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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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.
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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