Background: A common feature of functional measurements of data over time, space and other continua, is that salient features in the resulting curves and surfaces vary in position from one recording to the next. For example, the growth patterns of children vary in the timing of puberty, human movements in activities like handwriting and golf swings speed up and slow down from one instance to another, seasonal events like hurricanes arrive early some years and late in others, and traffic jams vary in location over city streets from one day to another. At the same time, each of the events can also vary in intensity. We refer to positional variation as phase variation, and intensity variation as amplitude variation. It is now evident that many processes unfold over a system time that not only does not unroll at the same rate as physical clock time, but also tends to vary in a significant way from one realization of a functional event to another.
The registration or alignment of features in curves and images by smooth, one-to-one transformations of time or space, respectively, is an emerging hot topic that presents many challenges. From its beginnings with dynamic time warping in the late 50's, followed by the landmark registration methods of Fred Bookstein, the registration of brain images to a fixed atlas, and its widespread application in functional data analysis, statisticians have realized that nonlinear phase variation is pervasive in data distributed over continua. Happily, a considerable variety of methods for separating amplitude from phase variation now exist, and connections with shape analysis methods have been made. It seems time to do some comparative tests, review progress to date, and consider new research opportunities.
Workshop Ideas: Instead of the usual passive speaker - audience format, workshop activities will be centered around applying a wide variety of statistical methods to a common collection of data sets. The focus will be the various analytic approaches of several different Analysis Groups, to some common data sets, featuring careful discussion of the strengths and weaknesses of the various analyses.
Main presentations will be made by the Analysis Groups, who will agree to analyze (before the workshop) each of the agreed upon data sets, and will present their results at the workshop. For context, each data set will have an associated workshop participant, responsible for answering questions about the data while the analysis is under way, and who will (at the beginning of the workshop) give a brief description of the data, plus the main statistical questions. Following the analytic presentations, there will be group discussion with the goal of evaluation of the different methods used. It is anticipated that this will result in a list of the pros and cons of each approach, and in particular a clear view of the varying circumstances under which each method has advantages over the others.
The current datasets planned for this workshop include:
To view these datasets, view the resource page.
Other function data sets where time warping and registration can play an important role (and that could be accessed freely) may be suggested by workshop participants, and will be posted for optional analyses and discussion during the workshop.
Dissemination of the results is intended to be through an article, co-authored by the major participants, aimed at a journal such as Statistical Science, or a top level computational statistics journal.