Adaptive Neuro Fuzzy Inference System For Classification Computer Science Essay

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Antenatal care in recent years has undergone a major change with the introduction of computer-based diagnostic systems. This study presents an intelligent Adaptive Neuro-Fuzzy Inference System (ANFIS) model for antepartum fetal evaluation. The model integrates adaptable fuzzy inputs with a modular neural network to deal with the imprecision and uncertainty in the interpretation of fetal heart rate (FHR) data. The parameters of diagnostic importance are derived from a non-invasive and cost-effective technique of antenatal care called fetal phonocardiography (fPCG).

and the diagnostic interpretations for doctors such as normal, suspicious, and pathological conditions of fetus are derived.

The recordings of the sounds, produced by the mechanical activity of the fetal heart are obtained using a wireless acoustic sensor


Classification of fetal heart rate (FHR) for fetal health assessment

Continuous fetal monitoring has taken an important place in assessment of fetal well-being. Earlier it was used in complex or high risk pregnancies only, but now-a-days being used in normal or low risk pregnancies also. Monitoring the fetal heart rate (FHR) patterns is an established way of fetal surveillance and offers important information about the fetus behavior. Some conditions such as hypoxia, acidemia and drug induction produce noticeable variations of FHR [6*]. Several studies and guidelines on Fetal Electronic Monitoring (EFM) based on analysis of FHR trace have been published during last two decades [*, *, *]. The goal of these guidelines is to assess the analytical values of monitoring to allow evidence based surveillance of the fetus during its intra uterine life and at the time of delivery. Proper interpretation of FHR trace requires clinical experience and significant expertise. It has been seen that this is often lacking in clinical settings which results in a large number of preventable fetal deaths and unnecessary interventions [4*, 5*].

With the advancements in medical technology, several devices and instruments have become available those provide reasonably reliable information and data instantaneously about the fetus [4, 5]. Mostly, the outcome of these devices is in the form of instantaneous value of FHR or FHR trace for long duration. There have been significant efforts to develop fetal monitoring methods through analysis of FHR patterns based on standard guidelines. A. K. A. Khandaker et al. (1998) described an improved scheme for detecting the presence of the QRS complexes from the enhanced fetal ECG signal obtained by using a fuzzy decision algorithm. M. G. Signorini et al. (2000) proposed new classifiers based on fuzzy inference systems for the FHR signal analysis. They include standard cardiotocographic parameters together with a set of frequency domain and nonlinear indices. O. Fontenla-Romero et al. (2000) presented several approaches to computer supported recognition of accelerative and decelerative patterns in the FHR signal. J F Skinner et al. (2001) described the findings of a research project with two main aims: to investigate whether fuzzy logic could offer an improvement in CTG analysis over the crisp expert system; and to investigate whether retrospective analysis of complete CTG traces could be automated. F. Gurgen et al. (2001); in their study defines an intelligent neuro-fuzzy system for antepartum fetal evaluation. Yo-Ping Huang et al. (2006) proposed a Fuzzy Inference Method-based Fetal Distress Monitoring System. T. M. Nazmy et al. (2009) presents an intelligent diagnosis system using hybrid approach of adaptive neuro-fuzzy inference system model for classification of Electrocardiogram signals.

All these methods are based on either ultrasound Doppler based fetal cardiotocography (fCTG) or fetal electrocardiography (fECG). These techniques can provide more direct evidence but require expensive equipments, specialized technicians to operate, experts to interpret the results, high maintenance cost, permanent placement and generally demand more resources to function properly. These requirements can only be met in the advanced hospitals and are way beyond the rural health-care centers as well as for urban clinics [10].

On the other hand, fetal phonocardiography (fPCG) is a low cost, non-invasive (passive) and simple technique [11]. It is a suitable tool for long-term surveillance of the fetus [12]. In this technique, natural vibroacoustic signals (also called as fPCG signals) from the maternal abdominal surface are recorded and processed. These signals are linear summation of fetal heart sound (FHS), maternal heart sound, internal and external noises. The fPCG signal carries valuable information about physiological parameters such as FHS, FHR and fetal breathing movements [22]. The proposed fPCG technique is also capable of recognizing additional dysfunctioning of the fetal heart such as: cardiac murmurs, split effect and breathing movements, which are impossible to detect with the fCTG technique due to its principle of operation. Moreover, phonocardiography is an outstanding tool for auscultation training to the undergraduate medicos and it helps to understand the hemodynamic of the fetal heart [l].

