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Principal Component Analysis of a Finite Number of Curves

Abstract

We introduce and discuss Principal Component Analysis (FPCA) of curves, using only relatively simple matrix algebra and optimization results. Different loss functions, and various ways to impose constraints on the solution, are also discussed. The techniques are applied first to some theoretical examples involving smooth curves, and subsequently to a data set with one year of hourly ozone measurements in Lebec, Kern County, California. R code for all functions, tables, and figures is included for reproducibility.

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