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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Communication dans un congrès
M M Novak. Fractals 98, Oct 1998, Valleta, Malta. World Scientific, 1998
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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. M M Novak. Fractals 98, Oct 1998, Valleta, Malta. World Scientific, 1998. 〈inria-00593254〉

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