Change of Location:
This talk will be in Room FINE 214 (second floor of Fine Hall) !
Gilad Lerman
Multiscale geometric clustering of data sets
Abstract:We present a theory and a fast algorithm for partitioning
a low-dimensional data
set in Rn into disjoint clusters of different geometric
structures. The main tool used is an
L2 variant of Jones' beta numbers, which measure
the scaled deviations of the data set from
approximating d-planes at different scales and locations.
The Jones function is formed by
adding the squares of the L2 Jones numbers at different
scales and the same location. A theory
by Peter W. Jones and the speaker shows that a set with low values
of the d-dimensional Jones
function is "well-approximated" by a certain d-dimensional
surface with small d-volume.
We suggest a fast algorithm for computing a numerical approximation
of the Jones function and
use it to cluster the given set according to the computed values of
this function. Here we apply
this procedure to blocks of pixels taken from images (the highet ambient
dimension is 25) and to
a six-dimensional set of currency exchange rates.