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This version is not peerreviewed
Submitted:
30 August 2023
Posted:
05 September 2023
You are already at the latest version
This version is not peerreviewed
Submitted:
30 August 2023
Posted:
05 September 2023
You are already at the latest version
Feature Selection 
Classifiers  Accuracy (%)  Error Rate (%)  F1 Score (%)  MCC  Jaccard Index (%) 
gmean (%) 
Kappa 
KL Divergence 
SVM  82.24  17.76  80.89  0.65  67.91  82.77  0.64 
KNN  91.07  8.94  90.30  0.82  82.31  91.61  0.82  
Random Forest  81.56  18.44  81.62  0.63  68.95  81.56  0.63  
Decision Tree  77.35  22.66  76.80  0.55  62.34  77.39  0.55  
Softmax Discriminant  79.67  20.33  78.31  0.60  64.35  80.05  0.59  
Multilayer Perceptron  79.44  20.56  78.97  0.59  65.25  79.49  0.59  
Bayesian LDC  80.42  19.58  79.96  0.61  66.61  80.47  0.61  
IWO  SVM  91.06  8.94  90.86  0.82  83.24  91.13  0.82 
KNN  85.50  14.51  85.36  0.71  74.46  85.50  0.71  
Random Forest  90.26  9.74  90.35  0.81  82.39  90.27  0.81  
Decision Tree  91.57  8.43  91.71  0.83  84.70  91.87  0.83  
Softmax Discriminant  85.13  14.87  85.71  0.70  75.00  85.32  0.70  
Multilayer Perceptron  85.21  14.79  85.77  0.71  75.09  85.39  0.70  
Bayesian LDC  88.62  11.38  89.38  0.78  80.80  89.25  0.77 
Statistical Parameters  PSO  GWO  
Malignant  Normal  Malignant  Normal  
Mean  0.8598080214  0.1109701363  0.01878313748  0.01751341349 
Variance  0.05867975074  0.07425036326  0.07492946326  0.07494543857 
Skewness  19.87029488  19.83047771  22.52231557  22.56212107 
Kurtosis  441.8828416  444.9961882  509.1565306  510.3537192 
Pearson CC  0.9019022281  0.9269991469  0.9985202125  0.997858273 
CCA  0.12309  0.11291 
Classifiers  Optimal Parameters of the Classifiers 
Support Vector Machine  Kernel  RBF; α – 1; Kernel width parameter (σ) – 100; w – 0.85; b  0.01; Convergence Criterion – MSE. 
KNearest Neighbor  K  5; Distance Metric – Euclidian; w  0.5; Criterion – MSE. 
Random Forest  Number of Trees – 200; Maximum Depth – 10; Bootstrap Sample – 20; Class Weight – 0.45. 
Decision Tree  Maximum Depth – 20; Impurity Criterion – MSE; Class Weight – 0.4. 
Softmax Discriminant Classifier  λ = 0.5 along with mean of each class target values as 0.1 and 0.85. 
Multilayer Perceptron  Learning rate – 0.3; Learning Algorithm – LM; Criterion – MSE. 
Bayesian Linear Discriminant Classifier  Prior Probability P(x) – 0.5; Class mean ${\mu}_{x}$= 0.8 and ${\mu}_{y}$= 0.1, Criterion = MSE. 
