The L1-norm best-fit hyperplane problem

Appl Math Lett. 2012 Jan 1;26(1):51-56. doi: 10.1016/j.aml.2012.03.031. Epub 2012 Apr 10.


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.