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06106995
j
06106995
Brooks, J.P.
Dul\'a, J.H.
The $L_1$-norm best-fit hyperplane problem.
Appl. Math. Lett. 26, No. 1, 51-55 (2013).
2013
Elsevier Science Ltd. (Pergamon), Oxford
EN
$L_1$ norm
$L_1$ regression
linear programming
subspace fitting
algorithm
best-fit hyperplane problem
$L_{1}$ projection
location theory
computer vision
multivariate statistics
doi:10.1016/j.aml.2012.03.031
Summary: 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.