Clustering with Pairs of Prototypes to Support Automated Assessment of the Fetal State

ABSTRACT

Cardiotocographic (CTG) monitoring, consisting in analysis of the fetal heart rate, uterine contractions, and fetal movements is the primary noninvasive method for the fetal state assessment. The visual interpretation of the CTG signals is characterized by the large inter- and intraobserver disagreement. Hence, the automated methods supporting the diagnosis process are the topic of researches. In the presented study, the evaluation of the CTG signals, based on fuzzy clustering with pairs of prototypes, is described. The efficiency of the proposed method is verified using two benchmark datasets of the CTG signals (CTU-UHB and SisPorto), and the problems of the two- and three-class classification are considered. The obtained results show the improved quality of the automated fetal state assessment in accordance with the applied reference procedures: the fuzzy (c+p)-means clustering and the Lagrangian Support Vector Machines.

Introduction

Cardiotocographic (CTG) monitoring is the method for fetal state assessment during pregnancy and labour. It consists in simultaneous analysis of the fetal heart rate (FHR), uterine contractions, and fetal movements. The most popular method for the acquisition of the FHR signal is the noninvasive Doppler ultrasound technique (Jezewski et al. 2011). Because the visual assessment of the acquired signals is characterized by large inter- and intraobserver variability (Spilka et al. 2014), an automated analysis is used to support the diagnosis. The computer systems extract features, quantitatively describing the acquired signals (Wrobel, Matonia et al. 2015), which can be further analyzed by using computational-intelligence-based methods. Different classifiers were applied to support the automated fetal state assessment, including Support Vector Machines (SVMs), artificial neural networks (ANNs) and fuzzy systems. In Krupa et al. (2011), FHR features extracted by using empirical mode decomposition were the inputs of the SVM, whereas the reference records assessments were provided by a clinical expert. The SVM with the modified criterion function was applied to predict the risk of the metabolic acidosis in Georgoulas, Stylios, and Groumpos (2006). In Pedrinazzi, Magenes, and Signorini (2004), the independent component analysis was used to preprocess the input data for the SVM classification. The comparison of classification methods including the SVM was presented in Magenes et al. 2014. The classification of the CTG signals using ANN was the topic of Magenes et al. (2001), in which the multilayer perceptron was compared with other classification methods. The work by Georgoulas, Stylios, and Groumpos (2005) shows the wavelet neural networks optimized with the particle swarm optimization procedure. The committee of ANNs applied for the prediction of birth asphyxia was described in Georgieva et al. (2013). In Maeda et al. (2015), the ANN was used as one of the components of the FHR monitoring system. The dataset representation influences the efficiency of the CTG signals’ classification when applying ANN. In Jezewski, Wrobel, Horoba, et al. 2007 and Jezewski, Wrobel, Labaj, et al. 2007 the relation between dataset’s representation and classification efficiency was studied. Several fuzzy-logic-based procedures were also proposed for the automated analysis of FHR signals (Czabanski et al. 2013, 2012; Signorini et al. 2000). In Czabanski et al. (2013), several classification tasks concerning various datasets and various definitions of the fetal state were investigated. The two-step classification applying the fuzzy system and the ANN or the Lagrangian SVM was presented in Czabanski et al. (2012). The classification of FHR signals using fuzzy systems was also described in Signorini et al. (2000). A combination of neural networks and fuzzy systems leads to neurofuzzy systems. The assessment of the fetal state by applying the Artificial Neural Network Based on Logical Interpretation of fuzzy if-then Rules (ANBLIR) system with various learning algorithms based on deterministic annealing and ε-insensitive learning was examined in Czabanski et al. (2008).

