2007/12/01 by Gareth M. James · 79 citations
Computer Science · Mathematics · #Curve fitting #Data set #Equating #Medical Image Segmentation Techniques #Method of moments (probability theory) #Monotone polygon #Monotonic function #Morphological variations and asymmetry #Set (abstract data type) #Simple (philosophy) #Statistical Methods and Inference #stat.AP
paper · pdf · doi:10.1214/07-aoas127
published in The Annals of Applied Statistics 1(2) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/07-AOAS127 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2007/12/01 · arxiv created 2007/12/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.