Hindawi Publishing Corporation
Computational and Mathematical Methods in Medicine
Volume 2013, Article ID 898041, 9 pages
http://dx.doi.org/10.1155/2013/898041
Research Article
A Clinical Decision Support System for Femoral Peripheral
Arterial Disease Treatment
AlkJn Yurtkuran,1 Mustafa Tok,2 and Erdal Emel1
1 Department of Industrial Engineering, Faculty of Engineering, Görükle Campus, Uludag University, 16059 Bursa, Turkey
2Department of Thoracic and Cardiovascular Surgery, Faculty of Medicine, Görükle Campus, Uludag University, 16059 Bursa, Turkey
Correspondence should be addressed to Alkın Yurtkuran; alkin@uludag.edu.tr
Received 30 July 2013; Revised 4 November 2013; Accepted 7 November 2013
Academic Editor: Gabriel Turinici
Copyright © 2013 Alkın Yurtkuran et al. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
One of the major challenges of providing reliable healthcare services is to diagnose and treat diseases in an accurate and timely
manner. Recently, many researchers have successfully used artificial neural networks as a diagnostic assessment tool. In this study,
the validation of such an assessment tool has been developed for treatment of the femoral peripheral arterial disease using a radial
basis function neural network (RBFNN). A data set for training the RBFNN has been prepared by analyzing records of patients
who had been treated by the thoracic and cardiovascular surgery clinic of a university hospital. The data set includes 186 patient
records having 16 characteristic features associated with a binary treatment decision, namely, being a medical or a surgical one. K-
means clustering algorithm has been used to determine the parameters of radial basis functions and the number of hidden nodes
of the RBFNN is determined experimentally. For performance evaluation, the proposed RBFNN was compared to three different
multilayer perceptron models having Pareto optimal hidden layer combinations using various performance indicators. Results of
comparison indicate that the RBFNN can be used as an effective assessment tool for femoral peripheral arterial disease treatment.
1. Introduction can strike anyone, it is most common in people over age 65
[2].
Various engineering techniques have been adapted to health PAD is associated with a significant burden in terms
care delivery systems and the quality of health care services of morbidity and mortality, due to claudication, rest pain,
has been improved using these artificial intelligence tech- ulcerations, and amputations. In case of mild or moderate
niques. It has been proven that introducingmachine learning peripheral arterial diseases, amedical or conservative therapy
tools into clinical decision support systems can easily increase can be chosen but the gold-standard treatment of severe
the decision accuracy and decrease costs and the dependency PAD is a surgical or an endovascular revascularization [2].
on highly qualified specialists. Since artificial neural networks However, up to 30% of patients are not candidates for such
(ANN) can easily be trained for identifying the patterns and interventions, due to excessive surgical risks or unfavorable
extracting rules using a small number of cases, they arewidely vascular involvements. The presence of diffuses and multiple
used as a powerful tool for clinical decision support systems and distal arterial stenosis renders successful revasculariza-
[1]. tion sometimes impossible. These “no-option” patients are
Peripheral arterial disease (PAD) is a common pathologic left to medical therapy, which may slow the progression of
disease worldwide. Peripheral arterial disease is a disease in disease at best [3].
which plaque, which is made up of fat, cholesterol, calcium, It is very difficult to decide whether surgical or medical
fibrous tissue, and other substances in the blood, builds up in treatment is the best option since PAD depends on many
the arteries that carry blood to head, organs, and limbs. PAD factors like anatomic location, symptoms, comorbidities, and
affects more than 30 million people worldwide, and while it risk about cardiac condition or anesthesia. Cardiovascular
2 Computational and Mathematical Methods in Medicine
surgeons should prefer the best appropriate choice of treat- Wu et al. [19] used RBFNN to accurately identify Parkinson’s
ment and most of the time the decision allows the surgeon disease. The data for training the RBFNN was obtained by
with his own experience. Cardiovascular specialists widely means of deep brain electrodes implanted into a Parkinson’s
use intersociety Consensus for the classification of PADs’ disease patient’s brain. The output of the study indicated that
(TASC II) (Trans-Atlantic intersociety Consensus), which is RBFNNs could be successfully designed and used to identify
based on the anatomic locations of lesions [3]. tremors on set pattern even for small number of spikes.
