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The L1-Norm Best-Fit Hyperplane Problem

J.P. Brooks (jpbrooks***at***vcu.edu)
J.H. Dula (jdula***at***vcu.edu)

Abstract: We formalize an algorithm for solving the L1-norm best-fit hyperplane problem derived using first principles and geometric insights about L1 projection and L1 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 L1-norm best-fit hyperplane problem makes the procedure accessible to applications in areas such as location theory, computer vision, and multivariate statistics.

Keywords: L1-norm, L1 regression, linear programming, subspace fitting

Category 1: Applications -- Science and Engineering (Data-Mining )

Category 2: Applications -- Science and Engineering (Statistics )

Category 3: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: Applied Mathematics Letters, 26:51-55, 2013


Entry Submitted: 05/06/2009
Entry Accepted: 05/06/2009
Entry Last Modified: 03/15/2013

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