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A new complexity measure for time series analysis and classification

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 2013年第3-4期222卷 847-860页

作者： Nagaraj, Nithin Balasubramanian, Karthi Dey, Sutirth Amrita Vishwa Vidyapeetham Amrita Sch Engn Dept Elect & Commun Engn Kollam 690525 Kerala India Indian Inst Sci Educ & Res Div Biol Pune 411021 Maharashtra India Natl Inst Adv Studies Sch Nat Sci & Engn Adjunct Fac Bangalore 560012 Karnataka India

complexity measures are used in a number of applications including extraction of information from data such as ecological time series, detection of non-random structure in biomedical signals, testing of random number generators, language recognition and authorship attribution etc. Different complexity measures proposed in the literature like Shannon entropy, Relative entropy, Lempel-Ziv, Kolmogrov and algorithmic complexity are mostly ineffective in analyzing short sequences that are further corrupted with noise. To address this problem, we propose a new complexity measure ETC and define it as the "Effort To Compress" the input sequence by a lossless compression algorithm. Here, we employ the lossless compression algorithm known as Non-Sequential Recursive Pair Substitution (NSRPS) and define ETC as the number of iterations needed for NSRPS to transform the input sequence to a constant sequence. We demonstrate the utility of ETC in two applications. ETC is shown to have better correlation with Lyapunov exponent than Shannon entropy even with relatively short and noisy time series. The measure also has a greater rate of success in automatic identification and classification of short noisy sequences, compared to entropy and a popular measure based on Lempel-Ziv compression (implemented by Gzip).

关键词： complexity ETC classification Input sequence complexity Compression algorithms entropy time series analysis algorithmic complexity Electron transport chain Lempel-Ziv Time series European territorial cooperation Automatic toll collection

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On hierarchical partitioning of an ecological complexity function

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ECOLOGICAL MODELLING 2000年第1-2期132卷 51-62页

作者： Anand, M Orlóci, L Univ Western Ontario Dept Plant Sci London ON N6A 5B7 Canada

We examine a complexity function in terms of its partitionability across hierarchical levels. We use an ecological example and describe two models partitions by levels in the natural dominance structure of a plant community, and by levels in an analytical hierarchy, constructed from measured species associations. Our results help to answer the frequently asked question of how much the levels of a structured system contribute to total complexity. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： algorithmic complexity association boreal coding community entropy information model pattern scale stratification vegetation

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Entropy and complexity of finite sequences as fluctuating quantities

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BIOSYSTEMS 2002年第1-3期64卷 23-32页

作者： Jiménez-Montaño, MA Ebeling, W Pohl, T Rapp, PE Univ Americas Puebla Dept Fis & Matemat Puebla 72820 Mexico Univ Veracruzana Fac Fis & Inteligencia Artificial Xalapa 91000 Veracruz Mexico Humboldt Univ Inst Phys D-10115 Berlin Germany Med Coll Penn & Hahnemann Univ Dept Physiol Philadelphia PA 19129 USA

The paper is devoted to the analysis of digitized sequences of real numbers and discrete strings, by means of the concepts of entropy and complexity. Special attention is paid to the random character of these quantities and their fluctuation spectrum. As applications, we discuss neural spike-trains and DNA sequences. We consider a given sequence as one realization of finite length of certain random process. The other members of the ensemble are defined by appropriate surrogate sequences and surrogate processes. We show that n-gram entropies and the context-free grammatical complexity have to be considered as fluctuating quantities and study the corresponding distributions. Different complexity measures reveal different aspects of a sequence. Finally, we show that the diversity of the entropy (that takes small values for pseudorandom strings) and the context-free grammatical complexity (which takes large values for pseudorandom strings) give, nonetheless, consistent results by comparison of the ranking of sample sequences taken from molecular biology, neuroscience, and artificial control sequences. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

关键词： block entropies diversity of entropy algorithmic complexity spectrum of fluctuations spike trains DNA sequences

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Intermittent tACS during a visual task impacts neural oscillations and LZW complexity

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EXPERIMENTAL BRAIN RESEARCH 2020年第6期238卷 1411-1422页

作者： Castellano, Marta Ibanez-Soria, David Kroupi, Eleni Acedo, Javier Campolo, Michela Soria-Frisch, Aureli Valls-Sole, Josep Verma, Ajay Ruffini, Giulio Starlab Barcelona SL Av Tibidabo 47 Bis Barcelona 08035 Spain Neuroelectrics SLU Av Tibidabo 47 Bis Barcelona 08035 Spain Univ Barcelona Hosp Clin Neurol Dept EMG Unit Barcelona Spain Univ Barcelona Fac Med IDIBAPS Inst Inveatigacio Agusti Pi i Sunyer Barcelona Spain Biogen Inc 225 Binney St Cambridge MA 02142 USA Neuroelectrics Corp 2 10 BroadwaySuite 201 Cambridge MA 02139 USA