Antecedents of the rules defining the fuzzy classifiers can be determined using data clustering (Czabanski 2006; Jezewski, Leski, and Czabanski 2016; Leski 2015). Clustering consists in finding clusters (groups) of similar objects within a given dataset. Among clustering procedures, a group of fuzzy methods may be distinguished. The fuzziness of the methods is the application of a membership function, so a given object may partially belong to more than one cluster (with a given membership value within the range [0,1]). In contrast, the hard clustering considers only the full belonging to a given cluster. Hence, the fuzzy clustering might be better suited for real data, where groups or classes of objects might overlap. Moreover, the idea of the partial membership allows for selecting the objects that belong to a given cluster with the assumed level (i.e., satisfying the assumed membership threshold) for further processing. One of the most popular fuzzy clustering methods is the fuzzy c-means (FCM) method proposed by Bezdek (1981). In that case, the clustering results are described by locations of prototypes (centers of clusters) and membership values (forming the partition matrix). The FCM prototypes are a weighted means of the clustered objects, with the weights defined as the normalized memberships of the objects to a given cluster. In this study, we applied clustering with pairs of prototypes (Jezewski et al. 2015) based on the FCM procedure to find the antecedents of the fuzzy classifier supporting the qualitative assessment of the fetal state. Two datasets of the CTG signals—SisPorto (Ayres-de-Campos et al. 2000) and CTU-UHB (Chudacek et al. 2014)—were used to verify the efficiency of the automated evaluation. The first (SisPorto) consists of sets with quantitative parameters describing the signals. The CTU-UHB contains the raw signals, so our investigation involved also the reanalysis of them and determination of the quantitative parameters.

Fuzzy classifier based on clustering with pairs of prototypes

The idea of the presented clustering procedure consists of introducing the additional prototypes—“prototypes in between” (PB), to those that were obtained separately in each of two classes ω₁ and ω₂ by the FCM method—“ordinary prototypes” (OP). All prototypes—PB and OP—are used to determine the antecedents of the rules defining the fuzzy classifier. The main idea behind definition of PB is to create rules of the fuzzy classifier allowing for more accurate assessment of the objects located near the border between two classes. In practice, however, the PB are not always located near that border. However, we suppose that introducing additional rules determined by using PB could improve the classification quality. The PB are new prototypes determined by pairs of the OP (one prototype from the ω₁ class, and one from the ω₂). The pairs are found by using the algorithm based on distances between prototypes and groups’ densities. A disadvantage of the basal FCM method is its sensitivity to noisy data and outliers, as a result, the obtained prototypes (OP and PB) might be located undesirably. However, the clustering with pairs of prototypes also could be based on robust clustering procedures. The clustering procedure is outlined in the following steps:

1. find OPs using FCM clustering,

2. find the appropriate pairs of the OP,

3. determine the PBs by using OP.

We presented two variations of the procedure (Jezewski et al. 2015), without and with the rejection of the OP based on the groups’ densities analysis.

The procedure starts with the FCM clustering of each of the two considered classes into the initial number of clusters per class (c). Consequently, 2c of OP are obtained in total. Each of the two classes is clustered with the same fuzziness degree (m, m > 1). If the same FCM prototypes in a given class are determined, only one remains for the further processing. If the same prototypes are found in both classes, then all are rejected. In case of variation with the rejection, there is the additional step of the prototypes’ rejection. We remove the prototypes that represent groups with densities lower than the assumed density threshold. The density is calculated using the objects with membership value greater than or equal to the assumed membership threshold. Three types of the density of the ith group of the jth class were applied:

(1)

where , , denotes the number of ordinary prototypes (groups) of the jth class, is the ith ordinary prototype of the jth class, is the FCM membership of the object x_k to the ith cluster of the jth class, and denotes the number of objects with the membership value greater than or equal to the assumed threshold () in the ith cluster of the jth class. The sets , and define the indexes of these objects.

After each rejection, the partition matrix is updated; i.e., the appropriate rows of the matrix are removed and the objects with the zero summary memberships are excluded from further steps: finding the pairs, determining the PB, and calculating the clusters’ dispersions. After all rejections, finally, c⁽¹⁾ (c⁽²⁾) prototypes () in the ω₁ (ω₂) class remain.

The maximum number (N_p) of the pairs of ordinary prototypes is equal to . The detailed algorithm finding the pairs is presented as follows:

1. Fix the “window” length W and the density type (Equation (1)).

2. Calculate the densities of the groups of ω₁ and of ω₂.

3. Sort the prototypes of the class with the smaller number of OP in descending order according to groups’ densities.

4. Set i = 1 and assume j = C, where C = max (c⁽¹⁾,c⁽²⁾).

5. If W > j, then set W = j, for the ith sorted prototype, find W nearest prototypes (using the Euclidean distance) of the class with the greater number of OP.

