Apr, 2012 higuchis method is a procedure that, if applied appropriately, can determine in a reliable way the fractal dimension d of time series. Abstract this paper analyzes the complexity of stock exchanges through fractal theory. Fractal dimension algorithms and their application to. Detection of abnormality in electrocardiogram ecg signals. Fractal dimension analysis of the magnetic time series. Fractal analysis of the eeg and clinical applications openstarts.
Moreover, the proposed method is not restricted to higuchi s algorithm, as any 1d method of analysis, can be. Higuchi 1988, 1990 proposed a method to calculate the fractal dimension of selfaf. Signal pattern recognition based on fractal features and machine. The comparison of higuchis fractal dimension and sample. Eeg fractal dimension before and after human auditory. The main algorithm used to calculate the fractal dimension was higuchis algorithm. A comparison of waveform fractal dimension algorithms circuits. A fractal is a shape that retains its structural detail despite scaling and this is the reason why complex objects can be described with the help of fractal dimension. Everything you wanted to ask about eeg but were afraid to. Hfd algorithm calculates fractal dimension of time series directly in the time domain.
The implementation was tested with one thousand different fractional brownian motion signals each of fractal dimension 1. Application of combined nonlinear features provides better discrimination for depressed and normal subjects % comparedtoeegbandspower. The higuchis method is a method of analysis that is being increasingly used for the analysis of time series 2,3, it is a very ef. In this paper, we concentrate on recognition of inner emotions from electroencephalogram eeg signals. Differently from methods usually used in literature to evaluate the fractal dimension, the parameter used in this work has been extracted directly from the hrv sequences in the time domain, by means of the higuchis algorithm. A signal is fractal if the scaling properties fit a scalefree behavior, i. A fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale 1 several types of fractal dimension can be measured theoretically and empirically. The source code and files included in this project are listed in the project files section, please make sure whether the listed source code meet your needs there. Spectral asymmetry index and higuchis fractal dimension.
Higuchi and katz fractal dimension measures file exchange. Is there any algorithm to select the k max in higuchis. Pdf application of higuchis fractal dimension from basic to clinical. The main goal of this research was to examine accuracy that means sensitivity and specificity of these methods and. At last, through the similarity calculation, we can obtain the distance matrix, by which, the phylogenic tree can be constructed. Applying higuchis algorithm, we calculated fractal dimension fd values of sinus function and rat cerebellar signals before and after acute brain injury. Higuchis method is well accepted and widely applied, because it. Higuchi dimension of digital images pubmed central pmc. It is also observed that fractal dimensions, d, calculated with higuchis method may not be constant overall time scales. Complete higuchi fractal dimension algorithm file exchange. The mean fractal dimension of the horizontal landscape is denoted by d h, the mean fractal dimension of the vertical landscape is denoted by d v cf. The higuchi algorithm generates multiple time series. A comparison of waveform fractal dimension algorithms.
Katzs algorithm in contrast to petrosians method to be described in section iic, katzs fd calculation 2 is slightly slower, but it. Actual values for the fractal dimensions are reliable and an effective treatment of regions of interests is possible. The higuchis algorithm constructs k new time series as. Various sampling frequences of an artificial signal as of sinus function, for example may essentially change the function graphic and therefore the corresponding fractal dimension. Discretized functions or signals could be analyzed as time sequences x1, x2, xn. Effect of sampling frequency on acoustic emission onset. The higuchis algorithm shown in 7 performs approximated calculation of the fractal dimension df of time series directly in the. Application of higuchis fractal dimension from basic to. Fractal analysis of the eeg and clinical applications.
It is based on a measure of length of the curve that represents the considered time series while using a segment of samples as a unit if scales like the value of fractal dimension fd was calculated according to the. Eeg machine learning with higuchis fractal dimension and sample entropy as features for successful detection of depression milena cukic1,2, david pokrajac3, miodrag stokic4,5, slobodan simic6, vlada radivojevic6, and milos ljubisavljevic7 1 general physiology with biophysics, university of belgrade, belgrade, serbia. Higuchis fractal dimension hfd higuchi, 1988 which serves as a measure of signal complexity. A fractal dimension and wavelet transform based method for. Many algorithms are available to compute fd, like those proposed by higuchi 25, maragos and sun 26, katz 27 and petrosian 28, or the box counting method. Fractal dimensions of data series, particularly time series can be estimated very well by using higuchis algorithm. Pdf higuchi fractal dimension of the electroencephalogram. The main result is that higuchis algorithm allows a direction dependent as well as direction independent analysis. The onset is determined by detecting the change in fractal dimension. Is a twodimensional generalization of the higuchi algorithm. Computationalandmathematicalmethodsinmedicine 3 0 12345 time s. Fractal analysis of artificial and cerebellar signals at. Without phase space constructions, the fractal dimension of a onedimensional data stream is calculated.
