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Tight Semi-nonnegative Matrix Factorization

  • MATHEMATICAL THEORY OF IMAGES AND SIGNALS REPRESENTING, PROCESSING, ANALYSIS, RECOGNITION, AND UNDERSTANDING
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Abstract

The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization. A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix. The templates are chosen so that as far as possible only the initial data set can be represented this way. However, the templates are not required to be nonnegative nor convex combinations of the original data.

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Authors and Affiliations

  1. United States Census Bureau, Center for Economic Studies, 4600 Silver Hill Road, 20746, Suitland, MD, USA

    David W. Dreisigmeyer

  2. Department of Electrical and Computer Engineering, Colorado State University, 80523, Fort Collins, CO, USA

    David W. Dreisigmeyer

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

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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.

Additional information

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 formerly as a Federal Data Strategy Fellow, and is the author of 10 papers. His scientific interests include uses of differential geometry in optimization and pattern analysis.

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Dreisigmeyer, D.W. Tight Semi-nonnegative Matrix Factorization. Pattern Recognit. Image Anal. 30, 632–637 (2020). https://doi.org/10.1134/S1054661820040124

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  • DOI: https://doi.org/10.1134/S1054661820040124

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