6. From the W nearest prototypes, choose the one that represents the group of the highest density. If there are more such prototypes, choose the nearest one. The prototypes found in Steps 5 and 6 form the pair.

7. Stop the algorithm if all (N_p) possible pairs of prototypes are found, else set i = i + 1, j = j−1 and go to the Step 5. While finding W nearest prototypes (in Step 5), omit those previously chosen to form the pairs.

If c⁽¹⁾ = c⁽²⁾, the algorithm is repeated twice, and the solution leading to the lower mean Euclidean distance between prototypes forming the pairs is chosen.

The expected number (c^(b)) of PB was set as equal to . If the number of the determined pairs (N_p) is greater than c^(b), then c^(b) nearest pairs are chosen, otherwise, all N_p pairs are used. The PB are calculated as follows:

(2)

where: r and t denote the groups represented by the OP ( and ) forming the pair, the sets and include indexes of the objects satisfying the assumed membership threshold condition and were defined in the text following Equation (1).

The PB and OP form the set of K = c⁽¹⁾ + c⁽²⁾ + c^(b) prototypes (v_i), defining the centers of the Gaussian membership functions of fuzzy sets A_k in the antecedents of the following rules defining the fuzzy classifier:

(3)

where: n is the number of features, denotes the p-feature of the object , and is the location of the singleton in the consequent, which is determined using the gradient method (Leski 2015). The rule base of the classifier can be interpreted as an ensemble of experts, each represented by a single fuzzy rule. Each rule defines the relationship between the input data and the class assessment. The weighted average of the assessments from all rules (experts) formulates the final interpretation of the fetal state, and the fuzzy antecedents provide soft switching between the local areas of expertise.

The final output value of such classifier is given as:

(4)

(5)

The parameter γ is used for scaling the dispersions s_kp of the Gaussian membership functions, which are calculated using Equation (6) for the OP, and Equation (7) for the PB:

(6)

(7)

The symbol ^(•2) denotes component-by-component squaring . Dispersions , , and form the set of dispersions .Defining as the N × K matrix, where denotes the class label (equals or ) of the object , and N is the number of objects in the clustered set, we can determine the fuzzy rules’ outputs using the gradient method (Leski 2015) to minimize the Asymmetric SQuaRe (ASQR) loss function (Leski 2015):

(8)

where , for , and for , where , denotes the iteration number, and 1 is a vector with all entries equal to one.

The classification procedure using prototypes obtained in the variation without (with) the rejection of the OP based on analysis of the groups’ densities was denoted as (), where x represents the density type.

Research material

The efficiency of the automated fetal state assessment was verified using two sets of the CTG recordings: SisPorto (Ayres-de-Campos et al. 2000) and CTU-UHB (Chudacek et al. 2014; Goldberger et al. 2000).

The SisPorto database

The SisPorto dataset was obtained in August 2013 from the UCI Machine Learning Repository (Lichman 2013) and consisted of 2126 CTG signals, each described by 21 quantitative parameters. The reference signals’ assessments were provided by expert clinicians. As a result, 1655 recordings were labeled as normal, 295 as suspicious, and 176 as abnormal. We analyzed the three-class classification problem. Because the presented fuzzy classifier is a binary one, we used the class-class (one-against-one) approach. Consequently, three binary classifiers were defined as distinguishing cases: normal from suspicious (NS), normal from abnormal (NA), and suspicious from abnormal (SA) (Jezewski, Czabanski, and Leski 2015).

The CTU-UHB database

The CTU-UHB data is the set of raw 552 intrapartum CTG signals. In this case, the expert interpretation also can be used as the reference fetal state. However, due to a high level of the inter- and intraobserver disagreement (Spilka et al. 2014) we applied the retrospective analysis using fetal outcome attributes (the Apgar score, the percentile of the birth weight, and pH measurement of blood from the umbilical artery). Because only the raw CTG signals were available, the features that quantitatively describe the signals in the time domain were calculated by using the computerized fetal monitoring system (Wrobel, Jezewski et al. 2015). First, the fragments with the signal loss at the beginning or/and at the end of each recording were removed. Next, the possible artifacts were removed (Jezewski et al. 2010), and the signals were averaged using a moving window of 2.5 s width. Finally, 11 FHR signal parameters were analyzed:

1. The mean value of the FHR baseline [bpm] (Jezewski et al. 2010).

2. The fluctuation range of the FHR baseline [bpm], defined as the difference between the maximum and the minimum FHR baseline.

