Related papers: Information vs Dimension -- an Algorithmic Perspec…
Developing a robust generalization measure for the performance of machine learning models is an important and challenging task. A lot of recent research in the area focuses on the model decision boundary when predicting generalization. In…
After reviewing unnormalized and normalized information distances based on incomputable notions of Kolmogorov complexity, we discuss how Kolmogorov complexity can be approximated by data compression algorithms. We argue that optimal…
We characterize the algorithmic dimensions (i.e., the lower and upper asymptotic densities of information) of infinite binary sequences in terms of the inability of learning functions having an algorithmic constraint to detect patterns in…
This paper deals with an estimating of the Fractal Dimension of a hydrometeorology variables like an Air temperature or humidity at a different sites in a landscape (and will be further evaluated from the land use point of view). Three…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
We use Kolmogorov complexity methods to give a lower bound on the effective Hausdorff dimension of the point (x, ax+b), given real numbers a, b, and x. We apply our main theorem to a problem in fractal geometry, giving an improved lower…
Complexity measures are designed to capture complex behavior and quantify *how* complex, according to that measure, that particular behavior is. It can be expected that different complexity measures from possibly entirely different fields…
It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example,…
We develop the theory of multiresolutions in the context of Hausdorff measure of fractional dimension between 0 and 1. While our fractal wavelet theory has points of similarity that it shares with the standard case of Lebesgue measure on…
Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal…
We build information geometry for a partially ordered set of variables and define the orthogonal decomposition of information theoretic quantities. The natural connection between information geometry and order theory leads to efficient…
We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition…
The incomplete statistics for complex systems is characterized by a so called incompleteness parameter $\omega$ which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the…
A unified combinatorial definition of the information content and entropy of different types of patterns, compatible with the traditional concepts of information and entropy, going beyond the limitations of Shannon information interpretable…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between…
In this paper, we present some results on information, complexity and entropy as defined below and we discuss their relations with the Kolmogorov-Sinai entropy which is the most important invariant of a dynamical system. These results have…
The normalized information distance is a universal distance measure for objects of all kinds. It is based on Kolmogorov complexity and thus uncomputable, but there are ways to utilize it. First, compression algorithms can be used to…
Multifractals are inhomogeneous measures (or functions) which are typically described by a full spectrum of real dimensions, as opposed to a single real dimension. Results from the study of fractal strings in the analysis of their geometry,…