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Brooks JP, Dulá JH. The L1-norm best-fit hyperplane problem. Appl Math Lett. 2012;26(1):51-56doi: 10.1016/j.aml.2012.03.031.
Brooks, J. P., & Dulá, J. H. (2012). The L1-norm best-fit hyperplane problem. Applied mathematics letters, 26(1), 51-56. https://doi.org/10.1016/j.aml.2012.03.031
Brooks, J P, and Dulá, J H. "The L1-norm best-fit hyperplane problem." Applied mathematics letters vol. 26,1 (2012): 51-56. doi: https://doi.org/10.1016/j.aml.2012.03.031
Brooks JP, Dulá JH. The L1-norm best-fit hyperplane problem. Appl Math Lett. 2012 Jan 01;26(1):51-56. doi: 10.1016/j.aml.2012.03.031. Epub 2012 Apr 10. PMID: 23024460; PMCID: PMC3459998.
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Appl Math Lett. 2012 Jan 01;26(1):51-56. doi: 10.1016/j.aml.2012.03.031. Epub 2012 Apr 10.

The L1-norm best-fit hyperplane problem.

Applied mathematics letters

J P Brooks, J H Dulá

Affiliations

  1. Virginia Commonwealth University, 1015 Floyd Avenue, P.O. Box 843083, Richmond, VA 23284.

PMID: 23024460 PMCID: PMC3459998 DOI: 10.1016/j.aml.2012.03.031

Abstract

We formalize an algorithm for solving the L(1)-norm best-fit hyperplane problem derived using first principles and geometric insights about L(1) projection and L(1) regression. The procedure follows from a new proof of global optimality and relies on the solution of a small number of linear programs. The procedure is implemented for validation and testing. This analysis of the L(1)-norm best-fit hyperplane problem makes the procedure accessible to applications in areas such as location theory, computer vision, and multivariate statistics.

References

  1. IEEE Trans Pattern Anal Mach Intell. 2008 Sep;30(9):1672-80 - PubMed

Publication Types

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