The Annals of Applied Statistics

Curve alignment by moments

Gareth M. James

Full-text: Open access

Abstract

A significant problem with most functional data analyses is that of misaligned curves. Without adjustment, even an analysis as simple as estimation of the mean will fail. One common method to synchronize a set of curves involves equating “landmarks” such as peaks or troughs. The landmarks method can work well but will fail if marker events can not be identified or are missing from some curves. An alternative approach, the “continuous monotone registration” method, works by transforming the curves so that they are as close as possible to a target function. This method can also perform well but is highly dependent on identifying an accurate target function. We develop an alignment method based on equating the “moments” of a given set of curves. These moments are intended to capture the locations of important features which may represent local behavior, such as maximums and minimums, or more global characteristics, such as the slope of the curve averaged over time. Our method works by equating the moments of the curves while also shrinking toward a common shape. This allows us to capture the advantages of both the landmark and continuous monotone registration approaches. The method is illustrated on several data sets and a simulation study is performed.

Article information

Source
Ann. Appl. Stat., Volume 1, Number 2 (2007), 480-501.

Dates
First available in Project Euclid: 30 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1196438028

Digital Object Identifier
doi:10.1214/07-AOAS127

Mathematical Reviews number (MathSciNet)
MR2415744

Zentralblatt MATH identifier
1126.62001

Keywords
Curve registration moments landmark registration continuous monotone registration

Citation

James, Gareth M. Curve alignment by moments. Ann. Appl. Stat. 1 (2007), no. 2, 480--501. doi:10.1214/07-AOAS127. https://projecteuclid.org/euclid.aoas/1196438028


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