Supervised Scale-Regularized Linear Convolutionary Filters

Marco Loog and Francois Lauze

Abstract

We start by demonstrating that an elementary learning task—learning a linear filter from training data by means of regression can be solved very efficiently for feature spaces of very high dimensionality. In a second step, firstly, acknowledging that such high-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 satisfactory manner, we come to a combined resolution of both of these shortcomings by proposing a technique that we coin scale regularization. This regularization problem can also be solved relatively efficient. All in all, the idea is to properly control the scale of a trained filter, which we solve by introducing a specific regularization term into the overall objective function. We demonstrate, on an artificial filter learning problem, the capabilities of our basic filter.

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DOI

10.5244/C.31.162
https://dx.doi.org/10.5244/C.31.162

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Bibtex

            @inproceedings{BMVC2017_162,
                title={Supervised Scale-Regularized Linear Convolutionary Filters},
                author={Marco Loog and Francois Lauze},
                year={2017},
                month={September},
                pages={162.1-162.11},
                articleno={162},
                numpages={11},
                booktitle={Proceedings of the British Machine Vision Conference (BMVC)},
                publisher={BMVA Press},
                editor={Tae-Kyun Kim, Stefanos Zafeiriou, Gabriel Brostow and Krystian Mikolajczyk},
                doi={10.5244/C.31.162},
                isbn={1-901725-60-X},
                url={https://dx.doi.org/10.5244/C.31.162}
            }