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From Notices of the AMS

Uncovering Data Across Continua: An Introduction to Functional Data Analysis

Example of functional data. Represents the horizontal (X) and vertical (Y) positions of a pen while writing the word fda with the handwritten dataset from the R package fda, panel.

by Sophie Dabo-Niang
Camille Frévent
Communicated by Richard Levine

Introduction

Nowadays, advancements in data collection technologies like sensors, computer vision, medical imaging, IoT, and wearables have generated vast volumes of high-frequency data across various fields. These data are not just a collection of numbers and tables but a rich, dynamic tapestry of information that captures the essence of change over a continuum. Functional Data Analysis (FDA) [1][2][6][13]efficiently handles large-scale, high-dimensional datasets, extracting valuable insights from data containing structured information.

Unlike traditional statistics dealing with discrete data points, FDA focuses on entire functions, curves, or shapes, providing insights into continuous changes. Whether analyzing time series, spatial data, growth curves, or any structured dataset, FDA excels at capturing ongoing change. FDA's applications span various fields like medicine, biology, chemistry, economics, and environmental science, offering insights beyond isolated measurements. It aids in patient health tracking, economic trend analysis, and chemical or environmental management by modeling and understanding complex systems. In manufacturing, FDA can be applied to monitor continuous processes, such as chemical reactions, quality control measurements, and equipment performance. It helps detect deviations from the desired process behavior [12].

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