Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6869840 | Computational Statistics & Data Analysis | 2014 | 13 Pages |
Abstract
Minimization of the Lâ 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 Lâ norm minimization are slow, and therefore cannot be scaled to large problems. A new method for the minimization of the Lâ norm is presented here, which provides a speedup of multiple orders of magnitude for data with high dimension. This method, termed Fast  LâMinimization, allows robust regression to be applied to a class of problems which was previously inaccessible. It is shown how the Lâ 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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Fumin Shen, Chunhua Shen, Rhys Hill, Anton van den Hengel, Zhenmin Tang,