Feature Extraction  Classifiers  Confusion Matrix  MSE  
TP  TN  FP  FN  
PSO  SVM  3944  4009  991  1056  7.29E06 
KNN  4267  3725  1275  733  4.49E05  
Random Forest  2692  2933  2067  2308  1.60E05  
Decision Tree  3184  3217  1783  1816  3.60E07  
Softmax Discriminant  4033  3750  1250  967  4.00E08  
Multilayer Perceptron  3425  3675  1325  1575  2.25E06  
Bayesian LDC  4367  3975  1025  633  5.63E05  
GWO  SVM  3617  4175  825  1383  5.76E06 
KNN  3500  3725  1275  1500  1.44E05  
Random Forest  3967  3817  1183  1033  3.36E05  
Decision Tree  4517  3984  1016  483  8.41E06  
Softmax Discriminant  4083  4275  725  917  1.96E04  
Multilayer Perceptron  4050  4384  616  950  4.84E04  
Bayesian LDC  3967  3692  1308  1033  2.50E07 
Feature Selection 
Classifiers  Confusion Matrix  MSE  
TP  TN  FP  FN  
KL Divergence 
SVM  3297  2747  2253  1703  3.24E06 
KNN  3978  2605  2395  1022  8.41E06  
Random Forest  4115  3294  1706  885  2.30E05  
Decision Tree  3919  4089  911  1081  9.00E06  
Softmax Discriminant  4089  4258  742  911  4.84E06  
Multilayer Perceptron  4271  3633  1367  729  2.56E06  
Bayesian LDC  3298  3311  1690  1702  1.02E05  
IWO  SVM  3854  3503  1497  1146  2.21E05 
KNN  3490  3985  1016  1510  3.36E05  
Random Forest  3574  2757  2243  1426  1.94E05  
Decision Tree  2982  2871  2129  2018  7.84E06  
Softmax Discriminant  2734  3047  1953  2266  1.22E05  
Multilayer Perceptron  3047  2592  2408  1953  1.00E06  
Bayesian LDC  2681  2698  2302  2319  1.85E05 
Feature Selection 
Classifiers  Confusion Matrix  MSE  
TP  TN  FP  FN  
KL Divergence 
SVM  4029  2742  2258  971  1.00E06 
KNN  3789  4147  853  1211  4.90E05  
Random Forest  3490  4089  911  1510  6.40E07  
Decision Tree  3594  4147  853  1406  2.50E07  
Softmax Discriminant  4896  2668  2333  104  1.00E06  
Multilayer Perceptron  3737  2982  2018  1263  2.03E05  
Bayesian LDC  3460  2767  2233  1540  1.00E08  
IWO  SVM  4401  3262  1738  599  4.90E07 
KNN  3203  3880  1120  1797  1.60E05  
Random Forest  4440  2735  2265  560  1.52E05  
Decision Tree  4167  2620  2380  833  5.29E06  
Softmax Discriminant  4219  2687  2313  781  2.30E05  
Multilayer Perceptron  4375  2747  2253  625  9.61E06  
Bayesian LDC  3216  2760  2240  1784  6.89E05 
Feature Selection 
Classifiers  Confusion Matrix  MSE  
TP  TN  FP  FN  
KL Divergence 
SVM  4089  3568  1433  911  6.61E04 
KNN  4184  4487  514  817  1.44E05  
Random Forest  4555  3520  1480  445  2.72E04  
Decision Tree  3815  3809  1191  1185  6.72E05  
Softmax Discriminant  4392  3948  1052  608  2.40E05  
Multilayer Perceptron  3881  4048  952  1119  1.96E06  
Bayesian LDC  4156  3947  1053  844  8.41E06  
IWO  SVM  3599  4085  915  1401  8.10E05 
KNN  4058  4375  625  942  7.23E05  
Random Forest  4129  4038  962  871  9.00E08  
Decision Tree  3713  4308  692  1288  6.40E05  
Softmax Discriminant  4129  4161  839  871  4.00E04  
Multilayer Perceptron  4539  4024  976  461  2.50E05  
Bayesian LDC  3817  3797  1203  1183  1.44E05 
Feature Selection 
Classifiers  Confusion Matrix  MSE  
TP  TN  FP  FN  
KL Divergence 
SVM  3653  4466  534  1347  1.23E05 
KNN  4139  4948  52  862  7.23E05  
