New seismic attribute:Fractal scaling exponent based on gray detrended fluctuation analysis

Seismic attributes have been widely used in oil and gas exploration and development. However, owing to the complexity of seismic wave propagation in subsurface media, the limitations of the seismic data acquisition system, and noise interference, seismic attributes for seismic data interpretation have uncertainties. Especially, the antinoise ability of seismic attributes directly affects the reliability of seismic interpretations. Gray system theory is used in time series to minimize data randomness and increase data regularity. Detrended fluctuation analysis （DFA） can effectively reduce extrinsic data tendencies. In this study, by combining gray system theory and DFA, we propose a new method called gray detrended fluctuation analysis （GDFA） for calculating the fractal scaling exponent. We consider nonlinear time series generated by the Weierstrass function and add random noise to actual seismic data. Moreover, we discuss the antinoise ability of the fractal scaling exponent based on GDFA. The results suggest that the fractal scaling exponent calculated using the proposed method has good antinoise ability. We apply the proposed method to 3D poststack migration seismic data from southern China and compare fractal scaling exponents calculated using DFA and GDFA. The results suggest that the use of the GDFA-calculated fractal scaling exponent as a seismic attribute can match the known distribution of sedimentary facies.

Detrended cross-correlation analysis of electroencephalogram

In the paper we use detrended cross-correlation analysis （DCCA） to study the electroencephalograms of healthy young subjects and healthy old subjects. It is found that the cross-correlation between different leads of a healthy young subject is larger than that of a healthy old subject. It was shown that the cross-correlation relationship decreases with the aging process and the phenomenon can help to diagnose whether the subject＇s brain function is healthy or not.

CORRESPONDENCE ANALYSIS ON IMAGES OF JIANGXI PROVINCE AS A TOURIST DESTINATION

This paper delineates the images of Jiangxi Province as tourist destination perceived by about 2000 sample visitors at Lushan Mountain and other 3 famous resorts (Jinggangshan Mountains, Longhushan Mountain, and Sanqingshan Mountain), with a result that the most common image is the famous scenic mountain image with partial attribute of image of religious culture destination. In order to reveal the similarities and dissimilarities of images among the four destinations, a correspondence analysis on 16 image attributes was employed. The results indicate that the tourists’ images on Longhushan Mountain, Sanqingshan Mountain and Lushan Mountain are very similar: having a lot of good tourist sites, famous mountain scenery, being close to nature and having good guide service, and others, but religious culture and good shopping facilities having not made deep impression on tourist, while Jinggangshan Mountains is famous for its red culture. The correspondence analysis visualizes the strengths and weaknesses of the destinations, which is useful for market positioning among the competitive places. Finally, some marketing suggestions for the four destinations were provided.

Study on the Characteristics of Urban Air Pollution Based on Correspondence Analysis--A Case Study of Six Provincial Capitals in Central-south China

[Objective] The aim was to study the characteristics of urban air pollution on the basis of correspondence analysis.[Method] By using the correlated data from China Statistical Yearbook in 2010,a correspondence analysis on the air pollution indicators(like respirable particles,SO2 and NO2) of six provincial capitals in central-south China was carried out by means of SPSS software,and the characteristics of air pollution in the cities of China during different industrialization stages were summarized further.[Result] In the cities during early industrialization(like Nanning City and Guiyang City) and mineral resource-based cities(like Taiyuan City),the air was mainly polluted by SO2;for the cities in the middle industrialization(such as Changsha City,Wuhan City,Zhengzhou City and Chengdu City),the air was polluted by respirable particles chiefly;in the cities in late industrialization(like Guangzhou City and Shenzhen City) or completing industrialization(like Shanghai City),the air was mainly polluted by NO2;for the cities in pre-industrial stage(like Haikou City and Lhasa City),the characteristic of air pollution wasn’t obvious.[Conclusion] The study could provide references for the control of urban air pollution in China in the further.

Relationships of exponents in multifractal detrended fluctuation analysis and conventional multifractal analysis

Multifractal detrended fluctuation analysis （MF-DFA） is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis （DFA）, which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression r（q） = qh（q） - 1 stipulating the relationship between the multifractal exponent T（q） and the generalized Hurst exponent h（q）. As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as .t-（q） = qh（q） - qH - 1, where H is the nonconservation parameter in the universal multifractal formalism. The singular spectra, a and f（a）, are also derived according to this new relationship.

