Fuzzy Analysis of Delivery Outcome Attributes for Improving the Automated Fetal State Assessment

ABSTRACT

Cardiotocography (CTG) is a standard procedure for fetal monitoring during pregnancy and labor. A number of automated methods for the classification of CTG recordings are based on supervised learning. Machine learning requires a set of parameters that quantitatively describe the acquired signals accompanied by a reference interpretation. This article presents a method of retrospective fetal-state assessment using the results of the fuzzy analysis of delivery outcome attributes. In real clinical datasets the class of signals related to an abnormal fetal state is usually underrepresented, which adversely affects the efficiency of the automated evaluation. Additionally, a method for reducing the disproportion between the class sizes based on the proposed fuzzy model is described. The fuzzy-inference-based learning of the Lagrangian Support Vector Machine (LSVM) increased the resulting efficiency of the fetal-state assessment.

Introduction

Cardiotocography is one of the basic methods of biophysical monitoring intrauterine fetal development. It involves the simultaneous recording and analysis of the fetal heart rate (FHR) signal, fetal movement activity, and uterine contractile function. The correct interpretation of the FHR signal is of special importance because it is the most crucial for the reliable assessment of the fetal state. Computational intelligence methods and, in particular, procedures based on the supervised learning approach may be distinguished among the most efficient methods of automated quantitative analysis (Esfandiari et al. 2014). Classic examples are artificial neural networks of different types, which were used to assist the evaluation of the fetal state (Jezewski, Wrobel, Horoba, et al. 2007; Jadhav, Nalbalwar, and Ghatol 2011; Jezewski et al. 2010; Maeda et al. 2012; Noguchi et al. 2009). Supervised learning algorithms were also applied to extract the rules of FHR signal interpretation for fuzzy inference systems (Czabanski et al. 2008; Czabanski et al. 2010; Czabanski et al. 2015). Several methods for the automated evaluation of the fetal state were based on Support Vector Machines (SVMs) (Georgoulas, Stylios, and Groumpos 2006; Warrick et al. 2010). The two-stage assessment of FHR recordings using fuzzy inference methods and the Lagrangian SVM (Czabanski et al. 2012) resulted in the efficient prediction of newborn acidosis. Similarly, the procedure integrating the least square SVM with particle swarm optimization and binary decision tree (Yilmaz and Kilikcier 2013) provided high accuracy of fetal-state evaluation. Along with the SVMs, parametric and nonparametric Bayesian classifiers (Dash et al. 2012; Dash, Quirk, and Djuric 2014) as well as the generative models (GMs)(Dash, Quirk, and Djuric 2014) were examined and proved a better efficiency of GMs. A comprehensive research on machine learning techniques (Sahin and Subasi 2015) showed small differences in the final results but identified the random forest as the most efficient. Similar results were presented in Tomas et al. (2013).

Although SVMs do not always lead to the best results in the CTG recordings classification (Dash et al. 2012; Guidi et al. 2014; Sahin and Subasi 2015), they are considered as very efficient and very often are used as a reference. Hence, to explore the possibility of improving the efficiency of the fetal-state evaluation with supervised learning, we applied the Lagrangian Support Vector Machine (LSVM) (Mangasarian and Musicant 2001). Based on the linear convergent iterative algorithm, the LSVM procedure is characterized by a lower computational complexity in comparison to the classical SVM while maintaining its high learning efficiency.

During the supervised learning, the optimal classifier parameters are estimated by using an appropriate set of exemplary data (the training set). The machine fetal-state assessment requires a training set consisting of the parameters quantitatively describing the CTG signals and the corresponding reference interpretation. There are two basic approaches leading to determination of the reference fetal-state assessment. In the first, the reference signal’s interpretation is provided by a clinical expert. In the second, the delivery outcome is retrospectively assigned as the fetal state during the time of the monitoring. However, because the qualitative evaluation of the CTG signals by clinicians is highly subjective (Spilka et al. 2014), we proposed the method for determining the retrospective fetal-state assessment based on the fuzzy analysis of the delivery outcome attributes.