3. The number of identified acceleration patterns [1/h]. Acceleration was defined as the transient increase in FHR above the baseline by 15 bpm or more and lasting 15 s or more.

4. The number of deceleration patterns [1/h]. Deceleration was defined as the transient decrease in FHR below the baseline by 15 bpm or more and lasting 10 s or more.

5. Short-term variability (STV) [ms], defined as the mean of the differences in the one-minute window, where T_i is the equivalent of the ith R-R interval from the fetal ECG (Kupka et al. 2004). The final value of the STV was calculated as the mean of all one-minute values.

6. Long-term variability (LTV) [ms], defined as the difference between the maximum and the minimum T_i intervals in the one-minute window, excluding the periods with recognized accelerations with the amplitude greater than 20 bpm and lasting longer than 30 s, and decelerations with the amplitude greater than 10 bpm and lasting longer than 1 minute. The final value of the LTV was calculated as the mean of all one-minute values.

7. The ratio of STV/LTV.

8. The duration of the reduced long-term variability (LTV) of the FHR signal, expressed as the percentage of the signal length.

9. The oscillation amplitude [bpm] defined as the difference between the maximum and the minimum FHR in the one-minute window. The final value of the oscillation amplitude was calculated as the mean of all one-minute values.

10. The percentage of silent oscillation (amplitude ≤ 5 bpm) in a whole signal.

11. The percentage of saltatory oscillation (amplitude ≥ 25 bpm) in a whole signal.

Additionally, the number of detected uterine contractions [1/h] was used. The above parameters were chosen, according to the expert suggestion, as having significance for the diagnosis support. All the applied signal features come from selected clinical criteria of CTG signals interpretation (e.g., FIGO guidelines, point scales).

In the further considerations we assumed the binary classification of the CTU-UHB data. As the reference assessment, we used the result of the retrospective fetal state evaluation using the pH measurements only (the pH lower than 7.2 was assumed as abnormal), and the approach where the fetal state was retrospectively considered as abnormal if at least one of the fetal outcome attributes was outside its physiological range (OR), i.e., pH < 7.2, Apgar score in the 1st minute < 7, or the percentile of the birth weight < 10. The percentiles of the birth weight were calculated in accordance to the newborn sex and the gestational age during the delivery. Due to one missing value of the birth weight, one recording was excluded from the presented analysis. Finally, we evaluated the set of 551 signals, with 177 indicating the abnormal fetal state according to the pH level and 228 in accordance with the OR approach.

Experiments

The assessment of the classification efficiency

The efficiency of binary classifiers was measured by using the classification accuracy (ACC) and four prognostic indexes: sensitivity (Se), specificity (Sp), positive predictive value (PPV), and negative predictive value (NPV). The Se describes the classification accuracy of the positive (abnormal) cases, whereas Sp describes the negative (normal) ones. The quality of the binary classification was evaluated with the quality index (QI) defined as the geometric mean of Se and Sp.

The efficiency of the three-class classification was measured by using the overall classification accuracy (ACC) and classification accuracies for each of the classes: ACC_N, ACC_S, and ACC_A. The class accuracies were calculated as the percentage of the correctly classified cases in the given class. The mean class accuracy was introduced as well. Additionally, we defined QI_m as being the mean value of the three QIs calculated for NS, NA, and SA classifiers by using their testing sets. In the case of the NS classifier, the “suspicious” class was denoted as positive, whereas for NA and SA, the “abnormal” class. The QI_m describes the quality of binary classifiers used in the three-class classification and, hence, the quality of the three-class classification indirectly. All presented results are mean values and standard deviations calculated for 100 testing sets and are expressed in percents.

