: Lancaster University
Ying Sun: King Abdullah University of Science and Technology
Marc G. Genton: King Abdullah University of Science and Technology

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2025, vol. 34, issue 2, No 5, 459-482

Abstract: Abstract With the advance of technology, functional data are being recorded more frequently, whether over one-dimensional or multi-dimensional domains. Due to the high dimensionality and complex features of functional data, exploratory data analysis (EDA) faces significant challenges. To meet the demands of practical applications, researchers have developed various EDA tools, including visualization tools, outlier detection techniques, and clustering methods that can handle diverse types of functional data. This paper offers a comprehensive overview of recent procedures for exploratory functional data analysis (EFDA). It begins by introducing fundamental statistical concepts, such as mean and covariance functions, as well as robust statistics such as the median and quantiles in multivariate functional data. Then, the paper reviews popular visualization methods for functional data, such as the rainbow plot, and various versions of the functional boxplot, each designed to accommodate different features of functional data. In addition to visualization tools, the paper also reviews outlier detection methods, which are commonly integrated with visualization methods to identify anomalous patterns within the data. Finally, the paper focuses on functional data clustering techniques which provide another set of practical tools for EFDA. The paper concludes with a brief discussion of future directions for EFDA. All the reviewed methods have been implemented in an R package named EFDA .

Keywords: Clustering; Data visualization; Exploratory data analysis; Functional boxplot; Multivariate functional data; Outlier detection; 62R10; 62A09 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11749-024-00952-8

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