Comparison of neuro-fuzzy systems for classification of transcranial Doppler signals with their chaotic invariant measures
Introduction
TCD study of the adult intracerebral circulation is used to evaluate intracranial stenoses, cerebral arteriovenous malformations, cerebral vasospasm and cerebral hemodynamics in general (Evans, McDicken, Skidmore, & Woodcock, 1989). To make intra-brain blood flow measurements requires sophisticated imaging methods. The Doppler principle utilized in medicine is different from the classical Doppler method. Since the targets in the human body do not emit radiation, it is necessary to transmit a signal into the body and then observe the frequency changes between that transmitted signal and the received signals reflecting from the targets. Under these conditions, there is a shift in the ultrasound frequency given bywhere ft and fr are the transmitted and received ultrasound frequencies, ν is the velocity of the target, c is the velocity of the sound in the medium, and θ is the angle between ultrasound beam and the direction of motion of the target.
The TCD signals may be regarded as a series of discrete values varying in time. This kind of series is called a time series. If a time series produced by a nonlinear system is analysed by linear methods such as power analysis, linear transformations or parametric linear modelling, the critical features of it remains undetected and most parts of this time series can be incorrectly evaluated as random noise. Chaos theory (nonlinear time series analysis) provides some necessary tools to quantitatively analyse an experimental time series such as a TCD signal. The values such as maximum Lyapunov exponent and correlation dimension are some of the quantitative measures of chaos. For example, if the maximum Lyapunov exponent is found to be positive, then we say that there is an underlying chaotic behaviour in the system that generates the nonlinear time series. This means that the system has a picture of chaotic attractor embedded in the phase space which includes nearby orbits that diverges from each other in time. According to the Takens theorem (Takens, 1981), if the real dimension of the attractor is DA, then choosing the embedding dimension DE as DE > 2DA prevents the orbits from crossing each other resulting in a non-periodic flow. The chaotic attractors generally have a correlation dimension which is a fractional value greater than 2. On the other hand, in order to apply nonlinear time series analysis (chaos theory) methods, it must be proven that the TCD signals are both nonlinear and stationary.
The adaptive neuro-fuzzy inference system (ANFIS) (Jang, 1993) is a specific kind of neuro-fuzzy classifier approach of which successful implementations were reported in biomedical engineering (Belal et al., 2002). In this study, an ANFIS which has two inputs and one output has been trained with the chaotic invariant measures belonging to different classes. The output of ANFIS corresponds to the kind of disease. Since there are four different types of patients and also healthy subjects, the output will belong to one of five different classes according to the input.
NEFCLASS is able to learn fuzzy rules and fuzzy sets by simple heuristics. The main idea of NEFCLASS is to quickly create interpretable fuzzy classifiers. The learning algorithm of NEFCLASS has two stages: rule (structure) learning and parameter learning. Rule learning is achieved via a variation of the approach by Wang and Mendel (1992). Each input space corresponding to a feature is partitioned by a given number of initial fuzzy sets. Then, by processing the training data only once, the antecedents for the rules are created by checking which areas of the input space contain data. An evaluation procedure then creates a rule base by assigning appropriate consequents (class labels) to the discovered antecedents and selects only a certain number of rules with good performance (Nauck and Kruse, 1997, Nauck et al., 1996, Nauck et al., 1999). The NEFCLASS model used in this study had two input nodes corresponding to the chaotic invariant measures and five output nodes which represent the four different brain diseases and the healthiness.
In this study, it has been shown that all the TCD signals are not only nonlinear, but also stationary to an acceptable level. Two most strong chaos indicators, namely the maximal Lyapunov exponent and the correlation dimension were calculated for each signal. The results confirm that all of the signals are chaotic.
Both of the ANFIS and NEFCLASS models were evaluated against the test set and the performance measurements were reported to compare these two different neuro-fuzzy classification approaches.
Section snippets
Hardware
The hardware of the system used for this study involves a 2 MHz ultrasound transducer, analog Doppler unit (Multi Doppler Transducer XX, DWL Gmb, Uberlingen, Germany), analog/digital interface board (Sound Blaster Pro-16), and PIII 600 MHz microprocessor PC with printer. The Doppler unit is also equipped with imaging software that makes it possible to focus the sample volume at a desired location in the temporal region.
