Exploratory functional data analysis

Qu, Z. and Dai, W. and Euan, C. and Sun, Y. and Genton, M.G. (2024) Exploratory functional data analysis. Test. ISSN 1133-0686

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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.