Random Forest  4044  3913  1088  956  1.30E05  
Decision Tree  3635  3985  1016  1365  6.89E05  
Softmax Discriminant  3565  4297  703  1435  1.37E05  
Multilayer Perceptron  3740  4034  966  1260  6.40E07  
Bayesian LDC  3775  3987  1013  1225  4.90E07  
IWO  SVM  4339  4617  383  661  1.94E05 
KNN  4129  4321  680  871  5.76E06  
Random Forest  4509  4466  534  491  7.57E05  
Decision Tree  4617  4390  610  383  6.40E07  
Softmax Discriminant  4409  4005  995  592  1.04E04  
Multilayer Perceptron  4409  3913  1088  592  4.49E05  
Bayesian LDC  4754  3973  1027  246  4.90E07 
Feature Selection 
Classifiers  Confusion Matrix  MSE  
TP  TN  FP  FN  
KL Divergence 
SVM  4144  3668  1333  856  6.56E05 
KNN  4209  4537  464  792  2.92E05  
Random Forest  4575  3620  1380  425  1.09E05  
Decision Tree  3950  3859  1141  1050  5.93E05  
Softmax Discriminant  4417  4098  902  583  1.60E05  
Multilayer Perceptron  4011  4198  802  989  3.03E05  
Bayesian LDC  4245  4047  953  755  3.97E05  
IWO  SVM  3710  4235  765  1290  1.37E05 
KNN  4208  4375  625  792  4.22E05  
Random Forest  4229  4188  812  771  4.49E05  
Decision Tree  3813  4408  592  1188  4.36E05  
Softmax Discriminant  4229  4211  789  771  1.10E04  
Multilayer Perceptron  4558  4074  926  443  2.30E05  
Bayesian LDC  3917  3897  1103  1083  3.02E05 
Feature Selection 
Classifiers  Confusion Matrix  MSE  
TP  TN  FP  FN  
KL Divergence 
SVM  3758  4466  534  1242  1.37E05 
KNN  4159  4948  52  842  2.40E05  
Random Forest  4094  4063  938  906  1.02E05  
Decision Tree  3750  3985  1016  1250  1.23E05  
Softmax Discriminant  3670  4297  703  1330  4.76E05  
Multilayer Perceptron  3860  4084  916  1140  2.12E05  
Bayesian LDC  3905  4137  863  1095  9.61E06  
IWO  SVM  4439  4667  333  561  4.36E05 
KNN  4229  4321  680  771  5.48E05  
Random Forest  4559  4466  534  441  1.90E04  
Decision Tree  4667  4490  510  333  2.40E05  
Softmax Discriminant  4459  4055  945  542  5.33E05  
Multilayer Perceptron  4459  4063  938  542  5.04E05  
Bayesian LDC  4789  4073  927  211  1.09E05 
Performance Metrics  Equation  Significance  

Accuracy (%)  $Accuracy=\frac{TP+TN}{TP+TN+FP+FN}$  Average positivetonegative sample ratio. 

Error Rate  $Err=\frac{FP+FN}{TP+TN+FP+FN}$  The number of incorrect predictions, based on recorded observations. 

F1 Score (%)  $F1=\frac{2TP}{2TP+FP+FN}$  Average of precision and recall to obtain the classification accuracy of a specific class.  
MCC  $MCC=\frac{TN\times TPFN\times FP}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}}$  Pearson correlation between the actual output and the achieved output. 

Jaccard Index (%)  $Jaccard=\frac{TP}{TP+FP+FN}$  The number of predicted true positives exceeded the number of actual positives, regardless of whether they were real or predicted. 

gmean (%)  $gmean=\sqrt{\frac{TP}{TP+FN}*\frac{TN}{TN+FP}}$  Combination of sensitivity and specificity into a single value that balances both objectives.  
Kappa  $Kappa=\frac{\mathrm{Pr}\left(a\right)\mathrm{P}\mathrm{r}\left(e\right)}{1\mathrm{P}\mathrm{r}\left(e\right)}$  Interrater agreement measure for assessing agreement between two methods in categorizing cancer cases. 
