The L1-norm best-fit hyperplane problem

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.