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Appl Math Lett. 2012 Jan 1;26(1):51-56. Epub 2012 Apr 10.

The L1-norm best-fit hyperplane problem.

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

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.

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