Dimensionality Reduction

Sam Roweis
University of Toronto

In vision, as in many other modalities, we observe signals from many more 
sensors (pixels) than true degrees of freedom in the world we are measuring. As 
a result, nearby pixels are highly correlated and the images we observe have a 
lot of structure. Ideally, we would like to re-represent raw pixel maps using a 
much smaller number of underlying variables that still capture the essential 
degrees of freedom present in typical scenes. I will review the basic 
computational techniques for doing this, starting with linear methods such as 
MDS, PCA, ICA and factor analysis and moving on to more sophisticated nonlinear 
methods such as kernel PCA, laplacian eigenmaps, Isomap and LLE.

Sam Roweis is an Assistant Professor in the Department of Computer Science at 
the University of Toronto. His research interests are in machine learning, data 
mining, and statistical signal processing. Roweis did his undergraduate degree 
at the University of Toronto in the Engineering Science program and earned his 
doctoral degree in 1999 from the California Institute of Technology working with 
John Hopfield. He did a postdoc with Geoff Hinton and Zoubin Ghahramani at the 
Gatsby Unit in London, and has also worked in several industrial research labs 
including Bell Labs, and Whizbang! Labs. He is the holder of a Canada Research 
Chair in Statistical Machine Learning and the winner of a Premier's Research 
Excellence Award.