When analyzing the real-data collections, another problem is the insufficient number of recordings corresponding to an abnormal fetal state. Large disproportion between the number of recordings representing fetal well-being and abnormal state adversely affects the final results of classification. The differences between the class sizes can be reduced by appropriate reproduction of reference patterns indicating the abnormal fetal state (Czabanski et al. 2010; Stylios, Vlachos, and Androulidakis 2014). The result of fuzzy inference allows for choosing the signals related to fetal distress that are characterized with the highest diagnostic value—the highest fuzzy score. These signals, randomly added to the training sets of the LSVM classifier, increase the efficiency of the automated classification with LSVM supervised learning.

Retrospective fetal-state assessment

The qualitative assessment of the CTG signals involves assigning it to one of two classes, defining the fetal state as “normal” or “abnormal”. Several studies distinguish also the third, indecisive class called “suspicious” or “questionable”, which includes the cases that require further investigation. There is no other noninvasive diagnostic method that allows for confirming the real fetal state at the time of the fetal monitoring session. In perinatology it is assumed, however, that the fetal state cannot change rapidly during pregnancy (Rooth 1987). Hence, the results of the delivery outcome assessment can be used as the reference to verify the efficiency of the automated classification. Although this approach is not entirely correct because an abnormal outcome can be the result of complications during labor, it still remains the most objective method of determining the reference fetal-state interpretation for automated classification algorithms.

The delivery outcome can be determined based on the analysis of the three main attributes evaluated by clinicians: the Apgar score (AP) representing the result of the visual assessment of the newborn; the birth weight (BW), expressed in percentiles in relation to a given population of newborns; and the pH measurement of the acid-base balance of the umbilical cord blood (PH). For each of these attributes, there are ranges of values related to the particular classes of the delivery outcome (Table 1). Supervised learning is usually carried out on the basis of single-attribute values (Jezewski, Wrobel, Labaj et al. 2007; Czabanski et al. 2013). Consequently, the information about the delivery outcome, which can be obtained from the simultaneous analysis of all attributes, is lost. Hence, we proposed the fuzzy system for determining the retrospective assessment of the fetal state based on the analysis of all three attributes. The results of the fuzzy inference (the fuzzy score) also provides the diagnostic value of the final assessment of the reference fetal state, which can be used to improve the efficiency of the supervised learning.

Table 1. The class labels of the delivery outcome attributes.

	Attribute
Delivery outcome	AP	BW	PH
Normal	≥ 7	≥ 10	≥ 7.2
Suspicious	[5,6]	(5,10)	(7.1, 7.2)
Abnormal	< 5	≤ 5	< 7.1

Fuzzy analysis

The fuzzy inference is conducted on the basis of fuzzy conditional rules with three inputs, being the values of outcome attributes, and one output representing the final delivery outcome:

(1)

where: I is the number of rules, x_0j denotes inputs (Apgar score (x₀₁), birth weight (x₀₂), pH (x₀₃)), and y⁽ⁱ⁾ is the output. Symbol denotes the linguistic value representing the class of the delivery outcome as being the result of the assessment of a single outcome attribute. It is defined by a fuzzy set with a trapezoid membership function (Figure 1). The parameters of trapezoids (Table 2) were determined using simple statistical analysis of the delivery attributes dataset (Czabanski et al. 2012). The core of the fuzzy set (c,b) was defined as the interquartile range of parameter values of the particular class of delivery outcome. The limit values (a,d) were calculated to fulfill the assumption that the membership of the values defining the boundary between classes should be the same and equal to for both classes.

Table 2. Parameters of the membership functions that define classes of delivery outcome attributes.

Membership function	Normal			Suspicious			Abnormal
parameter	AP	BW	PH	AP	BW	PH	AP	BW	PH
a	6.00	−10.0	7.13	4.00	3.00	7.03	0.00	0.00	6.50
b	8.00	30.0	7.27	6.00	7.00	7.17	0.00	0.00	6.50
c	10.0	95.0	7.45	6.00	7.00	7.18	3.00	5.00	6.99
d	10.0	95.0	7.45	8.00	13.0	7.22	7.00	5.00	7.21

Figure 1. An example of a fuzzy rule indicating the suspicious delivery outcome. Because only one attribute is within the normal range and there are no attributes related to the abnormal state, the fuzzy rule output defines the suspicious delivery outcome.

