Faster estimation of the correlation fractal dimension using box-counting

TL;DR

This paper introduces a new, faster method for estimating the correlation fractal dimension using a single-pass algorithm, improving efficiency while maintaining accuracy in spatial data analysis.

Contribution

The paper presents a novel linear-time algorithm for correlation fractal dimension estimation that reduces dataset rescanning, enhancing speed without sacrificing accuracy.

Findings

The new method completes in a single dataset pass.

It maintains accuracy comparable to existing algorithms.

It outperforms previous methods in runtime efficiency.

Abstract

Fractal dimension is widely adopted in spatial databases and data mining, among others as a measure of dataset skewness. State-of-the-art algorithms for estimating the fractal dimension exhibit linear runtime complexity whether based on box-counting or approximation schemes. In this paper, we revisit a correlation fractal dimension estimation algorithm that redundantly rescans the dataset and, extending that work, we propose another linear, yet faster and as accurate method, which completes in a single pass.