Feature Extraction  Classifiers  Accuracy (%)  Error Rate (%)  F1 Score (%)  MCC  Jaccard Index (%)  gmean(%)  Kappa 
PSO  SVM  79.53  20.47  79.40  0.59  65.83  79.53  0.59 
KNN  79.92  20.08  80.95  0.60  68.00  80.21  0.60  
Random Forest  56.25  43.75  55.17  0.13  38.09  56.26  0.13  
Decision Tree  64.01  35.99  63.89  0.28  46.94  64.01  0.28  
Softmax Discriminant  77.83  22.17  78.44  0.56  64.53  77.90  0.56  
Multilayer Perceptron  71  29  70.26  0.42  54.15  71.04  0.42  
Bayesian LDC  83.42  16.58  84.05  0.67  72.48  83.59  0.67  
GWO  SVM  77.92  22.08  76.62  0.56  62.09  78.21  0.56 
KNN  72.25  27.75  71.61  0.45  55.78  72.29  0.45  
Random Forest  77.84  22.16  78.17  0.56  64.16  77.86  0.56  
Decision Tree  85.01  14.99  85.77  0.70  75.08  85.33  0.70  
Softmax Discriminant  83.58  16.42  83.26  0.67  71.32  83.62  0.67  
Multilayer Perceptron  84.34  15.66  83.80  0.69  72.12  84.46  0.69  
Bayesian LDC  76.59  23.41  77.22  0.53  62.89  76.66  0.53 
Feature Selection 
Classifiers  Accuracy (%)  Error Rate (%)  F1 Score (%)  MCC  Jaccard Index (%) 
gmean (%) 
Kappa 
KL Divergence 
SVM  60.44  39.56  62.51  0.21  45.46  60.56  0.21 
KNN  65.83  34.17  69.96  0.33  53.79  66.96  0.32  
Random Forest  74.09  25.91  76.05  0.49  61.36  74.65  0.48  
Decision Tree  80.08  19.92  79.74  0.60  66.30  80.11  0.60  
Softmax Discriminant  83.47  16.53  83.18  0.67  71.21  83.50  0.67  
Multilayer Perceptron  79.04  20.96  80.30  0.59  67.08  79.43  0.58  
Bayesian LDC  66.08  33.92  66.04  0.32  49.30  66.08  0.32  
IWO  SVM  73.57  26.43  74.47  0.47  59.32  73.67  0.47 
KNN  74.74  25.26  73.43  0.50  58.01  74.95  0.49  
Random Forest  63.31  36.69  66.09  0.27  49.35  63.64  0.27  
Decision Tree  58.53  41.47  58.99  0.17  41.83  58.54  0.17  
Softmax Discriminant  57.81  42.19  56.45  0.16  39.32  57.84  0.16  
Multilayer Perceptron  56.39  43.61  58.29  0.13  41.13  56.44  0.13  
Bayesian LDC  53.79  46.21  53.71  0.08  36.72  53.79  0.08 
Feature Selection 
Classifiers  Accuracy (%)  Error Rate (%)  F1 Score (%)  MCC  Jaccard Index (%) 
gmean (%) 
Kappa 
KL Divergence 
SVM  67.72  32.28  71.40  0.37  55.52  68.80  0.35 
KNN  79.36  20.64  78.60  0.59  64.74  79.49  0.59  
Random Forest  75.78  24.22  74.24  0.52  59.03  76.09  0.52  
Decision Tree  77.41  22.59  76.09  0.55  61.41  77.69  0.55  
Softmax Discriminant  75.64  24.37  80.08  0.57  66.77  80.74  0.51  
Multilayer Perceptron  67.19  32.81  69.49  0.35  53.25  67.54  0.34  
Bayesian LDC  62.27  37.73  64.72  0.25  47.84  62.49  0.25  
IWO  SVM  76.63  23.37  79.02  0.55  65.31  77.82  0.53 
KNN  70.83  29.17  68.71  0.42  52.34  71.16  0.42  
Random Forest  71.75  28.25  75.87  0.46  61.12  74.14  0.43  
Decision Tree  67.87  32.13  72.18  0.38  56.47  69.50  0.36  
