Fast Approximate L_infty Minimization: Speeding Up Robust Regression [article]

Fumin Shen, Chunhua Shen, Rhys Hill, Anton van den Hengel, Zhenmin Tang
2013 arXiv   pre-print
Minimization of the L_∞ 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_∞ norm minimization are slow, and therefore cannot scale to large problems. A new method for the minimization of the L_∞ norm is presented here, which provides a speedup of multiple orders of magnitude for data with high dimension. This
more » ... method, termed Fast L_∞ Minimization, allows robust regression to be applied to a class of problems which were previously inaccessible. It is shown how the L_∞ 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.
arXiv:1304.1250v1 fatcat:fck5c6zao5dxfeq3ixnpz3wtly