The rule base Equation (1) defines a zero-order Takagi-Sugeno-Kang (TSK) fuzzy model (Takagi and Sugeno 1985). The consequence y⁽ⁱ⁾ is a fuzzy set with the singleton membership function. Its location is defined by assuming that a normal outcome corresponds to negative , whereas the abnormal to positive output value of a single fuzzy rule. To classify the delivery outcome as suspicious, a varying location is assumed (Figure 1), allowing for a different interpretation of delivery outcome attributes from the ranges corresponding to the suspicious class.

The proposed TSK model is equivalent to the Mamdani fuzzy reasoning system with the consequences of fuzzy sets in the form of isosceles triangular membership functions having the width of the base equal to 2 and the center of gravity defuzzification.

A complete rule base of the TSK fuzzy system consists of I = 3³ = 27 conditional statements. In the proposed solution, the delivery outcome is interpreted as

• abnormal, if any attribute indicates the abnormal state,

• normal, if two or more attributes indicate the normal and none indicates the abnormal state,

• suspicious, for all the remaining cases.

An example of a fuzzy rule indicating the suspicious delivery outcome is shown in Figure 1.

The final output value of the fuzzy model is calculated as a weighted mean of all rules outputs:

(2)

where

The above equation can be interpreted as an ensemble of experts, each represented by a single rule. The fuzzy rule defines the relationship between particular outcome attributes and the class of the final delivery outcome assessment. The weighted average of the assessments from all rules (experts) formulates the final interpretation of the delivery outcome.

In the further considerations, we assume two classes of the delivery outcome assessment—normal and abnormal. Consequently, a delivery outcome is classified as abnormal if the positive output value Equation (2) exceeds a predefined threshold y₀ ≥ Δ. When considering a three-class assessment problem, the suspicious state can be defined as corresponding to (y₀) < Λ, where Λ is the limit threshold value.

LSVM supervised learning

Among the machine learning procedures, a group of methods based on the structural risk minimization (SRM) principle (Vapnik 1999) can be distinguished. The SRM is an inductive rule that leads to high learning efficiency in terms of increased generalization ability. The most popular solutions include SVMs, which were successfully applied to support the process of automated fetal-state evaluation (Czabanski et al. 2012, 2015; Esfandiari et al. 2014; Georgoulas, Stylios, and Groumpos 2006; Warrick et al. 2010). The SVMs find an optimal hyperplane in multidimensional feature space, which separates the given classes with the highest separation margin. Data (input vectors) determining the margin are called the support vectors. In practical solutions, the learning speed is of special importance. Consequently, we used the Lagrangian Support Vector Machine (Mangasarian and Musicant 2001). Unlike the classical SVMs, in which the solution is based on quadratic programming, the LSVM uses a linearly convergent iterative algorithm. It significantly reduces the time required for the calculation without compromising the efficiency of the classifier.

Research material

The research material used in our experiments is the collection of the CTG recordings from one-hour fetal monitoring sessions. The FHR signal was recorded using a fetal bedside monitor from the patient’s abdomen via an external pulsed Doppler ultrasound transducer (Jezewski et al. 2011; Kupka et al. 2004). In order to identify uterine contractions, a strain gauge transducer was used. The FHR value was acquired with every 250 ms with a resolution of 0.25 bpm. Finally, we obtained a set of 685 antenatal recordings (the mean gestational age 33 weeks), which were derived from 189 patients.

Various methods were examined in order to identify the most discriminating set of features quantitatively describing the FHR signal (Georgoulas, Stylios, and Grumpos 2005; Hannah Inbarani, Nizar Banu, and Azar 2014; Xu et al. 2014). Also, different sets of parameters quantitatively describing the FHR signal (Alamedine, Khalil, and Marque 2013; Chudacek et al. 2011; Spilka et al. 2012) were studied. However, the linear time domain features are still the common basis for the classification algorithms due to their easy clinical interpretation. Hence, our input vector included 11 linear parameters of the FHR signal as well as features related to uterine contractions, fetal movement, and fetal gestational age (Table 3). The corresponding delivery outcome attributes were read from the neonatal forms (Wrobel et al. 2015).

