An AlBiruni Earth Radius OptimizationBased Deep Convolutional Neural Network for Classifying Monkeypox Disease
Abstract
:1. Introduction
 Offer machine learning techniques for predicting monkeypox disease;
 A new AlBiruni Earth radius (BER) optimizationbased stochastic fractal search (BERSFS) algorithm is suggested;
 To raise the tested dataset prediction accuracy, a BERSFSbased classifier is created.
 A comparison of the results of different algorithms to determine which is the most accurate is performed;
 The Wilcoxon ranksum and ANOVA tests are used to determine the statistical significance of the BERSFS algorithm;
 It is possible to generalize and test the BERSFSbased classification algorithm for different kinds of datasets.
2. Literature Review
3. Materials and Methods
3.1. Convolutional Neural Network (CNN)
3.2. AlBiruni Earth Radius (BER) Algorithm
Algorithm 1 ALBiruni Earth radius (BER) algorithm 

3.2.1. Exploration Operation
3.2.2. Exploitation Operation
3.2.3. Selection of the Best Solution
3.3. Stochastic Fractal Search (SFS) Algorithm
Algorithm 2 Stochastic fractal search (SFS) algorithm 

3.4. Proposed BERSFS Algorithm
 Initialize the parameters of the BERSFS algorithm: O(1);
 Calculate ${F}_{n}$ for each agent ${\mathbf{S}}_{i}$: O(n);
 Obtain the best agent ${\mathbf{S}}^{\ast}$: O (n);
 Update positions to head toward the best solution: O(${T}_{max}\times n$);
 Update positions for the elitism of the best solution: O(${T}_{max}\times n$);
 Update the positions for investigating the area around the best solution: O(${T}_{max}\times n$);
 Mutate the solution: O(${T}_{max}$);
 Calculate the updated best solution: O(${T}_{max}\times n$);
 Calculate ${F}_{n}$ for each agent ${\mathbf{S}}_{i}$: O(${T}_{max}$);
 Update the BERSFS parameters: O(${T}_{max}$);
 Obtain the best agent ${\mathbf{S}}^{\ast}$: O(${T}_{max}$);
 Obtain the best agent ${\mathbf{S}}^{\ast}$: O(1).
Algorithm 3 Proposed BERSFS algorithm 

4. Experimental Results
4.1. Dataset Description
4.2. Performance Metrics
4.3. Comparison with Basic Models
4.4. Comparison with Deep Learning Models
4.5. Comparison with OptimizationBased Models
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Parameter  Value 

Number of Agents  10 
Number of Iterations  80 
Number of Repetitions  20 
$\eta $  ∈[0, 1] 
${\eta}^{\prime}$  ∈[0, 1] 
Mutation probability  0.5 
Exploration percentage  70 
K (decreases from 2 to 0)  1 
Parameter  Value 

CNN training options (Default) Momentum Learn RateDropFactor L2Regularization LearnRateDropPeriod GradientThreshold GradientThresholdMethod ValidationData VerboseFrequency ValidationPatience ValidationFrequency ResetInputNormalization CNN training options (Custom) InitialLearnRate ExecutionEnvironment BatchSize MaxEpochs Verbose Shuffle LearnRateSchedule Optimizer  0.9000 0.1000 1.0000 × 10${}^{4}$ 10 Inf l2norm imds 50 Inf 50 1 0.001 gpu 32 40 0 everyepoch piecwise BERSFS 
No. Calculation  Metrics 

Accuracy  $\frac{TP+TN}{TP+TN+FP+FN}$ 
Sensitivity  $\frac{TP}{TP+FN}$ 
Specificity  $\frac{TN}{TN+FP}$ 
Precision (PPV)  $\frac{TP}{TP+FP}$ 
Negative Predictive Value (NPV)  $\frac{TN}{TN+FN}$ 
F1 Score  $2\times {\displaystyle \frac{PPV\times TPR}{PPV+TPR}}$ 
Accuracy  Sensitivity (TRP)  Specificity (TNP)  p Value (PPV)  N Value (NPV)  F1 Score  