The difference of mean higuchis fractal dimension are. The theoretical fractal dimension for this fractal is log32log8 1. Tikkuhirvi tietavainen and probably corrected by mr. Keywordsboxcounting, fractal dimension, higuchi method. Assessing entropy and fractal dimensions as discriminants. Higuchis algorithm calculates fractal dimension of a time series directly in the time domain. Assume a one dimensional time series x x1, x2, x3, xn where, n is the total number of samples, in this case the series x would be the successive values of ecg signal. We chose to use this method because it is widespread in the eeg scientific literature and this will facilitate the comparison of our results. It is based on a measure of length lk of the curve that represents the considered time series while using a segment of k samples as a unit if lk scales like lk k fd.
Higuchis fractal dimension of a time series is a number between 1 and 2, with higher hfd values corresponding to higher levels of signal complexity. Higuchis method applied to the detection of periodic. Compared with petrosians algorithm, higuchi s one does not depend on a binary sequence and, in many cases, it is less sensitive to noise 30. The algorithms were then com pared by evaluating not only the. The following matlab project contains the source code and matlab examples used for complete higuchi fractal dimension algorithm. The main goal of this research was to examine accuracy that means sensitivity and specificity of these methods and compare the applicability of both methods in the. In this paper we study the effect of higuchi fractal dimension for different phonemes. Briefly, from a given interval series rr or qt of points, n namely, xx1, x2, xn, the technique constructs k new time series, defined as. Higuchis fractal dimension is a nonlinear measure of waveform complexity in the time domain. Fractal analysis of rat brain activity after injury.
The hfd algorithm calculates fractal dimension of time series directly in the time domain 19. Methods and data higuchi fractal dimension 20 is a method developed for estimating the amount of selfsimilarity of the data. Comparison of higuchi, katz and multiresolution boxcounting. We propose to apply the higuchi fractal dimension hfd method for assessment of ans activity.
The method for calculating the fractal dimension of a curve in a plane was proposed by higuchi in 1988 21. Electroencephalographic fractal dimension in healthy. Application of higuchis fractal dimension in analysis of. Higuchis fractal dimension hfd is an appropriate method for analysing the fd of biomedical signals 9, as meg recordings, due to the following reasons. Download fulltext pdf download fulltext pdf using higuchi s fractal dimension in fine analysis of the effects of 2. We used higuchis algorithm 16 to estimate the fd because it is computationally efficient and provides a stable estimate of fd using a lower number of samples of data n 125 than other fd algorithms 10, which allowed us to estimate fd with good temporal resolution. This paper presents the implementation of fractal dimension theory to make a classification of phonocardiograms into a normal heart sound, a murmur, or an extrasystole. Higuchi 20 used his method for magnetic field data and in 21, 2325 higuchis method was used for electroencephalography. Pdf higuchis fractal dimension for analysis of the. Since living systems are nonlinear, evaluation of ans activity is difficult by means of linear methods. Higuchi s algorithm calculates fractal dimension of a time series directly in the time domain. However, when analyzing some time series with higuchis method, there are oscillations at the righthand side of the graph, which can cause a mistaken determination of. Higuchis fractal dimension originates from chaos theory and for almost thirty years it has been successfully applied as a complexity measure of artificial, natural or. Use of the higuchis fractal dimension for the analysis of meg.
Highlights new fractal method for grading anal intraepithelial neoplasia tumors is validated. For calculating the fractal dimension we used the higuchi algorithm 7. Higuchis fractal complexity of rr and qt interval series. Electroencephalographic fractal dimension in healthy ageing.
For calculation of higuchis fractal dimension our longtime experience suggested making use of moving window length of 100 points, moved each time 1 point, with k max 8. Closing price indices of four stock exchanges with different industry sectors are selected. Aug 21, 2018 analysis of heart rate variability hrv can be applied to assess the autonomic nervous system ans sympathetic and parasympathetic activity. Gomez, c, mediavilla, a, hornero, r, abasolo, d and fernandez, a 2009 use of the higuchis fractal dimension for the analysis of meg recordings from alzheimers disease patients med eng phys, 31 3. The ilf image landscapes fractal dimension method and d f 2 d method obtained by a 2d generalization of higuchis algorithm were applied to a set of 120 digital histological images of anal intraepithelial neoplasia ain. With application of the higuchi algorithm, fractal dimension fd values of the electrocortical activity of the rat parietal cerebral and paravermal cerebellar cortex were calculated, before and. Mar 27, 2015 in the file i offer the source code of. Research article spectral asymmetry and higuchi s fractal. Assessing entropy and fractal dimensions as discriminants of. Based on this result, higuchis fractal dimension was used to. Computing fractal dimension of signals using multiresolution boxcounting method, international journal of information and mathematical sciences, 6. Higuchis algorithm for fractal dimensions higuchis algorithm showed promise in differentiating between eeg segments with seizures and seizurefree eeg segments.
