seminar by Professor Ian Dryden (University of Nottingham) on June 3rd (monday) at 11.15 in seminar room D123 (Exactum, Kumpula campus, University of Helsinki).
Object data analysis is an important tool in the many disciplines where
the data have much richer structure than the usual numbers or vectors.
An initial question to ask is: what are the most basic data units? i.e.
what are the atoms of the data? We describe an introduction to this
topic, where the statistical analysis of object data has a wide variety
of applications. An important aspect of the analysis is to reduce the
dimension to a small number key features while respecting the geometry
of the manifold in which objects lie. Three case studies are given which
exemplify the types of issues that are encountered: i) describing
changes in shape variability in damaged DNA, ii) investigating
differences between authors in corpus linguistics, iii) testing for
geometrical differences in carotid arteries, where patients are at high
or low risk of aneurysm. In all three applications the structure of the
data manifolds is important, in particular the manifolds of covariance
matrices, networks and unlabelled size-and-shapes.