A note on fractal dimensions of biomedical waveforms.
ABSTRACT In this paper, we study performance of Katz method of computing fractal dimension of waveforms, and its estimation accuracy is compared with Higuchi's method. The study is performed on four synthetic parametric fractal waveforms for which true fractal dimensions can be calculated, and real sleep electroencephalogram. The dependence of Katz's fractal dimension on amplitude, frequency and sampling frequency of waveforms is noted. Even though the Higuchi's method has given more accurate estimation of fractal dimensions, the study suggests that the results of Katz's based fractal dimension analysis of biomedical waveforms have to be carefully interpreted.
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ABSTRACT: Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.Computational and Mathematical Methods in Medicine 01/2013; 2013:178476. · 0.79 Impact Factor
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ABSTRACT: The objective of the work was to develop a non-invasive methodology for image acquisition, processing and nonlinear trajectory analysis of the collective fish response to a stochastic event. Object detection and motion estimation were performed by an optical flow algorithm in order to detect moving fish and simultaneously eliminate background, noise and artifacts. The Entropy and the Fractal Dimension (FD) of the trajectory followed by the centroids of the groups of fish were calculated using Shannon and permutation Entropy and the Katz, Higuchi and Katz-Castiglioni's FD algorithms respectively. The methodology was tested on three case groups of European sea bass (Dicentrarchus labrax), two of which were similar (C1 control and C2 tagged fish) and very different from the third (C3, tagged fish submerged in methylmercury contaminated water). The results indicate that Shannon entropy and Katz-Castiglioni were the most sensitive algorithms and proved to be promising tools for the non-invasive identification and quantification of differences in fish responses. In conclusion, we believe that this methodology has the potential to be embedded in OPEN ACCESS Entropy 2014, 16 6134 online/real time architecture for contaminant monitoring programs in the aquaculture industry.Entropy 01/2014; 16:6133-6151. · 1.35 Impact Factor
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ABSTRACT: Abstract The study of electromyographic (EMG) signals has gained increased attention in the last decades since the proper analysis and processing of these signals can be instrumental for the diagnosis of neuromuscular diseases and the adaptive control of prosthetic devices. As a consequence, various pattern recognition approaches, consisting of different modules for feature extraction and classification of EMG signals, have been proposed. In this paper, we conduct a systematic empirical study on the use of Fractal Dimension (FD) estimation methods as feature extractors from EMG signals. The usage of FD as feature extraction mechanism is justified by the fact that EMG signals usually show traces of self-similarity and by the ability of FD to characterize and measure the complexity inherent to different types of muscle contraction. In total, eight different methods for calculating the FD of an EMG waveform are considered here, and their performance as feature extractors is comparatively assessed taking into account nine well-known classifiers of different types and complexities. Results of experiments conducted on a dataset involving seven distinct types of limb motions are reported whereby we could observe that the normalized version of the Katz׳s estimation method and the Hurst exponent significantly outperform the others according to a class separability measure and five well-known accuracy measures calculated over the induced classifiers.Engineering Applications of Artificial Intelligence 11/2014; 36:81 - 98. · 1.96 Impact Factor