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: | |
| Nonrigid Embeddings for Dimensionality Reduction | |
| From Subspaces to Submanifolds | |
| Continuous nonlinear dimensionality reduction by kernel eigenmaps | |
| Charting a manifold | |
Technology Areas:
Algorithms
Artificial Intelligence
Computer Vision
Modification Date: September 20, 2007