In this work, we present a clinical treatment decision
support system using a radial basis function neural network
(RBFNN) in order to help doctors to make an accurate 3. The Clinical Data
treatment decision for patients having femoral PAD. Pro- The input data set for training ANNs has been obtained from
posed RBFNN was compared to three different multilayer discharge reports dated from 2008 to 2012 within patient
perceptron (MLP) networks and results indicate that the records of the department of thoracic and cardiovascular
proposed RBFNN outperformsMLP networks. Based on our surgery clinic of a university hospital. 186 records with 114
extensive literature review, no previous study was carried male patients aged around 53 ± 7 and with 72 female patients
out which included a decision support system for clinical aged as 58 ± 5 have been analyzed. Each patient’s report
treatment of femoral PAD. contains one final treatment decision, which is taken here as
The remainder of this paper is organized as follows. an output class value of the corresponding input data set that
Section 2 summarizes previous studies; Section 3 covers the is as follows.
clinical data and input and output features of the proposed
model. Section 4 gives a brief introduction to the RBFNNand
experiments. Related results are given in Section 5 and finally (i) Class 1: medical treatment decision (89 patients).
Section 6 concludes the paper. (ii) Class 2: surgery or endovascular treatment decision
(97 patients).
2. Related Work All samples have a total of 16 features and these fea-
tures were determined by consultations with cardiologists,
In recent years, there have been many studies that focused surgeons, and anesthetists. Features, output classes and their
on decision support systems to improve the accuracy of normalized values are given inTable 1.Description of selected
decisions for diagnosis and treatment of diseases. Such features is summarized in Tables 2–5.
decision support systems frequently depend on ANN-based
perceptive algorithms that are built upon previous patient
records. 4. Radial Basis Function Neural
To cite a few but significant works of others, Mehrabi Network (RBFNN)
et al. [4] used a MLP network and a RBFNN to classify
chronic obstructive pulmonary (COPD) and congestive heart TheRBFNN [43] has a feed forward architecturewith 3 layers:
failure (CHF) diseases. They used Bayesian regularization (i) an input layer, (ii) a hidden layer, and (iii) an output
to enhance the performance of MLP network. Moreover, layer. A typical RBFNN is shown in Figure 1. The input layer
they integrated K-means clustering algorithm and k-nearest of 𝑚 nodes accepts 𝑚-dimensional features as input data
neighborhood, to define centers for hidden neurons and to vector.The hidden layer, which is fully connected to the input
identify the spread, respectively. They have shown that both layer, is composed of 𝑛 radial basis function neurons. Each
COPDandCHFhave been classified using theMLPnetworks hidden layer neuron operates as a radial basis function that
and the RBFNN accurately. does a nonlinear mapping of feature space into output space.
Subashini et al. [5] proposed a polynomial kernel for The output layer consists of 𝑐 neurons, which calculate the
the support vector machine (SVM) and the RBFNN for weighted sum of the output of the each hidden layer node.
ascertaining the diagnostic accuracy of cytological data The most commonly employed radial basis function for
obtained from the Wisconsin breast cancer database. They hidden layers is the Gaussian function [44, 45] and is deter-
have shown that RBFNN outperformed SVM for accurately mined by mean vectors (cluster centers) 𝜇𝑗 and covariance
classifying the tumors. Lewenstein [6] used RBFNN as a tool matrices C𝑗 where 𝑗 = 1, . . . , 𝑛. Covariance matrices are
for diagnosis of coronary artery disease. The research was assumed to be in the form C 2𝑗 = 𝜎𝑗 I.
performed using 776 data records and over 90% accuracy was Let Φ𝑗(x) be the Gaussian function representing the 𝑗thachieved for classifying. hidden node defined as
A short review of recent studies reveal numerous use
of ANN techniques for diagnosis of diabetes mellitus [7– 󵄩 󵄩2󵄩 󵄩
12], chest diseases [13–17], Parkinson disease [18, 19], breast 󵄩󵄩x − 𝜇 󵄩󵄩
Φ (x) = exp 󵄩 𝑗󵄩(− ) , (1)
cancer [5, 20–23], thyroid disease [24–26] and cardiovascular 𝑗 22𝜎𝑗
diseases [4, 6, 27–36].
Broomhead and Lowe [37] were the first to use the
RBFNN in designing neural networks. In recent years, the where x 𝑇= [𝑥1, 𝑥2, . . . , 𝑥𝑚] is the input feature vector,
RBFNN have attracted extensive research interest. [38–42] 𝑇 2𝜇𝑗 = [𝜇1𝑗, 𝜇2𝑗, . . . , 𝜇𝑚𝑗] and 𝜎𝑗 are the mean vector and the
Computational and Mathematical Methods in Medicine 3
Table 1: Features and their normalized values.
