Academic literature on the topic 'Higuchi's algorithm'

The fractal dimension of signals represents a powerful tool for analyzing the irregular behavior and state of the dynamical systems. Analysis of waveforms has been used to identify and distinguish specific complex patterns. A variety of algorithms are available for the computation of fractal dimension of waveforms. In this paper we evaluate the performance of our algorithm based on size measure relationship method, quantifying the synthetic waveforms and electroencephalographic signals. Compared to Katz's, Higuchi's and Petrosian's algorithm advantages of this method include greater speed and not affected by noise. The computation time for the algorithm suggested in this paper is much less than the other methods.

Arterial blood pressure is modulated by several physiological regulatory processes. The analysis of beat-to-beat blood pressure dynamics provides information about cardiovascular control and patho-physiological conditions. In this paper we investigated the long-term correlations and fractal dimension of systolic blood pressure time series applying detrended fluctuation analysis (DFA) and Higuchi's algorithm (HFD). Thirty-minute blood pressure recordings in 25 patients with dilated cardiomyopathy (DCM) and 27 healthy controls (CON) were analyzed. The DFA and HFD revealed multifractal features in the blood pressure dynamics of CON as well as of DCM. At small scales, DFA and HFD of CON were significantly different from those of CON, reflecting patho-physiological changes. In conclusion, scaling analysis of blood pressure dynamics might lead to an enhanced assessment of autonomic cardiovascular control in patients with DCM.

We propose a new method for calculating fractal dimension (DF) of a signal y(t), based on coefficients [Formula: see text], mean absolute values of its nth order derivatives (consecutive finite differences for sampled signals). We found that logarithms of [Formula: see text], n = 2,3,…,n max , exhibited linear dependence on n: [Formula: see text] with stable slopes and Y-intercepts proportional to signal DF values. Using a family of Weierstrass functions, we established a link between Y-intercepts and signal fractal dimension: [Formula: see text] and calculated parameters A(n max ) and B(n max ) for n max = 3,…,7. Compared to Higuchi's algorithm, advantages of this method include greater speed and eliminating the need to choose value for k max , since the smallest error was obtained with n max = 3.

(1) Background: An approach for skin cancer recognition and classification by implementation of a novel combination of features and two classifiers, as an auxiliary diagnostic method, is proposed. (2) Methods: The predictions are made by k-nearest neighbor with a 5-fold cross validation algorithm and a neural network model to assist dermatologists in the diagnosis of cancerous skin lesions. As a main contribution, this work proposes a descriptor that combines skin surface fractal dimension and relevant color area features for skin lesion classification purposes. The surface fractal dimension is computed using a 2D generalization of Higuchi’s method. A clustering method allows for the selection of the relevant color distribution in skin lesion images by determining the average percentage of color areas within the nevi and melanoma lesion areas. In a classification stage, the Higuchi fractal dimensions (HFDs) and the color features are classified, separately, using a kNN-CV algorithm. In addition, these features are prototypes for a Radial basis function neural network (RBFNN) classifier. The efficiency of our algorithms was verified by utilizing images belonging to the 7-Point, Med-Node, and PH2 databases; (3) Results: Experimental results show that the accuracy of the proposed RBFNN model in skin cancer classification is 95.42% for 7-Point, 94.71% for Med-Node, and 94.88% for PH2, which are all significantly better than that of the kNN algorithm. (4) Conclusions: 2D Higuchi’s surface fractal features have not been previously used for skin lesion classification purpose. We used fractal features further correlated to color features to create a RBFNN classifier that provides high accuracies of classification.

Epilepsy is a medical term which indicates a common neurological disorder characterized by seizures, because of abnormal neuronal activity. This leads to unconsciousness or even a convulsion. The possible etiologies should be evaluated and treated. Therefore, it is necessary to concentrate not only on finding out efficient treatment methods, but also on developing algorithm to support diagnosis. Currently, there are a number of algorithms, especially nonlinear algorithms. However, those algorithms have some difficulties one of which is the impact of noise on the results. In this paper, in addition to the use of fractal dimension as a principal tool to diagnose epilepsy, the combination between ICA algorithm and averaging filter at the preprocessing step leads to some positive results. The combination which improved the fractal algorithm become robust with noise on EEG signals. As a result, we can see clearly fractal properties in preictal and ictal period so as to epileptic diagnosis.

Epileptic diseases take EEG as an important basis for clinical judgment, and fractal algorithms were often used to analyze electroencephalography (EEG) signals. However, the variation trends of fractal dimension (D) were opposite in the literature, i.e., both D decreasing and increasing were reported in previous studies during seizure status relative to the normal status, undermining the feasibility of fractal algorithms for EEG analysis to detect epileptic seizures. In this study, two algorithms with high accuracy in the D calculation, Higuchi and roughness scaling extraction (RSE), were used to study D variation of EEG signals with seizures. It was found that the denoising operation had an important influence on D variation trend. Moreover, the D variation obtained by RSE algorithm was larger than that by Higuchi algorithm, because the non-fractal nature of EEG signals during normal status could be detected and quantified by RSE algorithm. The above findings in this study could be promising to make more understandings of the nonlinear nature and scaling behaviors of EEG signals.