This paper presents an adaptive neuro-fuzzy inference system (ANFIS) for diagnosing the fetal health status. The FHR trace is obtained from fetal heart sound signals recorded using wireless fetal phonocardiography. A set of features are extracted from each signal, which will be the input to the intelligent diagnostic system. The output of the proposed system will be classified diagnosis of the fetal health.

The subsequent parts of this paper are organized as follows:

Adaptive Neuro-Fuzzy Inference System (ANFIS):

Fuzzy inference system articulates aspects of human knowledge and interpretation in a linguistic fashion. It is a rule based system consists of three conceptual components. These are: (i) a rule-base, contains fuzzy if-then rules, (ii) a data-base, defines the membership function and (iii) an inference system, combines the fuzzy rules and produces the system results. A general structure of fuzzy system is demonstrated in Figure 1.

Decision System



Knowledge Base





The ANFIS consists of a combination of the artificial neural network and the fuzzy logic [1*]. It combines the fuzzy system's interpretability with neural network's adaptive learning ability. The use of neural network training techniques allows embedding empirical information into a fuzzy system.

The ANFIS is a multilayer feed-forward network uses ANN learning algorithms and fuzzy reasoning to characterize an input space to an output space in following steps:

It computes the membership function parameters that best allow the associated fuzzy inference system to track the given input/output data.

It constructs a fuzzy inference system whose membership function parameters are adjusted using either a backpropogation algorithm alone, or in combination with a least squares type of method.

A network-type structure similar to that of a neural network is used to interpret the input/output map. This network maps inputs through input membership functions and associated parameters, and then through output membership functions and associated parameters to outputs.

The parameters associated with the membership functions changes through the learning process.

The computation of these parameters (or their adjustment) is facilitated by a gradient vector. This gradient vector provides a measure of how well the fuzzy inference system is modeling the input/output data for a given set of parameters.

When the gradient vector is obtained, any of several optimization routines can be applied in order to adjust the parameters to reduce some error measure. This error measure (performance index) is usually defined by the sum of the squared difference between actual and desired outputs.

The ANFIS only supports Sugeno-type fuzzy inference systems, which must have the following properties:

The output is first or zeroth order Sugeno-type system.

It has a single output, obtained using weighted average defuzzification. All output membership functions must be either linear or constant.

It has no rule sharing. Different rules do not share the same output membership function, namely the number of output membership functions must be equal to the number of rules.

It has unity weight for each rule.

Assume that the fuzzy inference system has two inputs x1 and x2, and one output y. This system makes use of a hybrid learning rule to optimize the fuzzy system parameters of a first order Sugeno system. ANFIS implements rules of the form:

Rule 1: if (x1 is A1) and (x2 is B1) then (f1=p1x1+ q1x2+r1)

Rule 2: if (x1 is A2) and (x2 is B2) then (f2=p2x2+ q2x2+r2)

where x1 and x2 are the predefined membership functions, Ai and Bi are membership values, pi, qi, and ri are the consequence parameters.

The five layered architecture of an ANFIS for two inputs, two rules, first order Sugeno model is shown in Figure 2. The circle indicates a fixed node whereas a square indicates an adaptive node whose parameters are changed during training. For the training of the network, there is a forward pass and a backward pass. The forward pass propagates the input vector through the network layer by layer. In the backward pass, the error is sent back through the network.
















Layer 1

Layer 2

Layer 3

Layer 4

Layer 5

The computational details of ANFIS at each layer are explained as follows:

Layer 1: Each node in this layer generates membership grades of the crisp inputs which belong to each of convenient fuzzy sets by using the membership functions. The output of each node is:

Where and are the appropriate membership function for Ai and Bi fuzzy sets respectively. There are many membership functions are available such as trapezoidal, triangular, Gaussian function etc., which can be applied to determine the membership grades. In this work, the gauss membership function is used. The symmetric Gaussian function depends on two parameters σ and c as given by:

The parameters in this layer are referred to as premise parameters.

Layer 2: In this layer, the AND/OR operator is applied to get one output that represents the results of the antecedent for a fuzzy rule, which is firing strength. It means the degrees by which the antecedent part of the rule is satisfied and it indicates the shape of the output function for that rule. The outputs of the second layer, called as firing strengths (w), are the products of the corresponding degrees obtaining from layer 1.

Layer 3: This layer contains the fixed nodes which compute the ratio of firing strength of each ith rule to the sum of firing strength of all the rules.


Layer 4: The nodes in this layer are adaptive and perform the consequent of the rules.