Feature Comment
Age (years) Divided by 100
Sex Female = 0, male = 1
Fontaine stage Stage I = 0, stage II-a = 0, stage II-b = 2, stage III = 3, stage IV = 4 (see Table 4)
Lesion type (TASC classification) Type A = 0, type B = 1, type C = 3, type D = 4 (see Table 5)
Sensitivity to anesthesia Low = 0, medium-high = 1
Distal bed Absence = 0, presence = 1
Embolism (percent) Divided by 100
LDL cholesterol level Normal = 0, near/above normal = 1, BH = 2, high = 3, very high = 4 (see Table 3)
Smoking Absence = 0, presence = 1
Exsmoker Absence = 0, presence = 1
Hypertension Absence = 0, presence = 1
Blood pressure Normal = 0, pre-HTN = 1, stage I = 2, stage II = 3 (see Table 2)
Diabetes mellitus Absence = 0, presence = 1
Other peripheral disease history Absence = 0, presence = 1
Family history Absence = 0, presence = 1
Current medical treatment Absence = 0, presence = 1
Treatment decision Medical treatment = −1, operation = 1
Table 2: Blood pressure level categories in adults.
x1
Classification Systolic pressure Diastolic pressure(mmHg) (mmHg) Φ1(x)
Normal <120 <80 y1
Prehypertension 120–139 80–89 x2
Stage I 140–159 90–99
Φ (x)
Stage II 2>160 >100 y2
x3
. .
Table 3: Cholesterol level categories in adults. .. ..
..
LDL cholesterol level (mg/dL) LDL cholesterol category .
y
<100 Optimal cΦn(x)
100–129 Near optimal/above optimal xm
130–159 Borderline high
160–189 High Input layer Hidden layer Output layer
>190 Very high
Figure 1: An example of RBFNN.
Table 4: Fontaine stages [2].
Stages Details In (2), w𝑘 = [𝑤1𝑘, 𝑤2𝑘, . . . , 𝑤𝑛𝑘] is the vector of the weights
between hidden and output layer and 𝑤 is the bias for
Stage I Asymptomatic, incomplete blood vessel obstruction 0𝑘
𝑘 = 1, . . . , 𝑐. In order to design a RBFNN, the value of mean
Stage II-a Claudication at a distance of greater than 200 meters vectors (𝜇𝑗) representing the location of cluster centers andStage II-b Claudication distance of less than 200 meters variances ( 2𝜎 ) for hidden neurons have to be calculated first.
Stage III Rest pain, mostly in the feet 𝑗
Stage IV Necrosis and/or gangrene of the limb K-means clustering algorithm is used to determine the valueof mean vectors which is given as follows.
Step 1. Initialize by choosing 𝑚 random values for 𝑛 hidden
variance of the 𝑗th neuron, respectively.The 𝑘th output of the nodes (𝜇𝑖𝑗, 𝑖 = 1, . . . , 𝑚, 𝑗 = 1, . . . , 𝑛) as initial cluster centers.
RBFNN is computed according to (2)
Step 2. Assign a randomly selected input data sample x to the
𝑛 nearest 𝑗th cluster center using the Euclidean norm.
𝑦𝑘 = ∑𝑤𝑗𝑘Φ𝑗 (x) + 𝑤0𝑘. (2)
𝑗=1 Step 3. Recalculate 𝜇𝑗 including the assigned sample.
4 Computational and Mathematical Methods in Medicine
Table 5: TASC classification [3].