The learning procedures

The research material was 100 times randomly divided into training (50%) and testing (50%) parts to form training and testing sets maintaining the proportion between classes, the class ω₁ included negative cases with class labels equal to +1, and the ω₂ class contained positive cases with labels equal to −1. In the case of an odd number of cases, the additional case was added to the testing part. The obtained classification efficiency was compared with the efficiency of the classifier based on the fuzzy (c + p)-means clustering (Leski 2015) (for the ASQR loss function) and with the efficiency of the Lagrangian SVM (LSVM) (Mangasarian and Musicant 2001) with the Gaussian kernel . The LSVM was chosen because it is characterized by higher computational efficiency than the classical SVM procedure. In LSVM, the quadratic programming was replaced with the iterative solution, providing comparable or better testing results (Mangasarian and Musicant 2001). The LSVM parameters (v and χ), providing the best classification quality, were searched within the set {10^–5, 4·10^–5, 7·10^–5, 10^–4, 4·10^–4,…,7·10⁴,10⁵}, using 10 first pairs of training and testing sets. The remaining LSVM parameters were set to their default values. The LSVM input data were scaled to the range [–1, +1].

The ranges of the parameters for the fuzzy rule-based classifier with the proposed clustering (FCM_pbx or FCM_pbdx) were defined as follows:

• the fuzziness degree in the FCM clustering m, searched within the set ,

• the initial number of clusters per class c, changed from 2 to 16 with the step of ,

• three density types: D1, D2, D3 (Equation (1)),

• five values of the membership threshold: M₀ (0, i.e., all objects were used), M_m (mean), (1st quartile), (2nd quartile), (3rd quartile),

• four values of the density threshold (only in the variant): (mean), (1st quartile), (2nd quartile), (3rd quartile),

• the window length W changed from 1 to 5 with the step of 1,

• the parameter γ, scaling the dispersions, changed from 0.2 to 1.6 with the step of 0.1.

Because the maximum initial number of clusters per class was established at , the maximum number of all obtained prototypes () was equal to . If the numbers of prototypes were too small (i.e., or ) the clustering results were excluded from further analysis.

The clustering procedures (both the FCM and the -means) were initialized with prototypes selected from the boundary of the convex hull (Leski 2015) of the class being clustered. The clustering was performed as long as the absolute value of the difference between successive values of the criterion function was greater than or equal to . The maximum number of iterations was established at 500, squared distances between objects and prototypes less than were treated as equal to , and then the relevant update of the partition matrix was conducted. The remaining specifications of the -means were preserved as in (Leski 2015), however, we used , and scaling the dispersions (in the presented work denoted by ) changed from to with the step of . If any of the components of the resulting dispersions were equal to , we set them to . If the summary activation level of the rules was equal to , then for each rule was assumed.

To find the parameters of antecedents (centers and dispersions of the Gaussian membership functions), the first 10 training sets were merged into a single dataset and then clustered. The consequents (vector y) were determined separately for each of the first 10 training sets, and the parameters’ values providing the highest QI for the first 10 testing sets were chosen to calculate the final results. If the output value of any classifier was > 0 (≤ 0), then the ω₁ (ω₂) class was assigned.

Results and discussion

Table 1 presents the results of the two-class classification of the CTU-UHB dataset. The methods always provided higher QI and ACC than the procedures. For the algorithms, we identified the density as ensuring the highest values of QI and ACC for the pH reference assessment and for the OR approach. Table 2 compares in detail the results obtained using the proposed method with the LSVM and with the -means clustering. Both (c + p)-means and the outperformed the LSVM. Comparing the (c + p)-means and the , we observed higher values for all classification efficiency measures for the OR approach. For the pH, we achieved higher values of Se and NPV, but lower of ACC, Sp, and PPV. However, the increase level of the Se was higher then the decrease of Sp, and hence, we obtained the improvement of the QI.

Table 1. The classification results for the CTU-UHB dataset using the presented clustering.