Where is the output of the ith node from the previous layer. {pi, qi, ri}is the parameter set in the consequence function and also the coefficients of linear combination in Sugeno inference system.

Layer 5: This layer is called as the output node which computes the overall output by summing all the incoming signals. In this layer fuzzy results of each rule are transformed into a crisp output by defuzzification process.

Learning Algorithm: In this paper, a standard hybrid learning algorithm is used [2*]. The hybrid algorithm combines the gradient descent and the least-squares estimator method for the adjustment of the parameters of the adaptive network. At the forward run of the hybrid algorithm (from layer 1 to layer 5), the consequent parameters are identified using a recursive least squares estimator. At the backward run, the output error propagates backward (from layer 5 to layer 1) and the premise parameters are estimated using the gradient descent method.

Methodology/System Modeling:

Evaluation of the FHR and its variations provides essential information for fetal risk assessment. Hence FHR monitoring can be used to determine the well-being of the fetus during pregnancy and at the time of labour. FHR trace is a time versus heart rate (in bpm) waveform derived from fPCG signal. It provides a picture of overall heart activity for a considerably longer span of time. Visual inspection of FHR trace by the experts is one of the best ways to find presence of acceleration and deceleration. Figure 3 shows a process flow diagram for the development of an ANFIS based expert system for surveillance of fetal health status on the basis of FHR trace.

The fetal heart sounds (fPCG signals) are acquired and recorded using a Bluetooth based wireless data acquisition system []. The recorded signals are de-noised using wavelet based noise suppression procedure []. Segmentation of de-noised fPCG signals are then achieved through envelope detection and thresholding criterion []. The value of FHR is calculated in every 5 seconds running time from the segmented fPCG signals []. For this purpose, a Simulink model is developed using MatlabTM R2009a version 7.8.1. The details of this model can be found in []. The output of this model is a FHR trace with a length equal to the simulation time defined in the configuration parameters of the model.

Extraction of Diagnostic Parameters:

Clinical practice guidelines provide a clear and explicit list of physiological parameters that can be used for fetal health surveillance during the antenatal part of pregnancy. These parameters can be classified into four categories [3*]: baseline, accelerations, decelerations, and variability.

Baseline: It is an imaginary line formulated in the absence of accelerations and decelerations and calculated as mean of the FHR signal rounded to increments of 5 beats per minute (bpm). It is determined over a time period of 5 to 10 minutes and expressed in bpm. The normal FHR range is between 120 and 160 bpm. Abnormal baseline is termed bradycardia when the baseline FHR is less than 120 bpm; it is termed tachycardia when the baseline FHR is greater than 160 bpm.

Variability: It is the fluctuations in the baseline FHR occurring at three to five cycles per minute. Variability is measured by estimating the difference between the highest peak and lowest trough of fluctuations in a one minute segment of the FHR.

Accelerations: Accelerations are transient increment in the FHR above the baseline by at least 15 bpm and lasts more than 15 seconds and less than 2 minutes.

Decelerations: Deceleration is defined as the transient episode of slowing FHR below the baseline level by more than 15 bpm and lasting 10 seconds or more.

Interpretation of FHR Patterns: FHR patterns are dynamic and transient in nature and require frequent reassessment. FHR tracings commonly move from one category to another over time. The FHR tracing should be interpreted in the context of the overall clinical circumstances, and categorization of a FHR tracing is limited to the time period being assessed. The recommendations of clinical guidelines for above mentioned FHR parameters are summarized in Table 1.

Table 1: Summary of Guidelines for Interpretation of FHR Parameters

FHR Parameters

Baseline (bpm)

Variability (bpm)





≥5 and ≤25

0 or 1



100-109 or


>2 and <5


>25 and <50


0 or 1


< 100, or

> 180

<2 or >50


0 or 1

Fetal health status can be classified on the basis of parameters obtained from the pattern of the FHR trace as follows:

Normal: A FHR trace in which all four FHR parameters fall into the reassuring category.

Suspicious: A FHR trace in which any one of the FHR parameters fall into the non-reassuring category and the remainder of the parameters are normal.

Pathological: A FHR trace in which more than one FHR parameters fall into the non-reassuring category or one or more FHR parameters is in the abnormal category.

This classification may help clinicians to understand and communicate issues relating to fetal well-being in an objective manner.

Fuzzy Expert System:

In this study, the Fuzzy Logic Toolbox of Matlab R2009a version 7.8.0 is adapted. It provides tools to create and edit fuzzy inference systems within the framework of Matlab. This toolbox also provides graphical user interface (GUI) tools to facilitate work, besides command line functions.

