Mathematical Incorrectnes of So Called Higuchi‘S Fractal Dimension

So called Higuchi’s method of fractal dimension estimation is widely used and the term Higuchi’s fractal dimension even occurs in many publications. This paper deals with this method from mathematical point of view. Terms distance and dimension and its basic properties are explained and Higuchi’s dimension according the original source is defined. Definition of Higuchi’s dimension was comparated with mathematical definition of the distance and dimension. It is showed, that the definition of the Higuchi’s dimension does not satisfy axioms of distance and dimension. So called Higuchi’s method and Higuchi’s dimension are mathematically incorrect. Therefore, all results achieved by this method are scientifically unreliable.

Scikit-Dimension: A Python Package for Intrinsic Dimension Estimation

Dealing with uncertainty in applications of machine learning to real-life data critically depends on the knowledge of intrinsic dimensionality (ID). A number of methods have been suggested for the purpose of estimating ID, but no standard package to easily apply them one by one or all at once has been implemented in Python. This technical note introduces scikit-dimension, an open-source Python package for intrinsic dimension estimation. The scikit-dimension package provides a uniform implementation of most of the known ID estimators based on the scikit-learn application programming interface to evaluate the global and local intrinsic dimension, as well as generators of synthetic toy and benchmark datasets widespread in the literature. The package is developed with tools assessing the code quality, coverage, unit testing and continuous integration. We briefly describe the package and demonstrate its use in a large-scale (more than 500 datasets) benchmarking of methods for ID estimation for real-life and synthetic data.

An Efficient Method for Choosing Digital Cluster Size in Ultralow Latency Networks

The paper proposes a solution to the problem of choosing the size of a cluster in an ultralow latency network. This work is aimed at designing a method for choosing the size of the digital cluster in an ultralow latency network taking into account the lengths of connecting lines. If the linear dimension calculation is based only on the latency requirements without specifics of building the communication line, it negatively affects timing characteristics. This paper shows the method taking into account the communication line features and basing on the fractal dimension estimation of the road network. The proposed method could be used in planning and designing networks with ultralow latencies. Finally, a numerical experiment was carried out, based on the data of electronic maps, which showed that the assessment of the fractal dimension of roads in the network’s service area makes it possible to increase the accuracy of the size of the formed cluster. Moreover, the proposed method can allow you to reduce the error in estimating the length of connecting lines, which without using it can be on average about 30%.