Shen, F.Shen, C.Hill, R.Van Den Hengel, A.Tang, Z.2014-09-072014-09-072014Computational Statistics and Data Analysis, 2014; 77:25-370167-94731872-7352http://hdl.handle.net/2440/85034Minimization of the L<inf>∞</inf> norm, which can be viewed as approximately solving the non-convex least median estimation problem, is a powerful method for outlier removal and hence robust regression. However, current techniques for solving the problem at the heart of L<inf>∞</inf> norm minimization are slow, and therefore cannot be scaled to large problems. A new method for the minimization of the L<inf>∞</inf> norm is presented here, which provides a speedup of multiple orders of magnitude for data with high dimension. This method, termed Fast L<inf>∞</inf> Minimization, allows robust regression to be applied to a class of problems which was previously inaccessible. It is shown how the L<inf>∞</inf> norm minimization problem can be broken up into smaller sub-problems, which can then be solved extremely efficiently. Experimental results demonstrate the radical reduction in computation time, along with robustness against large numbers of outliers in a few model-fitting problems. © 2014 Elsevier B.V. All rights reserved.en© 2014 Elsevier B.V. All rights reserved.Least-squares regression; outlier removal; robust regression; face recognitionJournal article002013868510.1016/j.csda.2014.02.0180003378695000032-s2.0-8490192185714226Van Den Hengel, A. [0000-0003-3027-8364]