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A Regularization Approach to Fractional Dimension Estimation

Abstract : We propose a new way of evaluating the regularity of a graph of a function f. Our approach is based on measuring the growth rate of the lengths of less and less regularized versions of f. This leads to a new index, that we call regularization dimension, dim_R . We derive some analytical properties of dim_R and compare it with other fractional dimensions. A statistical estimator is derived, and numerical experiments are performed, which suggest that dim_R may be computed in a robust way. Finally, we apply the regularization dimension to the study of Ethernet traffic.
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https://hal.inria.fr/inria-00593254
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Submitted on : Friday, May 13, 2011 - 5:02:36 PM
Last modification on : Friday, February 4, 2022 - 3:10:13 AM
Long-term archiving on: : Sunday, August 14, 2011 - 2:35:10 AM

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  • HAL Id : inria-00593254, version 1

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François Roueff, Jacques Lévy Véhel. A Regularization Approach to Fractional Dimension Estimation. Fractals 98, Oct 1998, Valleta, Malta. ⟨inria-00593254⟩

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