Lesion type Description Visual display
Type A (i) Single stenosis ≤10 cm in length(ii) Single occlusion ≤5 cm in length
(i) Multiple lesions, each ≤5 cm
(ii) Single stenosis or occlusion ≤15 cm
Type B (iii) Single or multiple lesions in the absence of tibial vessels
(iv) Heavily calcified occlusion ≤5 cm
(v) Single popliteal stenosis
Type C (i) Multiple stenosis or occlusions totaling ≥15 cm(ii) Recurrent stenosis or occlusions that need treatment
(i) Chronic total occlusions of common femoral artery or superficial femoral
Type D artery
(ii) Chronic total occlusion of popliteal artery
Table 6: Confusion matrix for binary classification. In (4), Y is the (𝑛 × 1) dimensional output vector, H is the
(𝑛 × (𝑚 + 1)) dimensional hidden neuron matrix, and W is
Class/classified As positive As negative the ((𝑚 + 1) × 1) dimensional weight vector. To reduce the
Positive tp fn computational effort W is directly calculated from the least
Negative fp tn squares pseudoinverse by (5)
𝑇 −1 𝑇 (5)
Step 4. W = (H H) H Y.Repeat Steps 2 and 3 until mean vectors do not change
new old
(𝜇𝑗 ≅ 𝜇𝑗 ). 5. Experiments
The number of hidden neurons 𝑛, which should be
determined experimentally, is effective on the performance 5.1. Measures for Performance Evaluation. In our experi-
of the RBFNN. Generally, it is assumed that variances of all ments, in order to evaluate the performance of the proposed
2 RBFNN effectively and accurately, several performance indi-clusters are identical and equal to 𝜎 which is calculated as cators such as area under the receiving operating character-
follows istics curve (AUC), accuracy, sensitivity (recall), specificity,
2 positive predictive value (PPV) (precision), negative predictive
2 𝜂𝑑
𝜎 = , (3) value (NPV), F-score, and Yuden Index are analyzed [35, 36].
2 All these performance indicators are determined by using
a confusion matrix, which is composed of the results of
where𝑑 is themaximumdistance between cluster centers and a binary (true/false) classification in terms of true positive
𝜂 is an empirical scale factor and controls the smoothness of (tp), false positive (fp), false negative (fn), and true negative
the nonlinearmapping function. Once the location of centers (tn) counts. A confusion matrix for a binary classification is
and their variances are determined, weights between the presented in Table 6. Accuracy is used to assess the overall
hidden layer and the output layer can be calculated. Equation effectiveness of the classifier (see (6)). Sensitivity is the ratio
(2) may be rewritten in the vector form as of correctly classified samples to all samples in that class
(see (7)). Specificity measures the proportion of negatives,
Y = H ⋅W. (4) which are correctly identified (see (8)). PPV is the accuracy
Computational and Mathematical Methods in Medicine 5
Table 7: Selected MLP networks.
Network name Training algorithm Hidden activation Output activation Number of hiddenfunction function units
MLP-13 BFGS tanh Logistic 13
MLP-23 BFGS Identity Logistic 23
MLP-7 CGA Logistic Identity 7
Table 8: Mean of performance indicators for MLP networks and networks accurately by reducing the bias and the variance on
RBFNN. predicted results, 10-fold cross-validation method is used in
MLP-13 MLP-23 MLP-7 RBFNN this study. Multifold cross-validation, in which dynamic sets
AUC 0.873 0.839 0.793 0.949 of validation and test data are used, is an efficient technique toavoid overfitting compared to regularization, early stopping,
Cutoff point 0.443 0.542 0.392 0.510 or data pruning especially when data are very scarce [43]. In
Accuracy 0.881 0.838 0.800 0.950 10-fold cross-validation, a data set is randomly partitioned
Sensitivity 0.896 0.835 0.816 0.953 into 10 equal subsamples having approximately equal number
Specificity 0.868 0.840 0.788 0.948 of samples from each class. Using this data set, while the
PPV 0.849 0.824 0.753 0.942 RBFNN training is done by the first nine subsamples, the
NPV 0.909 0.851 0.843 0.958 validation is done only by the last subsample. This training
F-score 0.872 0.829 0.783 0.947 and testing process is repeated for 10 times by rotating each
Yuden index 0.764 0.675 0.604 0.901 subsample to be used only once as the validation subsample.
H-L 10.386 10.211 11.632 7.880 The mean and standard deviation of performance indicators
for each neural network model are then reported.
In this study, as mentioned in Section 4, the cluster center
in a specified class (see (9)) and NPV is the proportion locations for all Gaussian functions, which are employed
of cases with negative results that are correctly classified as radial basis functions, are determined using K-means
(see (10)). Finally, F-measure and Yuden Index, which are clustering algorithm. Network weights of the output layer
widely used performance indicators to assess neural network are determined by the pseudoinverse method (4). Following
classification performances, are depicted in (11) and (12). preliminary tests, the empirical scale factor is set to 𝜂 =
Another important performance indicator of neural net- 0.6. For simplicity and ease of calculation, it is assumed that
works is the area under the receiving operating characteristics all variances are identical and equal to 2𝜎 . A program is
curve (AUC). Receiving operating characteristics curve is written in C++ language to employ the proposed RBFNN
constructed by plotting the sensitivity versus (1-specificity) model.