Detrended Fluctuation Analysis on Correlations of Complex Networks Under Attack and Repair Strategy

We analyze the correlation properties of the Erd6s-Rdnyi random graph （RG） and the Barabdsi-Albert scale-free network （SF） under the attack and repair strategy with detrended fluctuation analysis （DFA）. The maximum degree kmax, representing the local property of the system, shows similar scaling behaviors for random graphs and scale-free networks. The fluctuations are quite random at short time scales but display strong anticorrelation at longer time scales under the same system size N and different repair probability pre. The average degree 〈k〉, revealing the statistical property of the system, exhibits completely different scaling behaviors for random graphs and scale-free networks. Random graphs display long-range power-law correlations. Scale-free networks are uncorrelated at short time scales; while anticorrelated at longer time scales and the anticorrelation becoming stronger with the increase of pre.

Extracting a seizure intensity index from one-channel EEG signal using bispectral and detrended fluctuation analysis

Epilepsy is a medical condition that produces seizures affecting a variety of mental and physical functions. Seizures can last from a few seconds to a few minutes. They can have many symptoms, from convulsions and loss of consciousness to blank staring, lip smacking, or jerking movements of arms and legs. If early warning signals of an upcoming seizure (diagnosis of preictal period) are detected, proper treatment can be applied to the patient to help prevent the seizure. In this research, an epileptic disorder has been divided into three subsets: Normal, Preictal (just before the seizure), and Ictal (during seizure). By using Detrended Fluctuation Analysis (DFA), Bispectral Analysis (BIS), and Standard Deviation (SD) three features from single-channel EEG signals have been derived in the foresaid groups. A fuzzy classifier is used to separate the three groups which can successfully separate them with a separation degree of 100% and further a fuzzy inference engine is used to extract a Seizure Intensity Index (SII) from the Electroencephalogram (EEG) signals of the three different states. One can apparently see the distinction of SII amounts between the three states. It is more important when one remembers that these results are just from single-channel EEG signal.

Correlation between detrended fluctuation analysis and the Lempel-Ziv complexity in nonlinear time series analysis

We study the correlation between detrended fluctuation analysis（DFA） and the Lempel-Ziv complexity（LZC） in nonlinear time series analysis in this paper.Typical dynamic systems including a logistic map and a Duffing model are investigated.Moreover,the influence of Gaussian random noise on both the DFA and LZC are analyzed.The results show a high correlation between the DFA and LZC,which can quantify the non-stationarity and the nonlinearity of the time series,respectively.With the enhancement of the random component,the exponent α and the normalized complexity index C show increasing trends.In addition,C is found to be more sensitive to the fluctuation in the nonlinear time series than α.Finally,the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve,and an effective fault diagnosis result is obtained.

Detrended Fluctuation Analysis of the Human EEG during Listening to Emotional Music

A nonlinear method named detrended fluctuation analysis （DFA） was utilized to investigate the scaling behavior of the human electroencephalogram （EEG） in three emotional music conditions （fear, happiness, sadness） and a rest condition （eyes-closed）. The results showed that the EEG exhibited scaling behavior in two regions with two scaling exponents β1 and β2 which represented the complexity of higher and lower frequency activity besides α band respectively. As the emotional intensity decreased the value of β1 increased and the value of β2 decreased. The change of β1 was weakly correlated with the ＇approach-withdrawal＇ model of emotion and both of fear and sad music made certain differences compared with the eyes-closed rest condition. The study shows that music is a powerful elicitor of emotion and that using nonlinear method can potentially contribute to the investigation of emotion.

A Multifractal Detrended Fluctuation Analysis of the Ising Financial Markets Model with Small World Topology

We present a multifractal detrended fluctuation analysis （MFDFA） of the time series of return generated by our recently-proposed Ising financial market model with underlying small world topology. The result of the MFDFA shows that there exists obvious multifractal scaling behavior in produced time series. We compare the MFDFA results for original time series with those for shuffled series, and find that its multifractal nature is due to two factors： broadness of probability density function of the series and different correlations in small- and large-scale fluctuations. This may provide new insight to the problem of the origin of multifractality in financial time series.

