# Unbiased estimation of multi-fractal dimensions of finite data sets

@article{Roberts1996UnbiasedEO, title={Unbiased estimation of multi-fractal dimensions of finite data sets}, author={Anthony J. Roberts and A. Cronin}, journal={Physica A-statistical Mechanics and Its Applications}, year={1996}, volume={233}, pages={867-878} }

## 20 Citations

Use the information dimension, not the Hausdorff

- Mathematics
- 2005

Multi-fractal patterns occur widely in nature. In developing new algorithms to determine multi-fractal spectra of experimental data I am lead to the conclusion that generalised dimensions Dq of order…

Image Processing of Finite Size Rat Retinal Ganglion Cells Using Multifractal and Local Connected Fractal Analysis

- BiologyAustralian Conference on Artificial Intelligence
- 2004

Three methods were applied to elucidate the variation within 16 rat retinal ganglion cells: local connected fractal dimension (LCFD), mass-radius (MR) and maximum likelihood multifractal (MLM) analyses, concluding that the latter method warrants further attention as it may improve results in other application areas.

The neural network model synthesis based on the fractal analysis

- Computer ScienceOptical Memory and Neural Networks
- 2017

The set of indicators characterizing the data sample properties from the unified position based on the fractal analysis principles and the methods of sample fractal dimension determining are proposed and can be used to solve the problem of data dimensionality reduction.

Using fractals and power laws to predict the location of mineral deposits

- Geology
- 2001

Around the world the mineral exploration industry is interested in getting that small increase in probability measure on the earth's surface of where the next large undiscovered deposit might be…

THE FRACTAL ANALYSIS OF SAMPLE AND DECISION TREE MODEL

- Computer Science
- 2020

The conducted experiments confirmed the operability of the proposed mathematical support and allow recommending it for use in practice for solving the problems of model building by the precedents.

Chaos theory in chemistry and chemometrics: a review

- Psychology
- 2006

Since the initial development of chaos theory and corollary concepts such as the strange attractor and fractal dimensionality, there has been a nontrivial effort to apply these concepts to the…

Soil Variability Assessment with Fractal Techniques

- Environmental Science
- 2005

Understanding soil variability becomes imperative as the management tools become more sophisticated and soil uses become more multifaceted. The importance of spatial and temporal variations in soil…

Tumor Growth in the Brain: Complexity and Fractality

- Medicine
- 2016

Emphasis is done on scaling analysis techniques applicable to multifractal systems, proposing new descriptors to advance the understanding of tumor growth dynamics in brain, to develop innovative practical growth models for therapy simulation and optimization, drug delivery, and the evaluation of related neurological disorders.

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