	FCMpb1	FCMpb2	FCMpb3	FCMpbd1	FCMpbd2	FCMpbd3
pH
QI	62.83 (4.27)	63.52 (3.94)	63.66 (3.89)	57.09 (3.95)	60.80 (3.86)	61.05 (3.80)
ACC	72.24 (1.87)	72.70 (2.09)	73.37 (2.31)	70.86 (2.06)	71.65 (1.91)	72.13 (1.94)
OR
QI	68.29 (2.77)	67.90 (2.75)	67.68 (2.52)	60.08 (2.60)	63.12 (3.12)	64.02 (2.54)
ACC	70.68 (2.59)	70.21 (2.52)	69.92 (2.17)	64.04 (2.36)	66.65 (2.69)	67.42 (2.04)

Table 2. Comparison of the results for the CTU-UHB dataset with the applied reference methods.

	pH			OR
	LSVM	(c + p)-means	FCMpb3	LSVM	(c + p)-means	FCMpb1
	ν = 70,000	m = 1.1, c = 20	m = 1.1, c = 16	ν = 700	m = 1.1, c = 20	m = 1.1, c = 14
	χ = 0.1	K = 40, γ = 0.2	K = 40, Mq3	χ = 0.1	K = 40, γ = 0.5	K = 35, Mq3
			W = 5, γ = 0.9			W = 1, γ = 1.2
QI	52.32 (3.34)	62.76 (3.94)	63.66 (3.89)	54.78 (2.97)	65.78 (3.24)	68.29 (2.77)
ACC	58.78 (2.74)	73.70 (1.84)	73.37 (2.31)	58.25 (2.46)	68.83 (2.26)	70.68 (2.59)
Se	41.08 (5.77)	45.57 (6.68)	47.58 (6.13)	44.46 (5.41)	55.82 (6.53)	59.61 (4.82)
Sp	67.20 (4.49)	87.08 (3.41)	85.64 (3.22)	67.96 (4.39)	77.98 (3.97)	78.46 (4.20)
PPV	37.40 (3.48)	63.06 (4.31)	61.47 (4.98)	49.45 (3.37)	64.22 (3.21)	66.32 (4.28)
NPV	70.58 (1.85)	77.15 (1.82)	77.49 (1.89)	63.52 (2.02)	71.62 (2.50)	73.46 (2.21)

The statistical significance of the obtained results was verified using the paired-sample t-test. The proposed procedures were tested against the applied reference methods. In the case of CTU-UHB classification and the OR approach, all differences were statistically significant. The results for the pH are presented in Table 7, the symbol “+” denotes the difference that was statistically significant ( value < 0.05). The statistically insignificant differences were observed only in relation to (c + p)-means clustering.

Table 3. The classification results for the SisPorto dataset using the presented clustering.

	FCMpb1	FCMpb2	FCMpb3	FCMpbd1	FCMpbd2	FCMpbd3
QIm	92.77 (1.05)	92.91 (1.01)	92.66 (1.19)	91.37 (2.65)	91.55 (1.25)	91.47 (2.49)
ACCm	87.32 (1.57)	87.81 (1.62)	87.75 (1.90)	85.13 (3.47)	85.36 (1.86)	85.63 (2.95)
ACC	91.81 (0.66)	91.69 (0.71)	91.60 (1.04)	86.74 (0.94)	89.89 (0.73)	87.87 (0.89)

Table 4. Comparison of the results for the SisPorto dataset with the applied reference methods.

	LSVM	(c + p)-means	FCMpb2
QIm	90.65 (1.26)	91.79 (1.14)	92.91 (1.01)
ACC	92.16 (0.74)	86.59 (0.79)	91.69 (0.71)
ACCm	84.72 (1.96)	85.62 (1.49)	87.81 (1.62)
ACCN	96.28 (0.90)	87.56 (1.07)	94.10 (0.80)
ACCS	74.04 (4.40)	78.77 (3.40)	79.03 (4.64)
ACCA	83.84 (4.41)	90.53 (3.10)	90.28 (2.79)

Table 5. The binary classifiers in the three-class classification of the SisPorto dataset.

