Chaos and time-series analysis

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Book Chapter•DOI•

Computational Intelligence: An Introduction

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John Fulcher¹•Institutions (1)

University of Wollongong¹

01 Jan 2008

TL;DR: The general public becomes rapidly jaded with such ‘bold predictions’ that fail to live up to their original hype, and which ultimately render the zealots’ promises as counter-productive.

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Abstract: The Artificial Intelligence field continues to be plagued by what can only be described as ‘bold promises for the future syndrome’, often perpetrated by researchers who should know better. While impartial assessment can point to concrete contributions over the past 50 years (such as automated theorem proving, games strategies, the LISP and Prolog high-level computer languages, Automatic Speech Recognition, Natural Language Processing, mobile robot path planning, unmanned vehicles, humanoid robots, data mining, and more), the more cynical argue that AI has witnessed more than its fair share of ‘unmitigated disasters’ during this time – see, for example [3,58,107,125,186]. The general public becomes rapidly jaded with such ‘bold predictions’ that fail to live up to their original hype, and which ultimately render the zealots’ promises as counter-productive.

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846 citations

Cites background from "Chaos and time-series analysis"

...Nowadays, most authors would agree on a core definition of fuzzy, neural and evolutionary (data-driven) methodologies, but some extend this to cover granular computing [190,240,326,330], probabilistic reasoning, Bayesian (belief) networks [147, 161, 216], fuzzy Petri nets, constrained reasoning, case-based reasoning [231, 304], Support Vector Machines [1, 270, 297], rough sets [140, 189, 237], learning/adaptive classifiers, fractals [85, 200], wavelets [198,242], and/or chaos theory [228,282], not to mention the intelligent agents [229] alluded to earlier....
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Dissertation•

Analysis of observed chaotic data

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Mehmet Emre Çek

01 Jan 2004

602 citations

Cites background or methods from "Chaos and time-series analysis"

...3 Detrending The Data To reduce the nonstationary of the time series, the data is detrended [6]....
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...For an attractor with uniform measure, it is expected that D0=D2, otherwise D0<D2 [6]....
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...A sample estimate of the probability density function P(X) which is called as the histogram of the data, can be obtained by partitioning the interval from minimum to the maximum of x(t) into some specified numbers which may be N where N is the data number in the time series [6]....
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...Besides experimental time series will be contaminated by measuring and rounding errors when represent an analogue signal digitally [6]....
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...Two methods are given in [6] and [9] for determining embedding dimension which are time delay coordinates and derivative coordinates respectively....
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Journal Article•DOI•

Recurrence networks—a novel paradigm for nonlinear time series analysis

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Reik V. Donner¹, Yong Zou², Jonathan F. Donges³, Jonathan F. Donges², Norbert Marwan², Jürgen Kurths³, Jürgen Kurths² - Show less +3 more•Institutions (3)

Max Planck Society¹, Potsdam Institute for Climate Impact Research², Humboldt University of Berlin³

15 Mar 2010-New Journal of Physics

TL;DR: In this article, a new approach for analyzing the structural properties of time series from complex systems is presented, which can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases.

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Abstract: This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis.

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548 citations

Journal Article•DOI•

The dynamics of human gait

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Matjaž Perc¹•Institutions (1)

University of Maribor¹

01 May 2005-European Journal of Physics

TL;DR: It is shown that short continuous recordings of the human locomotory apparatus possess properties typical of deterministic chaotic systems, and user-friendly programs are provided for each implemented method.

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Abstract: We analyse the dynamics of human gait with simple nonlinear time series analysis methods that are appropriate for undergraduate courses. We show that short continuous recordings of the human locomotory apparatus possess properties typical of deterministic chaotic systems. To facilitate interest and enable the reproduction of presented results, as well as to promote applications of nonlinear time series analysis to other experimental systems, we provide user-friendly programs for each implemented method. Thus, we provide new insights into the dynamics of human locomotion, and make an effort to ease the inclusion of nonlinear time series analysis methods into the curriculum at an early stage of the educational process.

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385 citations

Cites background from "Chaos and time-series analysis"

...While there exist excellent monographs on nonlinear time series analysis [4–6], there is still a shortage of literature showing concrete applications of simple methods to real-life problems....
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Journal Article•DOI•

Complex network approaches to nonlinear time series analysis

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Yong Zou¹, Reik V. Donner², Norbert Marwan², Jonathan F. Donges³, Jonathan F. Donges², Jürgen Kurths⁴, Jürgen Kurths², Jürgen Kurths⁵ - Show less +4 more•Institutions (5)

East China Normal University¹, Potsdam Institute for Climate Impact Research², Stockholm Resilience Centre³, Humboldt University of Berlin⁴, Saratov State University⁵

21 Jan 2019-Physics Reports

TL;DR: An in-depth review of existing approaches of time series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments, and emphasizes which fundamental new insights complex network approaches bring into the field of nonlinear time series analysis.

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382 citations

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Journal Article•DOI•

Nonlinear Coherence in Multivariate Research: Invariants and the Reconstruction of Attractors

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Frederick David Abraham¹•Institutions (1)

Allen Institute for Brain Science¹

01 Jan 1997-Nonlinear Dynamics, Psychology, and Life Sciences

TL;DR: In this article, the problem of estimating the dimensionality of the state space (embedding dimension), the reconstruction of an attractor, and the evaluation of invariant properties of the attractor is discussed.

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Abstract: First, some linear techniques in multivariate time-series analysis in EEG research are reviewed to highlight the problem of estimating the dimensionality of the state space (embedding dimension), the reconstruction of an attractor, and the evaluation of invariant properties of the attractor. The traditional linear techniques included the usual spectral and cospectral measures of power, phase, and coherence to which stepwise discriminant analysis was applied for canonical representation of the attractor. Then, some traditional nonlinear techniques of attractor reconstruction and dimensional analysis which use the time-lagged univariate approach of Ruelle and Takens (Takens, 1981) are reviewed. Next, updates and multivariate generalizations that use singular-value decomposition (Broomhead & King, 1986) are reviewed. Finally, Stewart's (1995, 1996) multivariate generalization of the method of false nearest neighbors (Abarbanel, Brown, Sidorowich, & Tsimring, 1993; Kennel, Brown, & Abarbanel, 1992) is reviewed. These are particularly relevant for evaluating multivariate coherence in research on the complex cooperative dynamical systems found in neuroscience, psychology, and social science when time series of sufficient length are investigated.

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14 citations