Effects of quantization on detrended fluctuation analysis

Detrended fluctuation analysis （DFA） is a method foro estimating the long-range power-law correlation exponent in noisy signals. It has been used successfully in many different fields, especially in the research of physiological signals. As an inherent part of these studies, quantization of continuous signals is inevitable. In addition, coarse-graining, to transfer original signals into symbol series in symbolic dynamic analysis, can also be considered as a quantization-like operation. Therefore, it is worth considering whether the quantization of signal has any effect on the result of DFA and if so, how large the effect will be. In this paper we study how the quantized degrees for three types of noise series （anti-correlated, uncorrelated and long-range power-law correlated signals） affect the results of DFA and find that their effects are completely different. The conclusion has an essential value in choosing the resolution of data acquisition instrument and in the processing of coarse-graining of signals.

Crossover Phenomena in Detrended Fluctuation Analysis Used in Financial Markets

A systematic analysis of Shanghai and Japan stock indices for the period of Jan. 1984 to Dec. 2005 is performed. After stationarity is verified by ADF （Augmented Dickey-Fuller） test, the power spectrum of the data exhibits a power law decay as a whole characterized by 1/f^β processes with possible long range correlations. Subsequently, by using the method of detrended fluctuation analysis （DFA） of the general volatility in the stock markets, we find that the long-range correlations are occurred among the return series and the crossover phenomena exhibit in the results obviously.Further, Shanghai stock market shows long-range correlations in short time scale and shows short-range correlations in long time scale. Whereas, for Japan stock market, the data behaves oppositely absolutely. Last, we compare the varying of scale exponent in large volatility between two stock markets. All results obtained may indicate the possibility of characteristic of multifractal scaling behavior of the financial markets.

Usage as Complementary Correspondence Analysis and Logistic Regression in a Scientific Survey on Self Healing Methods

The aim of this study is to show complementary usage of logistic and correspondence analysis in a research subject to self-healing methodologies. Firstly, the number of the variables is reduced by logistic regression according to relationship between dependent and independent variables and then research carries on searching variables. The relationship among the behaviours of individuals and their demographic characteristics is modelled by logistic regression and shown graphically by correspondence analysis. In application, first of all, the effect of age, sex, marital status, education level, occupation and income level and present health condition, on appreciating self-health, is explained by a model. As a result of that model, it can be said that the effect of age, occupation and present health condition is reasonable. After analysing that model, the relationship between categorical variables (age, sex, occupation, preferred precautions, and worth of personal health) is shown graphically by multiple correspondence analysis.

Stock Pattern Mining and Correspondence Analysis Based on Association Rules

In this paper, association rules were applied to mining patterns in stock K-line trend. The pattern which ordinary investors interested in is defined as T-RG (Three-Red Guards). In the mining process, we take the K-line in A-share markets as objects. Through the analysis, investors can select the appropriate point of purchase and selling point. With the help of T-RG, investors can better improve the chance of short-term investment success in A-share markets. In order to explore and validate the T-RG, the main contents of this paper include the following aspects: putting forward a method that judge the validity of rules based on confidence-lift;proposing the meta rule that corresponds to the pattern of T-RG;developing a computer program to extract the T-RG using MATLAB, which supports batch mining;leading fundamental factors into correspondence analysis with identification indexes;reminding the selected stocks, so as to verify the reliability of the identification indexes. According to the above research, something can be learned: In A-share markets, the higher the discriminant index value is, the less number of shares meeting the requirements is;the same discriminant index value, the stock proportion has difference among plates. Confidence P1, P2 and Lift are extremely related to the GC (General Capital), and Lift is extremely related to the Ind (Industry). In the GEM, confidence P1 of mid-cap is near [0.7,1], Lift is near (1,3), confidence P1 of the manufacturing industry is near [0.7,1].

Correspondence Analysis on a Space-Time Data Set for Multiple Environmental Variables

Applications of the multivariate technique called correspondence analysis for environmental studies are relatively new and are limited to spatial multivariate data set. In this paper, a procedure of applying correspondence analysis to a large space-time data set for multiple environmental variables is shown. In particular, nitrogen dioxide and carbon monoxide hourly concentrations measured during January 1999 at several monitored stations in a district of Northern Italy are analyzed. The procedure consists in transforming the continuous variables into categorical ones by the means of appropriate indicator variables, generating special contingency tables and applying correspondence analysis. The use of this classical multivariate technique allows the identification of important relationships among pollution levels and monitoring stations and/or relationships among pollution levels and observation times.

