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GRASP Lab Seminar 2004-2005
September 3, 1:30 PM, Levine Hall 307.
Matthew Brand
Mitsubishi Electric Research Laboratories
Exact Nonlinear Dimensionality Reduction
Abstract: Nonlinear dimensionality reduction is rapidly advancing and may soon make the leap from "data visualization" to "useful signal processing tool." NLDR is in essence the problem of embedding a graph with local metric constraints derived from data. Since the graph is invented and the metric constraints are approximate, there is a nagging question as to whether NLDR methods actually maximize fidelity to the data manifold. I will examine two chronic sources of bias in NLDR graph and metric constraints and show how they can be eliminated. The resulting method, called Geodesic Nullspace Analysis, offers exact parameterizations of a useful class of manifolds including most R^3 developable surfaces, and performs very well outside that class. GNA revolves around a data linearizing operator that offers isometric immersions, data denoising, out-of-sample extensions thereof, and online updating, reproducing most of the functionality of subspace methods.
Biography: Matthew Brand studies unsupervised learning from sensory data. One goal is to make machines that learn to realistically mimic and augment human performances; another is to optimize systems that serve the conflicting interests of large numbers of people. Recent results include spectral solutions for reconstructing manifolds from samples, decision-theoretic elevator group control, a linear-time online SVD, video-realistic synthesis of humans and nature scenes, recovery of nonrigid 3D shape from ordinary video, and an entropy optimization framework for learning. Brand has been named one of the top innovators of his generation (Technology Review 1999) and one of industry's top "R and D stars" (Industry Week 2000). Recent academic honors include best paper awards in computer vision (CVPR2001) and scheduling (ICAPS2003).