		LSVM	(c + p)-means	FCMpb2
		v = 70	m = 1.1, c = 2	m = 1.5, c = 7, K = 17
		χ = 0.7	K = 4, γ = 0.3	Mm, W = 1, γ = 0.8
NS	QI	86.08 (2.01)	84.55 (2.29)	87.41 (2.39)
	ACC	93.61 (0.65)	87.28 (0.75)	92.40 (0.70)
		ν = 7000	m = 1.1, c = 11	m = 1.1, c = 9, K = 22
		χ = 0.007	K = 22, γ = 1.3	M0, W = 4, γ = 0.9
NA	QI	94.94 (1.54)	97.01 (1.26)	97.65 (0.91)
	ACC	98.63 (0.38)	98.37 (0.50)	98.83 (0.30)
		ν = 40	m = 1.1, c = 13	m = 1.1, c = 16, K = 40
		χ = 0.4	K = 26, γ = 1.6	Mq2, W = 1, γ = 0.6
SA	QI	90.93 (2.17)	93.82 (1.60)	93.66 (1.48)
	ACC	91.76 (1.79)	94.36 (1.46)	94.14 (1.35)

Table 6. Comparison of the classification results (from literature) for the SisPorto dataset.

Reference	Validating procedure	ACC	ACCN	ACCS	ACCA
(Tomas et al. 2013)	single division	93.7	97.5	75.3	91.4
(Yilmaz and Kilikcier 2013)	10-fold cross-validation	91.6	96.9	70.5	76.7
(Sundar, Chitradevi, and Geetharamani 2012)	10 trials	—	99.1	36.9	97.5
(Das, Roy, and Saha 2013)	5-fold cross-validation	94.6	90.3	78.0	87.5
(Menai, Mohder, and Al-Mutairi 2013)	100 trials	94.0	—	—	—
FCMpb2	100 divisions	91.7	94.1	79.0	90.3

Table 7. Statistical significance of the differences between the results for the pH approach; the symbol “+” denotes statistically significant difference (p-value < 0.05).

	FCMpb1	FCMpb2	FCMpb3	FCMpbd1	FCMpbd2	FCMpbd3
ACC
LSVM	+	+	+	+	+	+
(c + p)-means	+	+	0.245	+	+	+
QI
LSVM	+	+	+	+	+	+
(c + p)-means	0.880	0.102	0.068	+	+	+

The classification results of the CTU-UHB dataset were also reported in Rotariu et al. (2014) and Spilka et al. (2013). Spilka et al. (2013) used pH values as the reference, and the nearest mean classifier with adaboost was applied. From the presented cumulative confusion matrix, it is possible to calculate Se = 64.1% and Sp = 65.2%, whereas we achieved lower Se (47.6%) and higher Sp (85.6%). However, in Spilka et al. (2013) the limiting value of pH indicating the abnormal fetal state was set to 7.05, which might result in increase of the Se. In Rotariu et al. (2014), the CTG signals were classified as normal or abnormal based on accelerations and decelerations established in connection to the uterine contractions. The results were compared to the signals classification based on pH value and Apgar scores providing Se = 73.2% and Sp = 88.2%.

The quality of the three-class classification of the SisPorto dataset is summarized in Table 3. Similarly to the two-class classification, the methods provided higher mean values of the analyzed efficiency indexes. The best density type for the may be indicated with respect to the highest value of the ACC () or (). With the highest value of the was obtained as well. Table 4 compares in detail the three-class classification quality obtained using the presented procedure () with the applied reference methods. The LSVM achieved the highest ACC, however, it was characterized by lower values the and the when compared to the -means and to the . The -means was characterized by the lowest value of the , which results in the lowest ACC. We may conclude that the classification efficiency of the is better in terms of the highest values of the and . The parameters and the results of the binary classifiers providing the best classification efficiency are shown in Table 5.

The statistical significance of the obtained results is shown in Table 8. The insignificant differences were noted between the and -means methods only.

Table 8. Statistical significance of the differences between the results (ACC) for the SisPorto dataset, the symbol “+” denotes statistically significant difference (p-value < 0.05).

