Curve alignment by moments

By Gareth M. James. 2007

114 citations recorded by the source corpus.

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.

Subfields: Computer Vision and Pattern Recognition, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/80f516d9b6023925c425bfe3eab9f78a2b698eb0

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In Computer Vision and Pattern Recognition

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Citations in the corpus

Pairwise curve synchronization for functional data (2008, methodology): “…& Gasser, 2004); nonparametric maximum-likelihood warping (Rønn, 2001; Gervini & Gasser, 2005); functional convex synchronization (Liu & Müller, 2004); dynamic time warping (Wang & Gasser, 1997, 1999), and a synchronization method based on a novel definition of moments of curves (James, 2007).”