Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality
Marie Ferbus-Zanda (LIAFA)

TL;DR
This paper explores the role of Kolmogorov complexity in classification and information systems, highlighting dualities between operational modes and their connections to logic, set theory, and data analysis.
Contribution
It unifies diverse approaches to classification using Kolmogorov complexity, emphasizing the duality between Bottom-Up and Top-Down methods and their relation to logic and set theory.
Findings
Classification using compression relates to Kolmogorov complexity.
Duality between Bottom-Up and Top-Down modes in information processing.
Connections between Kolmogorov complexity, logic, and set theory.
Abstract
We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts published in a same volume. Part II is dedicated to the relation between logic and information system, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov complexity: classification using compression, an idea with provocative implementation by authors such as Bennett, Vitanyi and Cilibrasi. This stresses how Kolmogorov complexity, besides being a foundation to randomness, is also related to classification. Another approach to classification is also considered: the so-called "Google classification". It uses another original and attractive idea which is connected to the classification using…
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Logic, Reasoning, and Knowledge · Benford’s Law and Fraud Detection
