Course Announcement: STOR 891, Fall 2007
Object Oriented Data Analysis
J. S. Marron, Department of Statistics and Operations Research
Tu-Th 12:30 - 1:45, Smith 107
Object Oriented Data Analysis is the statistical
analysis of populations of complex objects. Examples
include data sets where the data points could be
curves, images, shapes, movies, or tree structured
objects. Understanding variation of such populations
is a key task, and methods such as principal components,
and various generalizations will be studied.
A second key task that is currently labeled "machine
learning", i.e. clustering/classification will also be
considered. Methods such as Support Vector Machines,
kernel embedding approaches, and various modifications
will be studied.
A common feature of such data sets is that often the
dimensionality is very high, which invalidates most
classical statistical methods, leaving a large area for
the development of new methodologies, some of which will
be studied. A new mathematical statistical theory,
relevant to such data will also be explored.
Another interesting direction, motivated by recent
developments in medical image analysis, is the
statistical analysis of populations of data objects
which are elements of mildly non-Euclidean spaces, such
as Lie Groups and Symmetric Spaces, and of strongly
non-Euclidean spaces, such as spaces of tree-structured
data objects. These new contexts for Object Oriented Data
Analysis create several potentially large new interfaces
between mathematics and statistics.