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A Quasi-Isometric Embedding Algorithm

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Abstract

The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an algorithm to find a projection that distorts the data as little as possible.

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Author information

Authors and Affiliations

  1. Center for Economic Studies, United States Census Bureau, Suitland, MD, USA

    David W. Dreisigmeyer

  2. Department of Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, USA

    David W. Dreisigmeyer

Authors
  1. David W. Dreisigmeyer
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Correspondence to David W. Dreisigmeyer.

Additional information

Any opinions and conclusions expressed herein are those of the author and do not necessarily represent the views of the U.S. Census Bureau. The research in this paper does not use any confidential Census Bureau information. This was authored by an employee of the US national government. As such, the Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

The article is published in the original.

David Wayne Dreisigmeyer was born in 1971. He graduated from Juniata College (BS in Pre-law, 1994) and Colorado State University (MS in Mathematics, 1999, and PhD in Electrical Engineering, 2004). He currently works at the United States Census Bureau’s Center for Economic Studies and as a Federal Data Strategy Fellow, and is the author of 8 papers. His scientific interests include uses of differential geometry in optimization and pattern analysis.

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Dreisigmeyer, D.W. A Quasi-Isometric Embedding Algorithm. Pattern Recognit. Image Anal. 29, 280–283 (2019). https://doi.org/10.1134/S105466181902007X

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  • DOI: https://doi.org/10.1134/S105466181902007X

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