Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/85034
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Type: | Journal article |
Title: | Fast approximate L∞ minimization: speeding up robust regression |
Other Titles: | Fast approximate L infinity minimization: speeding up robust regression |
Author: | Shen, F. Shen, C. Hill, R. Van Den Hengel, A. Tang, Z. |
Citation: | Computational Statistics and Data Analysis, 2014; 77:25-37 |
Publisher: | Elsevier Science |
Issue Date: | 2014 |
ISSN: | 0167-9473 1872-7352 |
Statement of Responsibility: | Fumin Shen, Chunhua Shen, Rhys Hill, Anton van den Hengel, Zhenmin Tang |
Abstract: | 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 be scaled 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 method, termed Fast L∞ Minimization, allows robust regression to be applied to a class of problems which was 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. © 2014 Elsevier B.V. All rights reserved. |
Keywords: | Least-squares regression; outlier removal; robust regression; face recognition |
Rights: | © 2014 Elsevier B.V. All rights reserved. |
DOI: | 10.1016/j.csda.2014.02.018 |
Published version: | http://dx.doi.org/10.1016/j.csda.2014.02.018 |
Appears in Collections: | Aurora harvest 7 Computer Science publications |
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