Data on Manifolds
Victor Patrangenaru, Leif Ellingson · 2015
There are many disciplines in which data arises on object spaces which are ma- nifolds. Among these are anthropology, astronomy, bioinformatics, computer vision, geology, image analysis, medical imaging, meteorology, and statistics. Over the next several chapters, this monograph will present the general the- ory and methodology underlying a nonparametric statistical analysis of data arising on manifolds. However, each application and type of data will have its own specific problems that need to be taken into consideration in the analysis, which will be addressed in later portions of this book. First, though, we wish to provide a number of examples of data lying on manifolds. In addition to showing applications in which such data arise, these example can help provide context in subsequent chapters focusing on theory.