A Sleep Scoring System Using EEG Combined Spectral and Detrended Fluctuation Analysis Features

Most of sleep disorders are diagnosed based on the sleep scoring and assessments. The purpose of this study is to combine detrended fluctuation analysis features and spectral features of single electroencephalograph (EEG) channel for the purpose of building an automated sleep staging system based on the hybrid prediction engine model. The testing results of the model were promising as the classification accuracies were 98.85%, 92.26%, 94.4%, 95.16% and 93.68% for the wake, non-rapid eye movement S1, non-rapid eye movement S2, non-rapid eye movement S3 and rapid eye movement sleep stages, respectively. The overall classification accuracy was 85.18%. We concluded that it might be possible to employ this approach to build an industrial sleep assessment system that reduced the number of channels that affected the sleep quality and the effort excreted by sleep specialists through the process of the sleep scoring.

Visualization of Special Features in “The Tale of Genji” by Text Mining and Correspondence Analysis with Clustering

In this paper, visualization of special features in “The Tale of Genji”, which is a typical Japanese classical literature, is studied by text mining the auxiliary verbs and examining the similarity in the sentence style by the correspondence analysis with clustering. The result shows that the text mining error in the number of auxiliary verbs can be as small as 15%. The extracted feature in this study supports the multiple authors of “The Tale of Genji”, which agrees well with the result by Murakami and Imanishi [1]. It is also found that extracted features are robust to the text mining error, which suggests that the classification error is less affected by the text mining error and the possible use of this technique for further statistical study in classical literatures.

Canonical Correspondence Analysis of Phytoplankton Community and Environmental Factors in Genhe River

To understand the status of phytoplankton community of the Genhe River in the summer of 2015,we investigated the phytoplankton in Genhe River. We identified 5 phyla and 36 species,among which Bacillariophyta(23) were the most,followed by Chlorophyta(10),Cyanophyta(1),Chrysophyta(1),Pyrrophyta(1). The phytoplankton abundance was(15. 6-810) × 104 ind·L^(-1); the biomass was(0. 07-2. 876) mg·L-1; Shannon-wiener index was 1. 05-3. 24; Pielou evenness index was 0. 27-0. 96. Using Shannon-wiener index and Pielou index,the water quality of Genhe River was assessed,and the results showed that the water quality was the best at 5# sampling point,the water quality was good in 3#,4#,7#,8#,9# sampling points,and there was a state of pollution at other sampling points. Canonical correspondence analysis and Pearson correlation analysis showed that iron ion,transparency,p H value,water depth and water temperature were important environmental factors that affect the distribution of phytoplankton,and copper ion,nitrite ion and COD also significantly affected the distribution of phytoplankton.

Elaboration of Explanatory Factors of Accidents in Cameroon by Factorial Correspondence Analysis

The aim of this paper is to examine the causes of road accidents in Cameroon. The Douala-Yaoundé highway was chosen as the case of study. Available field data recorded from the year 2006 to 2011, have enabled the analysis of each accident. The method used here is the factorial correspondence analysis;which aims to bring in a small number of dimensions, most of the initial information, focusing not on the absolute values, but the correspondence between the variables, that is to say the relative values. From this analysis, it appears that, of the 906 accidents recorded during this period, top five causes account for nearly 83% of the information provided by the set of variables on the occurrence of road accidents. These causes are: driver inattention, lack of control, over speeding, improper overtaking and tire puncture. These results require involvement in the construction of road safety policies through training, sensitization and adequate repressions as well as administrative reforms and research policy in road safety.

Applied research of correspondence analysis method in waste tailings reservoir heavy metal pollution monitoring points optimization

In order to optimize monitoring points and monitoring factor, the relationshipbetween pollutants and soil sample were established by correspondence analysis.Thestudy results show that the reflecting monitoring points and monitoring factors in thegraphic on the same factor axis can clearly express the intrinsic link between pollutantsand monitoring points and distribution characteristics.To determine the main monitoringpoint and the main monitoring indicators can reduce and optimize the number of monitoringpoints under the premise of ensuring the typical and representative of monitoring data.Using the correlation of pollutants can reduce the number of monitoring indicators and improvethe effectiveness of data collection.