The Weizmann Institute of Science
Faculty of Mathematics and Computer Science
Vision and Robotics Seminar
Amnon Shashua
School of Engineering \& Computer Science
Hebrew University
will speak on
Threading Kernel Functions: On the family of
all Algebraic Kernels over Sets of Vectors
with Varying Cardinality
Abstract:
In the area of learning from observations there are two main paths that are
often mutually exclusive: (i) the design of learning algorithms, and (ii) the
data representation scheme. The algorithm designers take pride in the fact that
their algorithm can generalize well given straightforward data representations,
whereas those who work on data representations demonstrate often remarkable
results with sophisticated data representations using only straightforward
learning algorithms. This dichotomy is probably most emphasized in the area of
computer vision, where image understanding from observations involve data
instances of images or image sequences containing huge amounts of data.
Our work is about bridging the gap between algorithms and representations. The
key is to allow advanced algorithms (which typically require metric structure
on the instance space) to work with advanced data representations (which are
often not easily embedded into a metric space).
I will present a general family of algebraic positive definite similarity
functions over spaces of matrices with varying column rank. The columns can
represent local regions in an image (whereby images have varying number of
local parts), images of an image sequence, motion trajectories in a multibody
motion, and so froth. The family of similarity measures will be shown to be
exhaustive, thus providing a cook-book of sorts covering the possible ``wish
lists" from similarity measures over sets of varying cardinality.
Joint work with Tamir Hazan.
The lecture will take place in the
Lecture Hall, Room 1, Ziskind Building
on Thursday, June 10, 2004
noon - 13:00