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Dimensionality Reduction

We developed methods for compressing high-dimensional signals that enable smooth interpolation and extrapolation between images, sounds, shapes, etc.

Background & Objective:  It may take millions of bytes to accurately record biometric data such as the shape of one's face, but it only takes a few hundred bytes to describe how one's face differs from similar faces. The distribution of all likely faces is presumed to form a smooth low-dimensional manifold. We have developed methods to model this manifold from data samples and assign it a coordinate system with which we can encode (compress) and decode (decompress) new samples. Navigating on this manifold makes it possible to interpolate and extrapolate.

Technical Discussion:  Given a few data samples (high dimensional vectors) and local distances between similar samples, we construct a convex optimization whose solution is an isometric mapping function taking the sample space into the low dimensional coordinate system.

Publications:
Brand, M., "Nonrigid Embeddings for Dimensionality Reduction", European Conference on Machine Learning (ECML), ISBN: 3-540-29243-8, Vol. 3720, October 2005 (Springer, TR2005-117)

Brand, M., "From Subspaces to Submanifolds", British Machine Vision Conference (BMVC), September 2004 (BMVC 2004, TR2004-134)

Brand, M.E., "Continuous Nonlinear Dimensionality Reduction by Kernel Eigenmaps", International Join Conference on Artificial Intelligence (IJCAI), August 2003 (IJCAI 2003, TR2003-021)

Brand, M., "Charting a Manifold", Neural Information Processing Systems (NIPS), December 2002 (NIPS 15, Paper AA61, TR2003-013)

Technology Areas:
Algorithms
Artificial Intelligence
Computer Vision

Modification Date:  May 28, 2009