This work examines if chaos and long memory exist in PM10 concentrations recorded in Athens, Greece. The algorithms of Katz, Higuchi, and Sevcik were employed for the calculation of fractal dimensions and Rescaled Range (R/S) analysis for the calculation of the Hurst exponent. Windows of approximately two months’ duration were employed, sliding one sample forward until the end of each utilized signal. Analysis was applied to three long PM10 time series recorded by three different stations located around Athens. Analysis identified numerous dynamical complex fractal time-series segments with patterns of long memory. All these windows exhibited Hurst exponents above 0.8 and fractal dimensions below 1.5 for the Katz and Higuchi algorithms, and 1.2 for the Sevcik algorithm. The paper discusses the importance of threshold values for the postanalysis of the discrimination of fractal and long-memory windows. After setting thresholds, computational calculations were performed on all possible combinations of two or more techniques for the data of all or two stations under study. When all techniques were combined, several common dates were found for the data of the two combinations of two stations. When the three techniques were combined, more common dates were found if the Katz algorithm was not included in the meta-analysis. Excluding Katz’s algorithm, 12 common dates were found for the data from all stations. This is the first time that the results from sliding-window chaos and long-memory techniques in PM10 time series were combined in this manner.

This paper analyzes the complexity of stock exchanges through fractal theory. Closing price indices of four stock exchanges with different industry sectors are selected. Degree of complexity is assessed through Higuchi’s fractal dimension. Various window sizes are considered in evaluating the fractal dimension. It is inferred that the data considered as a whole represents random walk for all the four indices. Analysis of financial data through windowing procedure exhibits multi-fractality. Attempts to apply moving averages to reduce noise in the data revealed lower estimates of fractal dimension, which was verified using fractional Brownian motion. A change in the normalization factor in Higuchi’s algorithm did improve the results. It is quintessential to focus on rural development to realize a standard and steady growth of economy. Tools must be devised to settle the issues in this regard. Micro level institutions are necessary for the economic growth of a country like India, which would induce a sporadic development in the present global economical scenario.

Fractal algorithms for signal analysis are developed from geometric fractals and can be used to describe various complex signals in nature. A roughness scaling extraction algorithm with first-order flattening (RSE-f1) was shown in our previous studies to have a high accuracy, strong noise resistance, and a unique capacity to recognize the complexity of non-fractals that are common in signals. In this study, its disadvantage of a long calculation duration was addressed by using a dichotomy-binary strategy. The accelerated RSE-f1 algorithm (A-RSE-f1) retains the three above-mentioned advantages of the original algorithm according to theoretical analysis and artificial signal testing, while its calculation speed is significantly accelerated by 13 fold, which also makes it faster than the typical Higuchi algorithm. Afterwards, the vibration signals of the milling process are analyzed using the A-RSE-f1 algorithm, demonstrating the ability to distinguish different machining statuses (idle, stable, and chatter) effectively. The results of this study demonstrate that the RSE algorithm has been improved to meet the requirements of practical engineering with both a fast speed and a high performance.