values for variety of cutoff points between 0.00 and 1.00. Fur- The optimum number of hidden nodes for a RBFNN
thermore, theHosmer-Lemeshow (H-L) chi-square statistic is model should be carefully determined as it directly affects the
used as a numerical indicator of overall calibration performance of the network. In this study, in order to choose
tp tn the optimum number of centers for the proposed network,Accuracy += , (6) several preliminary experiments are conducted by stepwisetp + fp + fn + tn change of the number of centers from 2 to 50. For each
tp case, an average mean square error (MSE) is calculated usingSensitivity = ,
tp fn (7) the 10-fold cross-validation. Figure 2 shows the MSE values+
with respect to the number of centers. Referring to Figure 2,
Specificity tn (8) the minimum MSE = 0.036 is achieved for 29 clusters and= ,tn + fp therefore the number of hidden nodes was set to 29.
tp After attaining the optimal RBFNN, the performance isPPV = , (9) compared to three different Pareto optimal three-layer MLPfp + tp networks. In our study, MLP models were generated and
tn implemented using the ANN module provided within theNPV = , (10)
tn fn STATISTICA software (v 11.0) published by the Statsoft, Inc.+ MLP networks were constructed using the Automated Net-
2 × Sensitivity × PPV
(11) work Search (ANS) strategy for creating predictive models𝐹score = ,Sensitivity + PPV of STATISTICA. Best three MLP networks were retained by
the ANS, trying different number of hidden units (1–30),
Yuden Index = sensitivity + specificity − 1. (12) different input/output activation functions (identity, logistic,
tanh, and exponential) and different training algorithms such
5.2. Computational Results. Neural networks are prone to as the Gradient Descent, the Broyden-Fletcher-Goldfarh-
overfitting, especially when there are only a limited number Shanno (BFGS) (Quasi-Newton), the Conjugate Gradient
of data. In order to estimate the performance of the neural Algorithm (CGA), or the Levenberg-Marquardt Algorithm
6 Computational and Mathematical Methods in Medicine
Table 9: Comparison of MLP-13 and RBFNN.
MLP-13 RBFNN Statistical significance
Mean ± SD 95% CI Mean ± SD 95% CI
AUC 0.873 ± 0.018 0.862–0.885 0.949 ± 0.028 0.931–0.966 +
Cutoff 0.443 ± 0.010 0.437–0.449 0.510 ± 0.011 0.503–0.517 +
Accuracy 0.881 ± 0.016 0.871–0.891 0.950 ± 0.022 0.936–0.964 +
Sensitivity 0.896 ± 0.021 0.883–0.909 0.953 ± 0.015 0.944–0.963 +
Specificity 0.868 ± 0.018 0.857–0.879 0.948 ± 0.030 0.929–0.966 +
PPV 0.849 ± 0.023 0.835–0.864 0.942 ± 0.034 0.920–0.963 +
NPV 0.909 ± 0.019 0.897–0.921 0.958 ± 0.013 0.949–0.966 +
F-score 0.872 ± 0.018 0.861–0.883 0.947 ± 0.024 0.932–0.962 +
Yuden index 0.764 ± 0.033 0.744–0.785 0.901 ± 0.044 0.873–0.928 +
H-L 10.386 ± 2.125 9.069–11.703 7.880 ± 1.557 6.915–8.845 +
Table 10: Comparison of MLP-23 and RBFNN.
MLP-23 RBFNN Statistical significance
Mean ± SD 95% CI Mean ± SD 95% CI
AUC 0.839 ± 0.018 0.828–0.850 0.949 ± 0.028 0.931–0.966 +
Cutoff 0.542 ± 0.016 0.532–0.552 0.510 ± 0.011 0.503–0.517 +
Accuracy 0.838 ± 0.017 0.827–0.848 0.950 ± 0.022 0.936–0.964 +
Sensitivity 0.835 ± 0.020 0.823–0.847 0.953 ± 0.015 0.944–0.963 +
Specificity 0.840 ± 0.018 0.829–0.851 0.948 ± 0.030 0.929–0.966 +
PPV 0.824 ± 0.021 0.811–0.836 0.942 ± 0.034 0.920–0.963 +
NPV 0.851 ± 0.019 0.839–0.862 0.958 ± 0.013 0.949–0.966 +
F-score 0.829 ± 0.018 0.818–0.840 0.947 ± 0.024 0.932–0.962 +
Yuden index 0.675 ± 0.034 0.654–0.697 0.901 ± 0.044 0.873–0.928 +
H-L 10.211 ± 3.409 8.098–12.324 7.880 ± 1.557 6.915–8.845 −
0.18 performance index at the current values of the weights and
biases. BFGS has high memory requirements due to storing
0.16 the Hessian matrix. On the other hand, MLP-7 utilizes the
0.14 CGA, which is a fast training algorithm for MLP networks
that proceeds by a series of line searches through error
0.12 space. In CGA, learning rate and momentum are calculated
adaptively in each iteration. In the ANS module, the learning
0.1 rate is calculated by the Golden Search rule while the Fletcher
0.08 and Reeves formula [46] is used for momentum calculations.