Table 3. The set of the analyzed signal features.

bFHR	bpm	the mean value of the FHR baseline (Wrobel et al. 2013)
mFHR	bpm	the fluctuation range of baseline values calculated as a difference between the maximum and minimum values
ACC	1/h	the number of identified acceleration patterns
DEC	1/h	the number of identified deceleration patterns
LOW	%	the duration of the low variability of the FHR signal, expressed as the percentage of the signal length
STV	ms	the short-term FHR variability index
LTV	ms	the long-term FHR variability index
SLR	—	the ratio of STV and LTV
OSC	bpm	the amplitude of FHR oscillation
OSE	%	the percentage of silent FHR oscillation (OSC ≤ 5 bpm) in a whole trace
OSY	%	the percentage of saltatory FHR oscillation (OSC ≥ 25 bpm) in a whole trace
UTE	1/h	the number of detected uterine contractions
MOV	1/h	the number of fetal movements perceived by mother during the entire monitoring
AGE	—	the fetal gestational age during monitoring

In highly developed countries, the percentage of newborns recognized as “abnormal delivery outcome” is very low. Data derived from clinics are usually characterized by a higher number of pregnancies at risk; however, in the analyzed research material, the class of CTG recordings corresponding to the abnormal delivery outcome and, hence, fetal distress is still underrepresented. Our database included 40 recordings (6% of the analyzed dataset) related to the low Apgar score, 54 (8%) indicating the low percentile of the newborn birth weight, and 15 (2%) with the abnormal pH level. The total number of abnormal patterns due to at least one abnormal outcome attribute is 92 (13%).

Experiments

The standard approach to fetal-state evaluation based on the LSVM supervised learning (STDL) is based on the reference assessment determined with a single delivery outcome attribute, using the class labels from Table 1. Additionally, we assumed a delivery outcome as abnormal if at least one outcome attribute was outside its physiological range (OR). For the purpose of binary classification, the recordings related to the class “suspicious” were assigned to the group indicating the normal state. Consequently, our task was the automated method that allows for assessing the risk of the fetal distress with highest certainty.

The efficiency of supervised learning depends on the training examples. Hence, in the first set of experiments we examined how the selection of the training data affects the results of the automated assessment of the fetal state. The LSVM training patterns were selected through fuzzy inference. The output of the TSK model (Equation (2)) can be interpreted as a degree of certainty in relation to the retrospective fetal-state evaluation based on delivery outcome attributes. This information can be used to select the proper LSVM training patterns, because the STDL training is performed regardless of any degree of certainty. Consequently, an additional parameter k, defining the threshold of the fuzzy output, was introduced to the LSVM learning. Hence, only the recordings whose degree of certainty of the retrospective assessment (y₀) was higher than k were included in the training set. We proposed three LSVM learning procedures based on the fuzzy analysis:

• DTDT (Direct Training Direct Testing), in which the reference assessment of the fetal state during training as well as during testing is a result of the direct evaluation of delivery outcome attributes used (shown in Table 1),

• FTDT (Fuzzy Training Direct Testing), in which the reference assessment of the fetal state for the training set is determined using the results of fuzzy inference, whereas, for the testing set, it is determined on the basis of attribute labels listed inTable 1,

• FTFT (Fuzzy Training Fuzzy Testing), in which the reference assessment of the fetal state for both the training and testing sets is determined with the fuzzy model.

From the learning point of view there is no difference between FTDT and FTFT procedures, however, in the FTFT procedure, the fuzzy assessment is used also during the classifier testing.

The results of fuzzy analysis can be used also for the selection of the abnormal fetal-state patterns characterized with the highest diagnostic value (highest fuzzy score). These patterns can be randomly reproduced to reduce the adverse disproportion between the class sizes in the training set. Studies on the efficiency of the supervised learning (Catley et al. 2006; Czabanski et al. 2010) have shown that the best classification results can be obtained if the percentage of the underrepresented class is at least 20%. Hence, we examined the influence of the reproduction on the LSVM classification efficiency.

