Matrix Perturbation and Manifold-based Dimension Reduction.

Applied and Computational Mathematics Seminar
Monday, November 23, 2009 - 1:00pm for 1 hour (actually 50 minutes)
Skiles 255
Xiaoming Huo – Georgia Tech (School of ISyE) – xiaoming@isye.gatech.edu
Sung Ha Kang
Many algorithms were proposed in the past ten years on utilizing manifold structure for dimension reduction. Interestingly, many algorithms ended up with computing for eigen-subspaces. Applying theorems from matrix perturbation, we study the consistency and rate of convergence of some manifold-based learning algorithm. In particular, we studied local tangent space alignment (Zhang & Zha 2004) and give a worst-case upper bound on its performance. Some conjectures on the rate of convergence are made. It's a joint work with a former student, Andrew Smith.