BERSFSCNN  0.9883  0.8571  0.9921  0.7595  0.9959  0.8054 
CNN  0.9337  0.7500  0.9693  0.8257  0.9524  0.7860 
SVMLinear  0.9213  0.8571  0.9231  0.2308  0.9959  0.3636 
KNN  0.8777  0.8000  0.9132  0.8081  0.9091  0.8040 
DT  0.8510  0.7273  0.9132  0.8081  0.8696  0.7656 
SS  DF  MS  F (DFn, DFd)  p Value  

Treatment (between columns)  0.1129  4  0.0282  F (4, 45) = 1258  p < 0.0001 
Residual (within columns)  0.0010  45  $2.24\times {10}^{5}$     
Total  0.1139  49       
BERSFSCNN  CNN  SVMLinear  KNN  DT  

Theoretical median  0  0  0  0  0 
Actual median  0.9883  0.9337  0.9213  0.8777  0.8511 
Number of values  10  10  10  10  10 
Wilcoxon signedrank test  
Sum of signed ranks (W)  55  55  55  55  55 
Sum of positive ranks  55  55  55  55  55 
Sum of negative ranks  0  0  0  0  0 
p value (twotailed)  0.002  0.002  0.002  0.002  0.002 
Exact or estimate?  Exact  Exact  Exact  Exact  Exact 
Significant (alpha = 0.05)?  Yes  Yes  Yes  Yes  Yes 
How big is the discrepancy?  
Discrepancy  0.9883  0.9337  0.9213  0.8777  0.8511 
Accuracy  Sensitivity (TRP)  Specificity (TNP)  p Value (PPV)  N Value (NPV)  F1 Score  

BERSFSCNN  0.9883  0.8571  0.9921  0.7595  0.9959  0.8054 
AlexNet  0.9459  0.7143  0.9524  0.2941  0.9917  0.4167 
GoogLeNet  0.9351  0.7143  0.9412  0.2500  0.9917  0.3704 
VGG19Net  0.9280  0.7143  0.9339  0.2273  0.9917  0.3448 
ResNet50  0.9208  0.6667  0.9266  0.1739  0.9917  0.2759 
SS  DF  MS  F (DFn, DFd)  p Value  

Treatment (between columns)  0.0284  4  0.0071  F (4, 45) = 363.3  p < 0.0001 
Residual (within columns)  0.0009  45  $0.1959\times {10}^{4}$     
Total  0.0293  49       
BERSFSCNN  AlexNet  GoogLeNet  VGG19Net  ResNet50  

Theoretical median  0  0  0  0  0 
Actual median  0.9883  0.9459  0.9351  0.928  0.9208 
Number of values  10  10  10  10  10 
Wilcoxon signedrank test  
Sum of signed ranks (W)  55  55  55  55  55 
Sum of positive ranks  55  55  55  55  55 
Sum of negative ranks  0  0  0  0  0 
p value (twotailed)  0.002  0.002  0.002  0.002  0.002 
Exact or estimate?  Exact  Exact  Exact  Exact  Exact 
Significant (alpha = 0.05)?  Yes  Yes  Yes  Yes  Yes 
How big is the discrepancy?  
Discrepancy  0.9883  0.9459  0.9351  0.928  0.9208 
Algorithm  Parameter (s)  Value (s) 

BER  Mutation probability  0.5 
Exploration percentage  70  
K (decreases from 2 to 0)  1  
SFS  $\eta $  ∈[0, 1] 
${\eta}^{\prime}$  ∈[0, 1]  
PSO  Acceleration constants  [2, 2] 
Inertia ${W}_{max}$, ${W}_{min}$  [0.6, 0.9]  
Particles  10  
Iterations  80  
GWO  a  2 to 0 
Iterations  80  
Wolves  10  
WOA  r  [0, 1] 
Iterations  80  
Whales  10  
a  2 to 0 
Accuracy  Sensitivity (TRP)  Specificity (TNP)  p Value (PPV)  N Value (NPV)  F1 Score  