Little is known about how transcranial alternating current stimulation (tACS) interacts with brain activity. Here, we investigate the effects of tACS using an intermittent tACS-EEG protocol and use, in addition to classical metrics, Lempel-Ziv-Welch complexity (LZW) to characterize the interactions between task, endogenous and exogenous oscillations. In a cross-over study, EEG was recorded from thirty participants engaged in a change-of-speed detection task while receiving multichannel tACS over the visual cortex at 10 Hz, 70 Hz and a control condition. In each session, tACS was applied intermittently during 5 s events interleaved with EEG recordings over multiple trials. We found that, with respect to control, stimulation at 10 Hz (tACS10) enhanced both alpha and gamma power, gamma-LZW complexity and gamma but not alpha phase locking value with respect to tACS onset (alpha-PLV, gamma-PLV), and increased reaction time (RT). tACS70 increased RT with little impact on other metrics. As trials associated with larger gamma-power (and lower gamma-LZW) predicted shorter RT, we argue that tACS10 produces a disruption of functionally relevant fast oscillations through an increase in alpha-band power, slowing behavioural responses and increasing the complexity of gamma oscillations. Our study highlights the complex interaction between tACS and endogenous brain dynamics, and suggests the use of algorithmic complexity inspired metrics to characterize cortical dynamics in a behaviorally relevant timescale.

关键词： Transcranial stimulation Entrainment algorithmic complexity LZW Visual cortex gamma oscillations

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THE complexity OF DETECTING CROSSING-FREE CONFIGURATIONS IN THE PLANE

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BIT 1993年第4期33卷 580-595页

作者： JANSEN, K WOEGINGER, GJ UNIV TRIER FACHBEREICH 4W-5500 TRIERGERMANY GRAZ TECH UNIV INST INFORMAT ARBEITUNGA-8010 GRAZAUSTRIA

The computational complexity of the following type of problem is studied. Given a geometric graph G = (P, S) where P is a set of points in the Euclidean plane and S a set of straight (closed) line segments between pairs of points in P, we want to know whether G possesses a crossingfree subgraph of a special type. We analyze the problem of detecting crossingfree spanning trees, one factors and two factors in the plane. We also consider special restrictions on the slopes and on the lengths of the edges in the subgraphs.

关键词： algorithmic complexity PLANAR LAYOUTS GEOMETRY

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complexity analysis of 24 hours heart rate variability time series

Complexity analysis of 24 hours heart rate variability time ...

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26th Annual International Conference of the IEEE-Engineering-in-Medicine-and-Biology-Society

作者： Ferrario, M Signorini, MG Cerutti, S Politecn Milan Dept Bioingn Milan Italy

ISBN: (纸本)0780384393

We propose to study the Heart Rate Variability (HRV) time series complexity by computing the Lempel Ziv complexity measure. LZ is sensitive to the rate of pattern recurrences in a time series. Analysis considers 24 h HRV time series of healthy subjects and patients with cardiovascular diseases. Analysis with simulated signals show the LZ measure can vary depending on the adopted coding process. The binary coding, proposed in this work, is sensitive to the different dynamical systems generating the time series, as the ternary coding is sensitive to the presence of stationary states, i.e. a consecutive repetition of the same RR interval value. LZ method reliably differentiates healthy vs. disease group. Further clinical investigations on the LZ complexity and on its relationship to the risk of sudden death, can supply new diagnostic indications.

关键词： algorithmic complexity heart rate variability Lempel Ziv complexity

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complexity of algorithms and software metrics 18

Complexity of algorithms and software metrics

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18th International Conference on Computers and Their Applications

作者： Burgin, M Debnath, N Univ Calif Los Angeles Dept Math Los Angeles CA 90095 USA

ISBN: (纸本)1880843463

The aim of this paper is to introduce a system structure in the diversity of algorithmic complexity measures for a study of computer software. We consider basic concepts and constructions from the theory of algorithmic complexity and develop a system structure in this theory, especially, for the axiomatic complexity theory. An important class of dual complexity measures is studied. We demonstrate how software metrics fit in the lattice of algorithmic complexity measures. Relations between software metrics and algorithmic complexity are analyzed.

