Shape-based functional data analysis

Yuexuan Wu (), Chao Huang () and Anuj Srivastava ()
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Yuexuan Wu: Florida State University
Chao Huang: Florida State University
Anuj Srivastava: Florida State University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 33, issue 1, No 1, 47 pages

Abstract: Abstract Functional data analysis (FDA) is a fast-growing area of research and development in statistics. While most FDA literature imposes the classical $$\mathbb {L}^2$$ L 2 Hilbert structure on function spaces, there is an emergent need for a different, shape-based approach for analyzing functional data. This paper reviews and develops fundamental geometrical concepts that help connect traditionally diverse fields of shape and functional analyses. It showcases that focusing on shapes is often more appropriate when structural features (number of peaks and valleys and their heights) carry salient information in data. It recaps recent mathematical representations and associated procedures for comparing, summarizing, and testing the shapes of functions. Specifically, it discusses three tasks: shape fitting, shape fPCA, and shape regression models. The latter refers to the models that separate the shapes of functions from their phases and use them individually in regression analysis. The ensuing results provide better interpretations and tend to preserve geometric structures. The paper also discusses an extension where the functions are not real-valued but manifold-valued. The article presents several examples of this shape-centric functional data analysis using simulated and real data.

Keywords: Functional data analysis; Shape analysis; Alignment; Registration; Shape statistics; Shape fPCA; Shape regression models; 62R10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11749-023-00876-9

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