The learning for the data with copied abnormal signals was performed using a standard LSVM learning procedure (STDL). In the first stage of our experiments, we used the signals that were interpreted as abnormal according to the direct evaluation of the delivery attributes. In the second, we reproduced only the recordings with abnormal fetal state that were characterized by the highest diagnostic value (fuzzy score y₀ ≥ 0.5, p⁽ⁱ⁾ = 0). In both approaches, the parameters quantitatively describing the selected signals were randomly modified in the range of their standard deviation and then added to the training sets (the testing sets remained unchanged), so that the proportions of signals corresponding to abnormal fetal state were, respectively, 20%, 30%, 40%, and 50% of the whole training dataset.

Algorithms specification

The learning was performed for 50 random divisions of the dataset into two parts: training (342 recordings) and testing (343 recordings). The divisions were controlled in such a way that all the recordings from a given patient were used either in the training or testing subset. Additionally, we maintained the original ratio between normal and abnormal fetal-state patterns in the training and testing subsets. The classifier settings were determined using the parameters characterized by the maximum QI for the 10 first divisions. The nonlinear classification problem was solved using kernel functions in a radial form . The dispersion σ of the kernel and the regularization factor γ were selected from the range of [10^–3,…, 10⁺⁴] with steps {10^–3,10^–2,…, 10³} changed every decade. The stop condition was the maximum number of 100 iterations or when the change of Lagrange multiplier values was less than 10^–5. The parameters p⁽ⁱ⁾ and Δ of the fuzzy model were changed in the range [–0.50, +0.50] with a step of 0.25, while k was changed in the range [0.00, 0.50] with the step of 0.25.

Classification efficiency

The classification accuracy was evaluated on the basis of confusion matrices. In addition to the percentage of the correct classifications (CC) of the signals from the testing set, we calculated sensitivity (SE), specificity (SP), as well as positive predictive value (PPV) and negative predictive value (NPV). To make the assessment of the learning results easier we used also the integrated quality index (G-measure) defined as .

Results and discussion

In the first stage of our study we applied the standard algorithm of LSVM learning, in which evaluation of the reference fetal state in both training and testing sets was defined based on the direct assessment of delivery outcome attributes. The results of the classification (the mean values for the testing data from all the 50 divisions) are shown in Table 4. It can be noted that the efficiency of the learning is highly dependent on the chosen method of the reference evaluation. Different definitions of the retrospective fetal-state assessments provided various levels of the classification quality. The highest QI = 65.1% was obtained for the OR approach, whereas the lowest QI = 36.7% was in relation to pH measurements. However, the learning based on pH allowed for the highest classification accuracy, CC = 95.0%. The high discrepancy between QI and CC is due to the small number of recordings indicating the abnormal delivery outcome.

Table 4. The efficiency of the LSVM classification for different definitions of the retrospective fetal-state assessment.

	AP		BW		PH		OR
Learning procedure	QI	CC	QI	CC	QI	CC	QI	CC
STDL	55.36	90.80	63.64	88.24	36.73	94.97	65.14	83.39
DTDT	62.42	88.78	67.25	87.03	44.68	95.40	70.39	79.92
FTDT	74.68	69.70	74.59	68.79	69.05	66.98	75.43	73.03
FTFT	81.62	82.47	81.53	82.67	81.12	82.16	81.87	82.65

In subsequent experiments, we used the learning procedures based on the fuzzy analysis of delivery outcome attributes while maintaining the same division of the research material for the training and testing parts. It should be noted that the training sets of the fuzzy-inference-based LSVM learning consisted only of the recordings for which the criterion for the fuzzy score (y₀) ≥ k was met. The lowest increase of the classification quality was obtained for DTDT (Table 4). For the FTDT (Table 4), we observed higher values of QI and decreased dependence between classification quality and type of testing reference assessment. The highest values of QI and the smallest decline of CC in relation to STDL learning was observed for the FTFT procedure (Table 4). The small differences between the FTFT results for BW, AP, PH, and OR are due to differences in random division of research material for the training and testing sets depending on the given outcome attribute. Table 5 shows confusion matrices of the procedures based on the fuzzy training (FTDT and FTFT), which provided the highest level of QI.

Table 5. The confusion matrices of the procedures based on the fuzzy training. Mean values of true positives (TP), true negatives (TN), false positives (FP) and false negatives (FN) for testing subsets are shown.