The analog Doppler unit can work in both continuous and pulse wave modes. The
Experimental results and discussion
In this study, the TCD signals belonging to 82 patients and 24 healthy people were recorded. Among 82 patients, 20 of them had cerebral aneurism, 10 patients had brain hemorrhage, 22 patients had cerebral oedema and the remaining 30 patients had brain tumour. It was found that both nonlinearity and stationarity existed for all the TCD time series. This proved that the methods which would be used to estimate the chaotic quantities like correlation dimension and Lyapunov exponents could be
Conclusion
In this study, the experimental results indicate that the TCD signals represent nonlinear dynamics having an underlying low-level determinism. All of the TCD signals were passed through the nonlinearity tests successfully and the maximum Lyapunov exponent (λ1) was found to be positive for all the TCD signals. The correlation dimension (D2) was found as greater than 2 and as fractional for all TCD signals. These results indicate that the nonlinear dynamics of the TCD signals corresponds to a
References (21)
- et al.
Automatic detection of distorted plethysmogram pulses in neonates and paediatric patients using an adaptive-network-based fuzzy inference system
Artificial Intelligence in Medicine
(2002) - et al.
A neuro-fuzzy method to learn fuzzy classification rules from data
Fuzzy Sets and Systems
(1997) - et al.
A practical method for calculating largest Lyapunov exponents from small data sets
Physica D
(1993) - et al.
Constrained-realization Monte-Carlo method for hypothesis testing
Physica D
(1996) - et al.
Ergodic theory of chaos and strange attractors
Reviews of Modern Physics
(1985) - et al.
Doppler ultrasound: physics instrumentation and clinical applications
(1989) - et al.
Independent coordinates for strange attractors from mutual information
Physical Review A
(1986) - et al.
Characterization of strange attractors
Physical Review Letters
(1983) - et al.
Practical implementation of nonlinear time series methods: the TISEAN package
Chaos
(1999) - et al.
A test for stationarity: finding parts in time series apt for correlation dimension estimates
International Journal of Bifurcation and Chaos
(1993)
Cited by (29)
Experimental entropy generation, exergy efficiency and thermal performance factor of CoFe<inf>2</inf>O<inf>4</inf>/Water nanofluids in a tube predicted with ANFIS and MLP models
2023, International Journal of Thermal SciencesCustomizable hardware design of fuzzy controllers applied to autonomous car driving
2014, Expert Systems with ApplicationsElimination of harmonics in multilevel inverters connected to solar photovoltaic systems using ANFIS: An experimental case study
2013, Journal of Applied Research and TechnologyCitation Excerpt :In the fourth layer, the output of every node is The ANFIS learning algorithm employs two methods for updating membership function parameters [34-35]: A hybrid method consisting of back-propagation for the parameters associated with the input membership functions, and least squares estimation for the parameters associated with the output membership functions.
A hybrid system based on information gain and principal component analysis for the classification of transcranial Doppler signals
2012, Computer Methods and Programs in BiomedicineCitation Excerpt :In the literature, various studies have classified the TCD signals. Ozturk et al. used two different neuro-fuzzy classifiers to classify the chaotic invariant features extracted from the TCD signals and compared the performance of the classifiers [3]. Serhatlioğlu et al. extracted the features with Fast Fourier Transform (FFT) and classified these features using a back propagation neural network and self-organizing map algorithms to compare the performance of these classifiers [4].
Manifestation of an adaptive neuro-fuzzy model on landslide susceptibility mapping: Klang valley, Malaysia
2011, Expert Systems with ApplicationsCitation Excerpt :An ANFIS model uses a hybrid learning algorithm that combines the least squares estimator and the gradient descent method (Jang, 1993). The least-squares method is, actually, the major driving force that leads to fast training, while the gradient descent serves to slowly change the underlying membership functions that generate the basis functions for the least-squares method (Ozturk, Arslan, & Hardalac, 2008). While training the ANFIS model, each epoch consists of a forward and a backward pass.
A variable speed wind generator maximum power tracking based on adaptative neuro-fuzzy inference system
2011, Expert Systems with Applications