A comparison of waveform fractal dimension algorithms
01 Feb 2001-IEEE Transactions on Circuits and Systems I-regular Papers (IEEE)-Vol. 48, Iss: 2, pp 177-183
TL;DR: This study demonstrates that a careful selection of fractal dimension algorithm is required for specific applications, and the most common methods of estimating the fractaldimension of biomedical signals directly in the time domain are analyzed and compared.
Abstract: The fractal dimension of a waveform represents a powerful tool for transient detection. In particular, in analysis of electroencephalograms and electrocardiograms, this feature has been used to identify and distinguish specific states of physiologic function. A variety of algorithms are available for the computation of fractal dimension. In this study, the most common methods of estimating the fractal dimension of biomedical signals directly in the time domain (considering the time series as a geometric object) are analyzed and compared. The analysis is performed over both synthetic data and intracranial electroencephalogram data recorded during presurgical evaluation of individuals with epileptic seizures. The advantages and drawbacks of each technique are highlighted. The effects of window size, number of overlapping points, and signal-to-noise ratio are evaluated for each method. This study demonstrates that a careful selection of fractal dimension algorithm is required for specific applications.
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Patent•
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TL;DR: A neurological control system for modulating activity of any component or structure comprising the entirety or portion of the nervous system, or any structure interfaced thereto, generally referred to herein as a “nervous system component,” is described in this article.
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TL;DR: A signal feature with low computational burden is presented as an efficient tool for seizure onset detection by evaluating 1,215 hours of intracranial EEG signal from 10 patients.
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252 citations
Cites methods from "A comparison of waveform fractal di..."
...This feature can be derived from the fractal dimension by Katz [5] studied in [6]-[7]; however, unlike fractal dimension is computationally more efficient and more accurate for seizure onset detection....
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...The results presented in [7] with simulated and experimental IEEG data were within the range of values for which the fractal dimension by Katz works well....
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TL;DR: This paper studies a new methodology to model and predict chaotic time series based on a new recurrent predictor neural network (RPNN) that realizes long-term prediction by making accurate multistep predictions.
Abstract: Chaos limits predictability so that the long-term prediction of chaotic time series is very difficult. The main purpose of this paper is to study a new methodology to model and predict chaotic time series based on a new recurrent predictor neural network (RPNN). This method realizes long-term prediction by making accurate multistep predictions. This RPNN consists of nonlinearly operated nodes whose outputs are only connected with the inputs of themselves and the latter nodes. The connections may contain multiple branches with time delays. An extended algorithm of self-adaptive back-propagation through time (BPTT) learning algorithm is used to train the RPNN. In simulation, two performance measures [root-mean-square error (RMSE) and prediction accuracy (PA)] show that the proposed method is more effective and accurate for multistep prediction. It can identify the systems characteristics quite well and provide a new way to make long-term prediction of the chaotic time series.
233 citations
Cites background from "A comparison of waveform fractal di..."
...In fact, the deterministic nature of chaotic dynamics and the universal approximation capabilities of neural networks make it possible to make reliable forecasts in complex systems [7], [8]....
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References
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TL;DR: In this article, a measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable, and the relation of this measure to fractal dimension and information-theoretic entropy is discussed.
Abstract: A new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable. The relation of this new measure to fractal dimension and information-theoretic entropy is discussed.
4,323 citations
TL;DR: In this paper, the existence of low-dimensional chaotic dynamical systems describing turbulent fluid flow was determined experimentally by reconstructing phase-space pictures from the observation of a single coordinate of any dissipative dynamical system and determining the dimensionality of the system's attractor.
Abstract: It is shown how the existence of low-dimensional chaotic dynamical systems describing turbulent fluid flow might be determined experimentally. Techniques are outlined for reconstructing phase-space pictures from the observation of a single coordinate of any dissipative dynamical system, and for determining the dimensionality of the system's attractor. These techniques are applied to a well-known simple three-dimensional chaotic dynamical system.
3,628 citations
TL;DR: In this article, the fractal dimension of the set of points (t, f(t)) forming the graph of a function f defined on the unit interval was measured using a self-similarity property.
1,825 citations
"A comparison of waveform fractal di..." refers background in this paper
...It consists of estimating the dimension of a time-varying signal (waveform) directly in the time domain, which allows significant savings in program run-time....
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