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MERL – Dimensionality Reduction

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.

Future Direction:  We are looking at ways of extending the framework to handle vector samples that lack simple correspondence properties.

Contact:  Matthew Brand

Technical Reports:
TR2005-117 Nonrigid Embeddings for Dimensionality Reduction
TR2004-134 From Subspaces to Submanifolds
TR2003-021 Continuous nonlinear dimensionality reduction by kernel eigenmaps
TR2003-013 Charting a manifold

Technology Areas:
Algorithms
Artificial Intelligence
Computer Vision

Modification Date:  September 20, 2007