The first step for the construction of the fuzzy inference system is to determine its structure, i.e. to obtain the number of input, number of membership functions for each input and rules. In this work, four number of inputs parameters are used: Baseline, Variability, Acceleration and Deceleration. Only one output is used to classify the health status of the fetus as Normal, Suspicious or Pathological. The ANFIS structure with first order Sugeno model (i.e. linear output layer) is considered. Gaussian membership functions with product inference rule are used for all the inputs. Hybrid learning algorithm that combines the least square and gradient descent methods is used to adjust the parameters of membership functions. The details of input and output fuzzy sets, number of membership functions in each input and their ranges are depicted in table *.

Fuzzy Set (Range)


Membership Function (Range)

Baseline (50-250) BPM


Verylow (50-100) BPM

Low (100-110)

Normal (110-160) BPM

High (160-180)

Veryhigh (180-250) BPM

Variability (0-50) BPM


Verylow (0-2) BPM

Low (2-5) BPM

Normal (5-25) BPM

High (25-50)

Acceleration (0-10)


Present (1-10)

Absent (0-1)

Deceleration (0-10)


Present (1-10)

Absent (0-1)



Normal (1)

Suspicious (2)

Pathological (3)

The ANFIS structure with first order Sugeno model containing 80 rules is shown in Figure 4.

Experimental Results:

Medical diagnosis of the unborn is an important but complicated task that should be performed accurately and efficiently and its automation would be very useful. The main objective of the proposed system is to automatically analyze the fPCG signals and assess the health status of the fetus. The fPCG signals were acquired and recorded through a wireless data recording system developed specially for this purpose []. These signals were then processed and analyzed to generate the FHR trace, which contains the parameters of diagnostic importance. A Simulink model was developed for de-noising, segmentation and FHR calculation from the fPCG signals [].

In the present study, fPCG signals were obtained from 60 subjects with 28 to 38 weeks of gestation. The recordings were performed in quite room under the supervision of an expert gynecologist and a trained nurse. A set of 400 data from various normal and pathological subjects, collected under the supervision of an expert gynecologist were used for system training and generation of the initial fuzzy inference system. As mentioned earlier bell type membership functions were selected to express the input and output variables. There are four inputs with 5, 4, 2 and 2 number of membership functions hence the number of rules are 5-4-2-2=80. The ANFIS learns features in the data set and adjusts the system parameters according to a given error criterion. Figs. 5 and 6 show the initial and final membership functions of all the four inputs using the generalized bell shaped membership function, respectively. The examination of initial and final membership functions indicates that there are considerable changes in the final membership functions of the FIS

After training, another 400 testing data were used to validate the accuracy of the ANFIS model for classification of fetal health status. Classification results of the ANFIS model are displayed by an assessment chart as shown in Table 1. This chart contains the pre-classified (desired) outputs for each class and actual output achieved from the model.

Table 1: Assessment Chart


















According to the assessment chart, two subjects were wrongly classified as suspicious from a set of 210 normal subjects. Three subjects were wrongly classified as Normal and one as pathological from a set of 150 suspicious subjects. Similarly, two subjects were wrongly classified as suspicious from a set of 40 pathological subjects.

The test performance of the classifiers can be determined by the computation of sensitivity and overall classification accuracy. The values of sensitivity and overall accuracy of the system can be calculated as:

Table 2: Test performance of ANFIS classifier

ANFIS Output



Overall Accuracy










Accurate diagnosis of fetal well-being through analysis of FHR trace is a challenging task. Manual interpretation of FHR trace is very difficult, requiring clinical experience and significant expertise. ANFIS is a modern technique for the development of a computationally intelligent system which parallels the extraordinary ability of the human mind. In this work, a new application of ANFIS for classification of the fPCG signals is presented. Diagnostic decision was obtained in two steps: first, the diagnostic parameters are extracted from fPCG signals. For this purpose, these signals were acquired and recorded through a wireless data acquisition system. The recorded signals were de-noised and processed to extract the FHR trace. Secondly, an ANFIS classifier was trained using the diagnostic parameters derived from the first step. The proposed ANFIS model combined adaptive capabilities of the neural network and qualitative approach of the fuzzy logic. The performance of the ANFIS model was evaluated in terms of testing performance and overall accuracy. The results show that the overall accuracy level of around 98%, which confirms that the proposed ANFIS model has potential in classifying the fPCG signals. This study provides prolific information to the monitoring gynecologist/obstetrician in the risk assessment of antenatal fetal evaluation.