	FCMpb1	FCMpb2	FCMpb3	FCMpbd1	FCMpbd2	FCMpbd3
LSVM	+	+	+	+	+	+
(c + p)-means	+	+	+	0.065	+	+

The three-class classification problem of the SisPorto dataset was also the topic of various researches (Das, Roy, and Saha 2013; Menai, Mohder, and Al-Mutairi 2013; Tomas et al. 2013; Yilmaz and Kilikcier 2013; Sundar, Chitradevi, and Geetharamani 2012), and the results are summarized in Table 6. In Tomas et al. (2013) among three classifiers analyzed, the Random Forest was indicated as providing the best results: ACC = 93.7%, , , . The classification procedure based on the least squares SVM and binary decision tree was presented in Yilmaz and Kilikcier 2013. The following results for the 10-fold cross-validation were obtained: ACC = 91.6%, , , . In Sundar, Chitradevi, and Geetharamani 2012, the classification quality obtained by the ANN, applying 10 trials, was reported by the Recall measures: 99.1% (for normal class), 36.9% (suspicious) and 97.5% (abnormal). The Fuzzy Unordered Rule Induction Algorithm (FURIA) fuzzy-rule-based classifier used in Das, Roy, and Saha 2013 provided ACC = 94.6% and the following Recall measures: 90.3% (for normal class), 78.0% (suspicious), and 87.5% (abnormal) applying 5-fold cross-validation. In Menai, Mohder, and Al-Mutairi et al. 2013 the influence of four feature selection methods on the three- and ten-class classification quality was examined. In the case of the three-class classification, the best results were reported by the accuracy equals to 94.0% being the average across 100 trials. Comparing the efficiency of the proposed classifier (ACC = 91.7%, , , ), we achieved higher value of , once of ACC and twice of . The presented classifier provided better classification accuracy for the class “suspicious,” however, improvement for two other classes is still needed.

The researches presented in Ocak and Ertunc (2013) and Sahin and Subasi (2015) describe the two-class classification of the SisPorto dataset (the “suspicious” class was excluded). In Ocak and Ertunc (2013), the adaptive neurofuzzy inference system was applied, and the following classification accuracies for the testing set were reported: 97.2% for normal and 96.6% for abnormal cases. The evaluation of eight different machine-learning methods was presented in Sahin and Subasi (2015), and the best results using the 10-fold cross-validation procedure were ACC = 99.2%, Se = 94.1%, and Sp = 99.7%. We can compare these results with the ACC = 98.8%, Se = 96.2%, and Sp = 99.1% provided by the binary classifier NA (Table 5). With the proposed method, we achieved lower Se and higher Sp compared to Ocak and Ertunc (2013), and higher Se and lower Sp compared to Sahin and Subasi (2015).

We investigated also the influence of the parameters’ values on the classification quality. We changed values of a given parameter while maintaining constant the remaining parameters. For each parameter, the range (rQI) of the QI was calculated as the difference between the maximum and minimum values (calculated as means for all 100 testing sets). The results of the CTU-UHB classification showed the highest influence of the initial number of clusters c (the rQI = 63.2% for pH and 23.8% for OR). For pH, we obtained rQI = 10.9%, 2.7%, 1.4%, and for OR approach rQI = 14.0%, 3.9% and 1.5%, respectively, for m, γ, W. With the increase of c, the increase of the QI was noticed also, but with higher m we got lower QI. In the case of the NA binary classifier for the SisPorto dataset, the highest rQI = 5.2% was observed for γ. In the case of m, c, and W, we got rQI = 4.5%, 4.0%, and 0.5%, respectively. The charts presenting the change of the classification quality with the change of the initial number of clusters per class are shown in Figure 1.

Figure 1. The influence of the initial number of clusters per class (c) on the classification quality (QI).

Conclusions

In the presented work, we discuss the problem of fetal state assessment based on the analysis of the cardiotocographic signals. The classification procedure based on fuzzy clustering with pairs of prototypes was proposed to support the qualitative fetal state evaluation. To verify the efficiency of the fuzzy classifier, two benchmark sets (CTU-UHB and SisPorto) containing the cardiotocographic data were used. In the case of the CTU-UHB, it was difficult to compare the obtained classification efficiency with the results from the literature due to different inputs and outputs of the classifiers. However, improvement was achieved in relation to the applied reference methods. In the case of the three-class analysis of the SisPorto dataset, the increased classification quality was noticed when compared with the applied reference procedures; nevertheless, we did not improve the overall classification accuracy. When relating to other methods described in the literature, we got better classification accuracy of the “suspicious” class recognition, but improvement of the three-class analysis of the SisPorto CTG signals can still be achieved.

Funding

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

Additional information

Funding

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