Table 8 lists the mean of performance indicator results
0.06 using the 10-fold cross-validation method for each network.
Considering Table 8, it is noticeable that the mean clas-
0.04 sification accuracy of RBFNN (0.950) is better than any
0.02 one of MLP networks (MLP-13 = 0.881, MLP-23 = 0.838,
0 10 20 30 40 50 and MLP-7 = 0.800). Prediction capabilities based on AUC
Number of clusters show that the proposed RBFNN outperforms all other MLP
Figure 2: MSE versus number of clusters for proposed RBFNN. networks (RBFNN = 0.949, MLP-13 = 0.873, MLP-23 =
0.839, and MLP-7 = 0.793). The average sensitivity values for
MLP networks are 0.896, 0.835, and 0.816 for MLP-13, MLP-
23, and MLP-7, respectively. On the other hand, proposed
using an error function of sum of squares. Moreover, a 10- RBFNN gives an average sensitivity of 0.953, which indicates
fold cross-validation technique is selected to avoid overfitting that the RBFNN performs better on classifying cases having
and oscillation. The best three MLP networks which were positive condition. Based on specificity, the RBFNN (94.8%)
determined using the ANS are summarized in Table 7. MLP- is superior to MLP-13 (86.8%), MLP-23 (84.0%), and MLP-7
13 and MLP-23 employs the BFGS algorithm where the (78.8%).𝐹-measure andYuden Index are themost widely used
weights and biases are updated using the Hessian matrix stand-alone performance indicators for classification studies.
MSE
Computational and Mathematical Methods in Medicine 7
Table 11: Comparison of MLP-7 and RBFNN.
MLP-7 RBFNN Statistical significance
Mean ± SD 95% CI Mean ± SD 95% CI
AUC 0.789 ± 0.019 0.778–0.801 0.949 ± 0.028 0.931–0.966 +
Cutoff 0.392 ± 0.009 0.386–0.398 0.510 ± 0.011 0.503–0.517 +
Accuracy 0.800 ± 0.020 0.787–0.812 0.950 ± 0.022 0.936–0.964 +
Sensitivity 0.823 ± 0.028 0.805–0.840 0.953 ± 0.015 0.944–0.963 +
Specificity 0.782 ± 0.017 0.772–0.792 0.948 ± 0.030 0.929–0.966 +
PPV 0.746 ± 0.021 0.733–0.759 0.942 ± 0.034 0.920–0.963 +
NPV 0.850 ± 0.025 0.834–0.865 0.958 ± 0.013 0.949–0.966 +
F-score 0.782 ± 0.022 0.769–0.796 0.947 ± 0.024 0.932–0.962 +
Yuden index 0.605 ± 0.041 0.579–0.630 0.901 ± 0.044 0.873–0.928 +
H-L 11.632 ± 2.169 10.288–12.976 7.880 ± 1.557 6.915–8.845 +
𝐹-measure and Yuden Index values are 0.947 and 0.901 for determine optimal design parameters of RBFNNs such as the
the proposed RBFNN while 0.872 and 0.764 for MLP-13, number and the location of centers or variances of clusters
0.829, and 0.675 for MLP-23 and 0.783 and 0.604 for MLP- and as a result enhance the classification performance.
7, respectively. The mean PPV’s are 0.849, 0.824, 0.753 and
0.942, while themeanNPV’s are 0.909, 0.851, 0.843, and 0.958
forMLP-13,MLP-23,MLP-7, and RBFNN, respectively.These Conflict of Interests
findings also show that a RBFNN performs better than MLP The authors declare that there is no conflict of interests
networks. In general, all models were good-fit models based regarding the publication of this paper.
on the𝐻-𝐿 statistics (𝐻-𝐿 < 12.0).
In order to make precise and pairwise comparison
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