2010/2011
Most of the knowledge about physiological systems has been learned using linear system theory. The randomness of many biomedical signals has been traditionally ascribed to a noise-like behavior. An alternative explanation for the irregular behavior observed in systems which do not seem to be inherently stochastic is provided by one of the most striking mathematical developments of the past few decades, i.e., chaos theory. Chaos theory suggests that random-like behavior can arise in some deterministic nonlinear systems with just a few degrees of freedom. One of the most evocative aspects of deterministic chaos is the concept of fractal geometry. Fractal structure, characterized by self-similarity and noninteger dimension, is displayed in chaotic systems by a subset of the phase space known as strange attractor. However, fractal properties are observed also in the unpredictable time evolution and in the 1/f^β power-law of many biomedical signals. The research activities carried out by the Author during the PhD program are concerned with the analysis of the fractal-like behavior of the EEG. The focus was set on those methods which evaluate the fractal geometry of the EEG in the time domain, in the hope of providing physicians and researchers with new valuable tools of low computational cost for the EEG analysis. The performances of three widely used techniques for the direct estimation of the fractal dimension of the EEG were compared and the accuracy of the fBm scaling relationship, often used to obtain indirect estimates from the slope of the spectral density, was assessed. Direct estimation with Higuchi's 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. Based on this result, Higuchi's fractal dimension was used to address three clinical issues which could involve abnormal complexity of neuronal brain activity: 1) the monitoring of carotid endarterectomy for the prevention of intraoperative stroke, 2) the assessment of the depth of anesthesia to monitor unconsciousness during surgery and 3) the analysis of the macro-structural organization of the EEG in autism with respect to mental retardation. The results of the clinical studies suggest that, although linear spectral analysis still represents a valuable tool for the investigation of the EEG, time domain fractal analysis provides additional information on brain functioning which traditional analysis cannot achieve, making use of techniques of low computational cost.
La maggior parte delle conoscenze acquisite sui sistemi fisiologici si deve alla teoria dei sistemi lineari. Il comportamento pseudo stocastico di molti segnali biomedici è stato tradizionalmente attribuito al concetto di rumore. Un'interpretazione alternativa del comportamento irregolare rilevato in sistemi che non sembrano essere intrinsecamente stocastici è fornita da uno dei più sorprendenti sviluppi matematici degli ultimi decenni: la teoria del caos. Tale teoria suggerisce che una certa componente casuale può sorgere in alcuni sistemi deterministici non lineari con pochi gradi di libertà. Uno degli aspetti più suggestivi del caos deterministico è il concetto di geometria frattale. Strutture frattali, caratterizzate da auto-somiglianza e dimensione non intera, sono rilevate nei sistemi caotici in un sottoinsieme dello spazio delle fasi noto con il nome di attrattore strano. Tuttavia, caratteristiche frattali possono manifestarsi anche nella non prevedibile evoluzione temporale e nella legge di potenza 1/f^β tipiche di molti segnali biomedici. Le attività di ricerca svolte dall'Autore nel corso del dottorato hanno riguardato l'analisi del comportamento frattale dell'EEG. L'attenzione è stata rivolta a quei metodi che affrontano lo studio della geometria frattale dell'EEG nel dominio del tempo, nella speranza di fornire a medici e ricercatori nuovi strumenti utili all'analisi del segnale EEG e caratterizzati da bassa complessità computazionale. Sono state messe a confronto le prestazioni di tre tecniche largamente utilizzate per la stima diretta della dimensione frattale dell'EEG e si è valutata l'accuratezza della relazione di scaling del modello fBm, spesso utilizzata per ottenere stime indirette a partire dalla pendenza della densità spettrale di potenza. Il metodo più adatto alla stima della dimensione frattale dell'elettroencefalogramma è risultato essere l'algoritmo di Higuchi, che produce stime accurate anche su segmenti di breve durata a patto che il segnale sia campionato alla minima frequenza di campionamento necessaria ad evitare il fenomeno dell'aliasing. Sulla base di questo risultato, la dimensione frattale di Higuchi è stata utilizzata per esaminare tre questioni cliniche che potrebbero coinvolgere una variazione della complessità dell'attività neuronale: 1) il monitoraggio dell'endoarterectomia carotidea per la prevenzione dell'ictus intraoperatorio, 2) la valutazione della profondità dell'anestesia per monitorare il livello di incoscienza durante l'intervento chirurgico e 3) l'analisi dell'organizzazione macro-strutturale del EEG nell'autismo rispetto alla condizione di ritardo mentale. I risultati degli studi clinici suggeriscono che, sebbene l'analisi spettrale rappresenti ancora uno strumento prezioso per l'indagine dell'EEG, l'analisi frattale nel dominio del tempo fornisce informazioni aggiuntive sul funzionamento del cervello che l'analisi tradizionale non è in grado di rilevare, con il vantaggio di impiegare tecniche a basso costo computazionale.
XXIV Ciclo
1984

The application of surface electromyography (sEMG) technique for muscle fatigue studies is gaining importance in the field of clinical rehabilitation and sports medicine. These sEMG signals are highly nonstationary and exhibit scale-invariant self-similarity structure. The fractal analysis can estimate the scale invariance in the form of fractal dimension (FD) using monofractal (global single FD) or multifractal (local varying FD) algorithms. A comprehensive study of sEMG signal for muscle fatigue using both multifractal and monofractal FD features have not been established in the literature. In this work, an attempt has been made to differentiate sEMG signals recorded nonfatigue and fatigue conditions using monofractal and multifractal algorithms, and machine learning methods. For this purpose, sEMG signals have been recorded from biceps brachii muscles of fifty eight healthy subjects using a standard protocol. The signals of nonfatigue and fatigue region were subjected to eight monofractal (Higuchi, Katz, Petrosian, Sevcik, box counting, multi-resolution length, Hurst and power spectrum density) and two multifractal (detrended fluctuating and detrended moving average) algorithms and 28 FD features were extracted. The features were ranked using conventional and genetic algorithms, and a subset of FD features were further subjected to Naïve Bayes (NB), Logistic Regression (LR) and Multilayer Perceptron (MLP) classifiers. The results show that all fractal features are statistically significant. The classification accuracy using feature subset of conventional method is observed to be from 83% to 88%. The highest accuracy of 93.96% was achieved using genetic algorithm and LR classifier combination. The result demonstrated that the performance of multifractal FD features to be more suitable for sEMG signals as compared to monofractal FD features. The fractal analysis of sEMG signals appears to be a very promising biomarker for muscle fatigue classification and can be extended to detection of fatigue onset in varied neuromuscular conditions.