The L1-norm best-fit hyperplane problem

We formalize an algorithm for solving the L1L1-norm best-fit hyperplane problem derived using first principles and geometric insights about L1L1 projection and L1L1 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 L1L1-norm best-fit hyperplane problem makes the procedure accessible to applications in areas such as location theory, computer vision, and multivariate statistics.