BERSFSCNN  0.9883  0.8571  0.9921  0.7595  0.9959  0.8054 
BERCNN  0.9759  0.7500  0.9796  0.3750  0.9959  0.5000 
SFSCNN  0.9720  0.6000  0.9796  0.3750  0.9917  0.4615 
PSOCNN  0.9680  0.4000  0.9796  0.2857  0.9877  0.3333 
GWOCNN  0.9636  0.4000  0.9767  0.2857  0.9859  0.3333 
WOACNN  0.9598  0.7674  0.9655  0.3976  0.9929  0.5238 
SS  DF  MS  F (DFn, DFd)  p Value  

Treatment (between columns)  0.0059  5  0.0012  F (5, 54) = 41.27  p < 0.0001 
Residual (within columns)  0.0016  54  $2.88\times {10}^{5}$     
Total  0.0075  59       
BERSFSCNN  BERCNN  SFSCNN  PSOCNN  GWOCNN  WOACNN  

Theoretical median  0  0  0  0  0  0 
Actual median  0.9883  0.9759  0.972  0.968  0.9636  0.9581 
Number of values  10  10  10  10  10  10 
Wilcoxon signedrank test  
Sum of signed ranks (W)  55  55  55  55  55  55 
Sum of positive ranks  55  55  55  55  55  55 
Sum of negative ranks  0  0  0  0  0  0 
p value (twotailed)  0.002  0.002  0.002  0.002  0.002  0.002 
Exact or estimate?  Exact  Exact  Exact  Exact  Exact  Exact 
Significant (alpha = 0.05)?  Yes  Yes  Yes  Yes  Yes  Yes 
How big is the discrepancy?  
Discrepancy  0.9883  0.9759  0.972  0.968  0.9636  0.9581 
BERSFSCNN  BERCNN  SFSCNN  PSOCNN  GWOCNN  WOACNN  

Number of values  10  10  10  10  10  10 
Minimum  0.9883  0.9659  0.962  0.9580  0.9536  0.9381 
25th percentile  0.9883  0.9734  0.9708  0.9680  0.9636  0.9488 
Median  0.9883  0.9759  0.972  0.9680  0.9636  0.9581 
75th percentile  0.9883  0.9759  0.972  0.9680  0.9636  0.9632 
Maximum  0.9883  0.9759  0.9772  0.9780  0.9736  0.9698 
Range  0  0.0100  0.0152  0.0200  0.0200  0.0317 
Mean  0.9883  0.9739  0.9710  0.9680  0.9636  0.9560 
Std. deviation  0  0.0042  0.0036  0.0047  0.0047  0.0097 
Std. error of mean  0  0.0013  0.0013  0.0015  0.0015  0.0031 
Geometric mean  0.9883  0.9739  0.9710  0.9680  0.9636  0.9559 
Geometric SD factor  1  1.0040  1.0040  1.0050  1.0050  1.0100 
Sum  9.8830  9.7390  9.7100  9.6800  9.6360  9.5600 
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Khafaga, D.S.; Ibrahim, A.; ElKenawy, E.S.M.; Abdelhamid, A.A.; Karim, F.K.; Mirjalili, S.; Khodadadi, N.; Lim, W.H.; Eid, M.M.; Ghoneim, M.E. An AlBiruni Earth Radius OptimizationBased Deep Convolutional Neural Network for Classifying Monkeypox Disease. Diagnostics 2022, 12, 2892. https://doi.org/10.3390/diagnostics12112892
Khafaga DS, Ibrahim A, ElKenawy ESM, Abdelhamid AA, Karim FK, Mirjalili S, Khodadadi N, Lim WH, Eid MM, Ghoneim ME. An AlBiruni Earth Radius OptimizationBased Deep Convolutional Neural Network for Classifying Monkeypox Disease. Diagnostics. 2022; 12(11):2892. https://doi.org/10.3390/diagnostics12112892
Chicago/Turabian StyleKhafaga, Doaa Sami, Abdelhameed Ibrahim, ElSayed M. ElKenawy, Abdelaziz A. Abdelhamid, Faten Khalid Karim, Seyedali Mirjalili, Nima Khodadadi, Wei Hong Lim, Marwa M. Eid, and Mohamed E. Ghoneim. 2022. "An AlBiruni Earth Radius OptimizationBased Deep Convolutional Neural Network for Classifying Monkeypox Disease" Diagnostics 12, no. 11: 2892. https://doi.org/10.3390/diagnostics12112892