Higuchis fractal dimension is a widely used index for evaluating fractality in brain activity, but temporalscalespecific characteristics are lost due to its requirement of averaging over the. Emotion recognition could be done from the text, speech, facial expression or gesture. Compared with petrosians algorithm, higuchis one does not depend on a binary sequence. Eeg machine learning with higuchis fractal dimension and. Analysis of heart rate variability hrv can be applied to assess the autonomic nervous system ans sympathetic and parasympathetic activity. Diagnostic and statistical manual of mental disorders 5th ed. Moreover, the proposed method is not restricted to higuchis algorithm, as any 1d method of analysis, can be. The aim is to provide a classifying parameter which can clearly demarcate normal heart sounds from those with murmurs. Higuchi fractal dimension hfd katz fractal dimension kfd the source code is properly commented in english. Pdf using higuchis fractal dimension in fine analysis. Fractal dimensions are used to characterize a broad spectrum of objects ranging from the abstract to practical phenomena, including.
On 2d generalization of higuchis fractal dimension. The difference of mean higuchis fractal dimension are not statistically significant between healthy and. The fractal dimension is an important characteristic of systems, because it contains information about their geometrical structure at multiple scales. We propose a new method for calculating fractal dimension df of a signal yt, based on coefficients, mean absolute values of its nth order derivatives consecutive finite differences for sampled signals. Direct estimation with higuchis algorithm turned out to be the most suitable methodology, producing correct estimates of the fractal dimension of the electroencephalogram also on short traces, provided that minimum sampling rate required to avoid aliasing is used. Higuchi proposed an efficient algorithm to calculate the fd directly from time series. Complex patterns in financial time series through higuchis. It is based on a measure of length lk of the curve that represents the considered time series while using a segment of k samples as a unit if lk scales like lk k fd 3 the value of the fractal dimension fd was. The main result is that higuchi s algorithm allows a direction dependent as well as direction independent analysis. Spectral asymmetry index and higuchis fractal dimension for. It is based on a measure of length, lk, of the curve that represents the considered time series while using a segment of k samples as a unit, if lk scales like.
Many studies on the presented topics demonstrated the advantage of hfd for measuring the complexity of neuronal activity. With application of the higuchi algorithm, fractal dimension fd values of the electrocortical activity of the rat parietal cerebral and paravermal cerebellar cortex were calculated, before and after unilateral discrete injury of the left parietal cortex. Use of the higuchis fractal dimension for the analysis of. The mistake is in the formula for lm,k or lm k as in some papers. A fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale. Comparison of fractal dimension estimation algorithms for epileptic seizure onset detection, journal of neural engineering, 046007, 18 pages. One of important advantages of higuchis algorithm is that the mean fractal dimension in different sleep stages is not very sensitive to artifacts 8.
The result is an algorithm for reliably estimating the fractal dimension of surfaces or, more. Comparison of higuchi, katz and multiresolution box. Fractal dimension of the eeg for detection of behavioural. A series of hybrid method involving discrete wavelet transform, fractal dimension calculation hwf with sliding window are then applied to form the feature vector. Spectral asymmetry and higuchis fractal dimension measures. Higuchis fractal dimension fractal behaviour displaying selfsimilarities across the time scale of the intervals series have been quantified using higuchis fractal dimension algorithm 9. Fractal dimension algorithms and their application.
In the curve of versus, the slope of the least squares linear best fit is the estimate of the fractal dimension 1. Fractal dimension fd refers to a noninteger or fractional dimension of a geometric object. We propose realtime fractal dimension based algorithm of quantification of. These signals, so called landscapes, are analyzed using higuchis fractal dimension. Higuchi fractal properties of onset epilepsy electroencephalogram. Fractal dimensions of data series, particularly time series can be estimated very well by using higuchi s algorithm. The following describes how to apply the higuchis method to a time series. It is based on a measure of length, of the curve that represents the considered time series while using a segment of samples as a unit, if scales like. Compared with petrosians algorithm, higuchis one does not depend on a binary sequence and, in many cases, it is less sensitive to noise 30. In this work, three algorithms are applied to nonlinear time series. Higuchi s fractal dimension originates from chaos theory and for almost thirty years it has been successfully applied as a complexity measure of artificial, natural or.
Degree of complexity is assessed through higuchis fractal dimension. Complete higuchi fractal dimension algorithm in matlab. Receiver operating characteristic curve analysis is used for grades discrimination. For more than 20 years, higuchis fractal dimension hfd, as a nonlinear method, has occupied an important.
The method is based on constructing from the analyzed 2d image two 1d quasisignals. Fractal analysis was performed by an fd calculating of electrophysiological signals from br neurons using higuchis method. Higuchis fractal dimension and fractal analysis higuchis fractal dimension is used as a nonlinear measure of signal complexity in the time domain higuchi, 1988. The stationary signal was composed of five harmonic waves of. Figure 2 displays a plot of fractal dimension calculated in seizure free intervals in the hippocampal regions of the brain. Pdf fractal dimension algorithms and their application to time. Fractal dimension was estimated using higuchis method 7. The performance of this method is verified against a continuous wavelet transform generated time scale domain method. An example of the recorded depression eeg signal in.
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