	FTDT				FTFT
Delivery outcomeattribute	TP	TN	FP	FN	TP	TN	FP	FN
AP	16.22	222.9	100.1	3.780	90.54	192.3	36.30	23.84
BW	22.32	213.6	102.4	4.680	89.66	193.9	34.78	24.66
PH	5.760	224.0	111.0	2.240	91.58	190.2	35.50	25.70
OR	36.42	214.1	82.92	9.580	91.34	192.1	36.24	23.28

We were not able to specify a unique set of LSVM parameters (γ, σ), which would lead to maximum classification quality regardless of the applied learning procedure and the reference assessment. It was also difficult to determine a single set of parameters of the fuzzy model (p⁽ⁱ⁾, Δ, k), which will guarantee the best results for all types of learning. The values of the parameters leading to the best classification quality using the OR approach are shown in Table 6. We identify, however, a set of parameters of the fuzzy inference, leading to satisfactory results for the proposed learning procedures regardless of the applied testing reference assessment (Table 7). Symbols QI_m and CC_m denote the mean values of QI and CC for the given learning procedure and the proposed sets of parameters. Symbols QI_mm and CC_mm are the mean values of QI and CC when the parameters of the fuzzy model were selected separately for each of the learning methods as well as the type of the testing reference. For comparison, the classification efficiency of the standard LSVM learning was QI_mm = 55.22% and CC_mm = 89.35%. The differences between the compared methods in accordance with CC and QI were statistically significant (p < 0.05).

Table 6. The specification of the learning procedures leading to the best classification quality for the OR approach. The classifier settings were determined using the parameter characterized by the maximum QI for the 10 first divisions.

	Inference parameters					Classification efficiency [%]
Learning procedure	p^(i)	Δ	k	γ	σ	SE	SP	PPV	NPV
STDL	—	—	—	7000	0.100	48.00	88.87	40.41	91.70
DTDT	−0.50	0.50	0.25	5000	0.090	60.00	83.01	35.63	93.07
FTDT	0.50	0.25	0.25	50.00	0.006	79.17	72.08	30.59	95.75
FTFT	0.25	0.25	0.25	6000	0.001	79.76	84.13	71.72	89.24

Table 7. The fuzzy reasoning parameters, which provide satisfactory learning results regardless of the applied definition of the testing reference assessment.

	Inference parameters			Classification efficiency [%]
Learning procedure	p^(i)	Δ	k	QIm	CCm	QImm	CCmm
DTDT	−0.50	0.50	0.25	60.58	87.79	61.19	87.78
FTDT	0.50	0.25	0.00	73.21	70.18	73.44	69.63
FTFT	0.25	0.25	0.25	81.53	82.46	81.53	82.49

The classifier training based on the patterns characterized by a high degree of certainty refines the estimated boundary between normal and abnormal patterns, resulting in the increased quality of the fetal-state assessment. Moreover, integrating the information from all considered delivery outcome attributes increases the probability that the reference interpretation represents the actual fetal state.

In the next stage of our study, we examined how the multiplication of the abnormal fetal state patterns in the training set affects the efficiency of the qualitative assessment using the STDL procedure. The increased proportion of the recordings related to the abnormal fetal state without the preliminary fuzzy analysis did not improve the classification results. The increase of QI was obtained only if the reference fetal state was defined using the procedure based on the AP approach. The maximum value QI = 57.9% was noticed when the proportion of signals corresponding to the low Apgar score was equal to 40%. Table 8 shows the classification results when the LSVM learning was based on the increased proportion of the abnormal fetal-state patterns, which were characterized by the high value of the fuzzy score (y₀ ≥ 0.5, p⁽ⁱ⁾ = 0). It can be noticed that the random reproduction of the abnormal fetal-state patterns with the highest diagnostic value leads to a significant increase of QI for all considered methods of the reference interpretation only if the proportion of the recordings related to the fetal distress is at least 30% (Table 9). The best improvement was obtained in the case of the pH measurement and the equal number of recordings indicating the normal and abnormal fetal state in the training sets. The highest increase of the QI was noticed with the 50% reproduction of the abnormal fetal-state patterns. The resulting confusion matrix is shown in Table 10. The differences between examined reproduction levels in accordance with CC were statistically significant (p < 0.05).

