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A key feature of information theory is its universality, as it can be applied to study a broad variety of complex systems. However, many information-theoretic measures can vary significantly even across systems with similar properties,…

Information Theory · Computer Science 2024-10-16 Alberto Liardi , Fernando E. Rosas , Robin L. Carhart-Harris , George Blackburne , Daniel Bor , Pedro A. M. Mediano

Existing sequence alignment algorithms use heuristic scoring schemes which cannot be used as objective distance metrics. Therefore one relies on measures like the p- or log-det distances, or makes explicit, and often simplistic, assumptions…

Genomics · Quantitative Biology 2015-05-19 Orion Penner , Peter Grassberger , Maya Paczuski

We present a metric embedding that captures spatiotemporal patterns of cell signaling dynamics in 5-D $(x,y,z,channel,time)$ live cell microscopy movies. The embedding uses a metric distance called the normalized information distance (NID)…

Computer Vision and Pattern Recognition · Computer Science 2026-01-16 Layton Aho , Mark Winter , Marc DeCarlo , Agne Frismantiene , Yannick Blum , Paolo Armando Gagliardi , Olivier Pertz , Andrew R. Cohen

We describe a compression-based distance for genomic sequences. Instead of using the usual conjoint information content, as in the classical Normalized Compression Distance (NCD), it uses the conditional information content. To compute this…

Genomics · Quantitative Biology 2014-01-21 Diogo Pratas , Armando J. Pinho

Computable Information Density (CID), the ratio of the length of a losslessly compressed data file to that of the uncompressed file, is a measure of order and correlation in both equilibrium and nonequilibrium systems. Here we show that…

Statistical Mechanics · Physics 2020-10-26 Stefano Martiniani , Yuval Lemberg , Paul M. Chaikin , Dov Levine

The recent developments in machine learning have highlighted a conflict between online platforms and their users in terms of privacy. The importance of user privacy and the struggle for power over user data has been intensified as…

Machine Learning · Computer Science 2026-03-09 Charles Meyers , Aaron MacSween , Erik Elmroth , Tommy Löfstedt

In the field of biological research, it is essential to comprehend the characteristics and functions of molecular sequences. The classification of molecular sequences has seen widespread use of neural network-based techniques. Despite their…

Machine Learning · Computer Science 2024-02-14 Sarwan Ali , Tamkanat E Ali , Prakash Chourasia , Murray Patterson

In this paper we apply different techniques of information distortion on a set of classical books written in English. We study the impact that these distortions have upon the Kolmogorov complexity and the clustering by compression technique…

Information Theory · Computer Science 2008-05-09 Ana Granados , Manuel Cebrian , David Camacho , Francisco de B. Rodriguez

There is a great deal of work in cognitive psychology, linguistics, and computer science, about using word (or phrase) frequencies in context in text corpora to develop measures for word similarity or word association, going back to at…

Computation and Language · Computer Science 2009-05-26 Rudi L. Cilibrasi , Paul M. B. Vitanyi

We survey the emerging area of compression-based, parameter-free, similarity distance measures useful in data-mining, pattern recognition, learning and automatic semantics extraction. Given a family of distances on a set of objects, a…

Computer Vision and Pattern Recognition · Computer Science 2007-05-23 Rudi Cilibrasi , Paul Vitanyi

The main contribution of this paper is to design an Information Retrieval (IR) technique based on Algorithmic Information Theory (using the Normalized Compression Distance- NCD), statistical techniques (outliers), and novel organization of…

Information Retrieval · Computer Science 2016-11-17 Rafael Martinez , Manuel Cebrian , Francisco de Borja Rodriguez , David Camacho

Information distance can be defined not only between two strings but also in a finite multiset of strings of cardinality greater than two. We give an elementary proof for expressing the information distance in terms of plain Kolmogorov…

Information Theory · Computer Science 2019-08-29 P. M. B. Vitanyi

The Kolmogorov complexity of x, denoted C(x), is the length of the shortest program that generates x. For such a simple definition, Kolmogorov complexity has a rich and deep theory, as well as applications to a wide variety of topics…

Computational Complexity · Computer Science 2017-02-17 Stephen Fenner , Lance Fortnow

This paper investigates model reduction methods for efficiently approximating the solution of parameter-dependent PDEs with a multi-parameter vector $\vec{\mu} \in \mathbb{R}^p$. In cases where the Kolmogorov $N$-width decays fast enough,…

Numerical Analysis · Mathematics 2026-01-21 Joubine Aghili , Hassan Ballout , Yvon Maday , Christophe Prud'homme

Kolmogorov complexity measures the algorithmic complexity of a finite binary string $\sigma$ in terms of the length of the shortest description $\sigma^*$ of $\sigma$. Traditionally, the length of a string is taken to measure the amount of…

Computational Complexity · Computer Science 2019-06-14 Cameron Fraize , Christopher P. Porter

Link prediction in graphs is an important task in the fields of network science and machine learning. We investigate a flexible means of regularization for link prediction based on an approximation of the Kolmogorov complexity of graphs…

Machine Learning · Computer Science 2021-02-24 Paris D. L. Flood , Ramon Viñas , Pietro Liò

The word "complexity" is most often used as a meta--linguistic expression referring to certain intuitive characteristics of a natural system and/or its scientific description. These characteristics may include: sheer amount of data that…

History and Overview · Mathematics 2013-01-03 Yuri I. Manin

In neural networks, task-relevant information is represented jointly by groups of neurons. However, the specific way in which this mutual information about the classification label is distributed among the individual neurons is not well…

Information Theory · Computer Science 2023-06-08 David A. Ehrlich , Andreas C. Schneider , Viola Priesemann , Michael Wibral , Abdullah Makkeh

Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…

Information Theory · Computer Science 2015-04-21 Alexander Shen

This paper investigates methods for quantifying similarity between audio signals, specifically for the task of of cover song detection. We consider an information-theoretic approach, where we compute pairwise measures of predictability…

Information Retrieval · Computer Science 2015-05-19 Peter Foster , Simon Dixon , Anssi Klapuri