关键词： software software metrics complexity measures algorithmic complexity axiomatic complexity measures dual complexity measures

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Natural scene statistics mediate the perception of image complexity

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VISUAL COGNITION 2014年第8期22卷 1084-1091页

作者： Gauvrit, Nicolas Soler-Toscano, Fernando Zenil, Hector Ecole Prat Hautes Etud CHArt PARIS Reasoning Paris France Univ Seville Grp Log Lenguaje & Informac Seville Spain Karolinska Inst Ctr Mol Med Unit Computat Med Solna Sweden

Humans are sensitive to complexity and regularity in patterns (Falk & Konold, 1997;Yamada, Kawabe, & Miyazaki, 2013). The subjective perception of pattern complexity is correlated to algorithmic (or Kolmogorov-Chaitin) complexity as defined in computer science (Li & Vitanyi, 2008), but also to the frequency of naturally occurring patterns (Hsu, Griffiths, & Schreiber, 2010). However, the possible mediational role of natural frequencies in the perception of algorithmic complexity remains unclear. Here we reanalyze Hsu et al. (2010) through a mediational analysis, and complement their results in a new experiment. We conclude that human perception of complexity seems partly shaped by natural scenes statistics, thereby establishing a link between the perception of complexity and the effect of natural scene statistics.

关键词： Randomness Visual perception algorithmic complexity Visual complexity

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Ecosystem complexity Through the Lens of Logical Depth: Capturing Ecosystem Individuality

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Biological Theory 2014年第4期9卷 440-451页

作者： Gaucherel, Cédric French Institute of Pondicherry (IFP-CNRS) Pondicherry India

In this article, I will discuss possible differences between ecosystems and organisms on the basis of their intrinsic complexity. As the concept of complexity still remains highly debated, I propose here a practical and original way to measure the complexity of an ecosystem or an organism. For this purpose, I suggest using the concept of logical depth (LD) in a specific manner, in order to take into account the difficulty as well as the time needed to generate the studied object. I illustrate this method with fully controlled Daisyworld simulations (i.e., simulations based on the Gaia hypothesis) that have often been proposed to mimic living systems. The method consists of the following sequential stages: (1) identification of the shortest program able to numerically model the studied system (also called the Kolmogorov–Solomonoff complexity);(2) running the program, once if there are no stochastic components in the system, several times if stochastic components are there;and (3) computing the time needed to generate the system with LD complexity. This measure is supposed to estimate the system complexity. It appears in this study that LD estimations fit well with the intuition we have of complex systems, with higher complexities being found for more realistic Daisyworlds. With such a method of capturing the time needed to build a system, we expect to detect in future studies any quantified differences between complex ecosystems and organisms. © 2014, Konrad Lorenz Institute for Evolution and Cognition Research.

关键词： algorithmic complexity Darwinism Gaia hypothesis Lamarckism Lattice

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Analysis of Electrogram complexity during Atrial Fibrillation for Ablation duration Assessment

Analysis of Electrogram Complexity during Atrial Fibrillatio...

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41st Computing in Cardiology Conference (CinC)

作者： Kosna, Katarzyna Podziemski, Piotr Wilson, Lauren Stolcman, Simon Sanders, Prashanthan Gieraltowski, Jan Zebrowski, Jan J. Kuklik, Pawel Warsaw Univ Technol Fac Phys Koszykowa 75 PL-00662 Warsaw Poland Royal Adelaide Hosp Cardiovasc Res Ctr Adelaide SA 5000 Australia Univ Hosp Eppendorf Dept Electrophysiol Hamburg Germany

ISBN: (纸本)9781479943463

The aim of this study was to assess the reliability of the complexity analysis of single electrogram as an estimator of the length of the ablation procedure necessary for AF termination. Left and right atrial endocardial bipolar electrograms were recorded during ablation procedure of AF in 27 patients. Up to 30 second electrogram samples were measured at baseline, after each stage of ablation (LPV, roof, CFAE etc.) and prior to termination. For each electrogram, algorithmic complexity was calculated. Electrograms had significantly lower algorithmic complexity for patients who had two or less ablation stages performed than for patients for whom more than two ablation stage was performed (p < 0.001). ROC analysis showed 100% statistical sensitivity for 81% statistical specificity. These results show that algorithmic complexity increases with a number of ablation stages needed to terminate AF, which is related with the duration of the ablation procedure.

关键词： computational complexity data analysis diseases electrocardiography medical computing radiation therapy sensitivity analysis statistical analysis AF ablation duration assessment AF termination CFAE ablation stage LP V ablation stage ROC analysis ablation procedure length estimator ablation stage number ablation termination algorithmic complexity calculation atrial fibrillation baseline measurement complexity analysis reliability assessment endocardial bipolar electrogram recording left atrial endocardial bipolar electrogram right atrial endocardial bipolar electrogram roof ablation stage single electrogram complexity analysis statistical sensitivity statistical specificity time 30 s Abstracts Algorithm design and analysis Analysis of variance complexity theory Physics Algorithm design and analysis ROC Curve algorithmic complexity medical computing Baseline measurements electrogram complexity theory Data analysis Statistical analysis ABLATION Electrocardiography complexity classes Analysis of Variance Radiotherapy Statistical methods

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