Table 8. The efficiency of the LSVM classification with training based on the reproduction of the abnormal fetal-state patterns, which were characterized by the high value of the fuzzy score (the testing sets remained unchanged).

	Resampling rate [%]
	20		30		40		50
Delivery outcomeattribute	QI	CC	QI	CC	QI	CC	QI	CC
AP	54.46	91.47	60.04	88.69	69.36	79.74	68.98	77.90
BW	62.61	86.58	66.61	85.84	76.12	80.93	77.72	74.71
PH	44.20	91.14	46.15	89.31	49.56	88.52	56.87	71.29
OR	65.24	82.78	67.25	84.90	73.97	78.83	77.06	74.59

Table 9. The results of the statistical evaluation of QI differences between the methods based on the reproduction of the abnormal fetal-state patterns (p < 0.05) and the standard learning. The p-values of differences, which were statistically insignificant, are shown.

	Resampling rate [%]
Delivery outcome attribute	20	30	40	50
AP	0.54	+	+	+
BW	0.22	+	+	+
PH	+	+	+	+
OR	0.84	+	+	+

The selection of the training patterns based on fuzzy inference in all our experiments led to the improved classification quality (QI) at the expense of the classification accuracy (CC). The increased contribution of the underrepresented class of abnormal patterns shifts the separating hyperplane and provides a higher number of false positive assessments as a result of the higher classifier sensitivity. In the case of medical applications, this cost is acceptable against the improvement of true positive recognitions.

Table 10. The confusion matrix of the LSVM classifier with the 50% reproduction of the abnormal fetal state patterns in the training set. Mean values of true positives (TP), true negatives (TN), false positives (FP) and false negatives (FN) for testing subsets are shown.

Delivery outcome attribute	TP	TN	FP	FN
AP	12.18	255.0	68.00	7.820
BW	22.06	234.2	81.80	4.940
PH	3.740	240.8	94.20	4.260
OR	37.24	218.6	78.38	8.760

Introducing the automated recognition of the fetal state based on the results of quantitative analysis of monitored signals, which leads to increased effectiveness of fetal screening tests is of significant clinical importance. However, the proposed methodology can be applied in any medical application based on supervised learning where the reference assessment is defined with a set of quantitative indicators.

Conclusions

The presented study examined the possibility of improving the efficiency of the automated fetal-state assessment with the fuzzy analysis of the delivery outcome attributes. The proposed fuzzy system based on the Takagi-Sugeno-Kang model uses the information behind the values of the delivery attributes to provide an integrated assessment of the delivery outcome (fuzzy score). Because the delivery outcome can be retrospectively assigned to the fetal state during the time of the monitoring, the fuzzy inference determined the reference assessment of the fetal state for the purpose of machine learning. Since the fuzzy score can be interpreted as a degree of certainty of the reference fetal-state evaluation, the inference results were also used to identify the CTG recordings of the highest diagnostic value. The fuzzy model was included in the process of the supervised learning classifier based on the Lagrangian Support Vector Machine. The parameters quantitatively describing the signals were used as inputs of the LSVM classifier. The learning procedures based on the fuzzy reasoning improved the efficiency of the LSVM classification when compared with the standard learning, which is solely based on the direct assessment of the selected delivery outcome attribute. The fuzzy inference results were also used to reduce the large disproportion between the patterns of the normal and abnormal fetal states, which adversely affects the efficiency of the automated evaluation. The supervised learning with the increased number of recordings related to the abnormal fetal state and characterized by the high fuzzy score led to a significant increase in efficiency of the qualitative assessment of the fetal state.

Funding

This work was partially supported by the Ministry of Science and Higher Education funding for statutory activities (BK-220/RAu-3/2016) and the Ministry of Science and Higher Education funding for statutory activities of young researchers (BKM-508/RAu-3/2016).

Additional information

Funding

This work was partially supported by the Ministry of Science and Higher Education funding for statutory activities (BK-220/RAu-3/2016) and the Ministry of Science and Higher Education funding for statutory activities of young researchers (BKM-508/RAu-3/2016).