Fast approximate L∞ minimization: speeding up robust regression
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2014
Authors
Shen, F.
Shen, C.
Hill, R.
Van Den Hengel, A.
Tang, Z.
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Computational Statistics and Data Analysis, 2014; 77:25-37
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Fumin Shen, Chunhua Shen, Rhys Hill, Anton van den Hengel, Zhenmin Tang
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Abstract
Minimization 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.
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© 2014 Elsevier B.V. All rights reserved.