Curve registration
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1998 · Volume 60 · Issue 2
Abstract
Functional data analysis involves the extension of familiar statistical procedures such as principal components analysis, linear modelling, and canonical correlation analysis to data where the raw observationxiis a function. An essential preliminary to a functional data analysis is often the registration or alignment of salient curve features by suitable monotone transformationshiof the argumentt, so that the actual analyses are carried out on the valuesxi{hi(t)}. This is referred to as dynamic time warping in the engineering literature. In effect, this conceptualizes variation among functions as being composed of two aspects: horizontal and vertical, or domain and range. A nonparametric function estimation technique is described for identifying the smooth monotone transformationshi, and is illustrated by data analyses. A second-order linear stochastic differential equation is proposed to model these components of variation.
Keywords
Dynamic time warping, Geometric Brownian motion, Monotone functions, Spline, Stochastic time, Time warping
Enable JavaScript for citation tools and additional paper interactions.