Title:
Discovering low-dimensional structure in high-dimensional data sets.
Abstract: This talk reviews diffusion methods to identify
low-dimensional manifolds underlying high- dimensional datasets, and
illustrates that by pinpointing additional mathematical structure,
improved results can be obtained. Much of the talk draws on a case
study from a collaboration with biological morphologists, who compare
different phenotypical structures to study relationships of living or
extinct animals with their surroundings and each other. This is
typically done from carefully defined anatomical correspondence points
(landmarks) on e.g. bones; such landmarking draws on highly
specialized knowledge. To make possible more extensive use of large
(and growing) databases, algorithms are required for automatic
morphological correspondence maps, without any preliminary marking of
special features or landmarks by the user.