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.