## Supervised scale-regularized linear convolutionary filters

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**Supervised scale-regularized linear convolutionary filters.** / Loog, Marco; Lauze, Francois Bernard.

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings

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*Proceedings of BMVC 2017.*British Machine Vision Conference, British Machine Vision Conference 2017, London, Storbritannien, 04/09/2017.

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*Proceedings of BMVC 2017*British Machine Vision Conference.

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TY - GEN

T1 - Supervised scale-regularized linear convolutionary filters

AU - Loog, Marco

AU - Lauze, Francois Bernard

PY - 2017/7

Y1 - 2017/7

N2 - We start by demonstrating that an elementary learning task—learning a linear filterfrom training data by means of regression—can be solved very efficiently for featurespaces of very high dimensionality. In a second step, firstly, acknowledging that suchhigh-dimensional learning tasks typically benefit from some form of regularization and,secondly, arguing that the problem of scale has not been taken care of in a very satis-factory manner, we come to a combined resolution of both of these shortcomings byproposing a technique that we coin scale regularization. This regularization problem canalso be solved relatively efficient. All in all, the idea is to properly control the scale of atrained filter, which we solve by introducing a specific regularization term into the overallobjective function. We demonstrate, on an artificial filter learning problem, the capabil-ities of our basic filter. In particular, we demonstrate that it clearly outperforms the defacto standard Tikhonov regularization, which is the one employed in ridge regression orWiener filtering.

AB - We start by demonstrating that an elementary learning task—learning a linear filterfrom training data by means of regression—can be solved very efficiently for featurespaces of very high dimensionality. In a second step, firstly, acknowledging that suchhigh-dimensional learning tasks typically benefit from some form of regularization and,secondly, arguing that the problem of scale has not been taken care of in a very satis-factory manner, we come to a combined resolution of both of these shortcomings byproposing a technique that we coin scale regularization. This regularization problem canalso be solved relatively efficient. All in all, the idea is to properly control the scale of atrained filter, which we solve by introducing a specific regularization term into the overallobjective function. We demonstrate, on an artificial filter learning problem, the capabil-ities of our basic filter. In particular, we demonstrate that it clearly outperforms the defacto standard Tikhonov regularization, which is the one employed in ridge regression orWiener filtering.

M3 - Article in proceedings

BT - Proceedings of BMVC 2017

PB - British Machine Vision Conference

Y2 - 4 September 2017 through 7 September 2017

ER -

ID: 183735818