Softmax Discriminant  69.06  30.94  73.17  0.40  57.69  70.74  0.38  
Multilayer Perceptron  71.22  28.78  75.25  0.45  60.32  73.33  0.42  
Bayesian LDC  59.76  40.24  61.52  0.20  44.42  59.84  0.20 
Feature Selection 
Classifiers  Accuracy (%)  Error Rate (%)  F1 Score (%)  MCC  Jaccard Index (%) 
gmean (%) 
Kappa 
KL Divergence 
SVM  76.56  23.44  77.72  0.53  63.56  76.80  0.53 
KNN  86.70  13.30  86.30  0.74  75.96  86.81  0.73  
Random Forest  80.75  19.25  82.56  0.63  70.30  81.86  0.62  
Decision Tree  76.24  23.76  76.26  0.52  61.63  76.24  0.53  
Softmax Discriminant  83.40  16.60  84.11  0.67  72.58  83.62  0.67  
Multilayer Perceptron  79.28  20.72  78.93  0.59  65.20  79.31  0.59  
Bayesian LDC  81.03  18.97  81.42  0.62  68.67  81.08  0.62  
IWO  SVM  76.84  23.16  75.66  0.54  61.84  77.05  0.54 
KNN  84.33  15.67  83.82  0.69  72.14  84.44  0.69  
Random Forest  81.67  18.33  81.83  0.63  69.25  81.68  0.63  
Decision Tree  80.21  19.79  78.95  0.61  65.23  80.56  0.60  
Softmax Discriminant  82.90  17.10  82.84  0.66  70.71  82.90  0.66  
Multilayer Perceptron  85.64  14.36  86.28  0.72  75.88  85.94  0.71  
Bayesian LDC  76.14  23.86  76.19  0.52  61.54  76.14  0.52 
Feature Selection 
Classifiers  Accuracy (%)  Error Rate (%)  F1 Score (%)  MCC  Jaccard Index (%) 
gmean (%) 
Kappa 
KL Divergence 
SVM  78.11  21.89  79.11  0.56  65.44  78.32  0.56 
KNN  87.45  12.55  87.02  0.75  77.03  87.58  0.75  
Random Forest  81.95  18.05  83.53  0.65  71.71  82.92  0.64  
Decision Tree  78.09  21.91  78.19  0.55  64.19  78.10  0.54  
Softmax Discriminant  85.15  14.85  85.61  0.70  74.84  85.27  0.70  
Multilayer Perceptron  82.09  17.91  81.75  0.64  69.13  82.12  0.64  
Bayesian LDC  82.92  17.08  83.25  0.66  71.31  82.96  0.66  
IWO  SVM  79.45  20.55  78.31  0.59  64.35  79.72  0.59 
KNN  85.83  14.17  85.59  0.72  74.81  85.86  0.72  
Random Forest  84.17  15.83  84.23  0.68  72.76  84.17  0.68  
Decision Tree  82.21  17.79  81.08  0.65  68.18  82.58  0.64  
Softmax Discriminant  84.40  15.60  84.43  0.69  73.05  84.40  0.69  
Multilayer Perceptron  86.32  13.68  86.95  0.73  76.91  86.59  0.73  
Bayesian LDC  78.14  21.86  78.29  0.56  64.21  78.14  0.56 
Feature Selection 
Classifiers  Accuracy (%)  Error Rate (%)  F1 Score (%)  MCC  Jaccard Index (%) 
gmean (%) 
Kappa 
KL Divergence 
SVM  81.19  18.81  79.53  0.63  66.02  81.88  0.62 
KNN  90.87  9.14  90.06  0.83  81.92  91.71  0.82  
Random Forest  79.56  20.44  79.83  0.59  66.43  79.58  0.59  
Decision Tree  76.20  23.81  75.33  0.53  60.43  76.30  0.52  
Softmax Discriminant  78.62  21.38  76.93  0.58  62.51  79.13  0.57  
Multilayer Perceptron  77.74  22.26  77.07  0.56  62.69  77.82  0.55  
Bayesian LDC  77.62  22.38  77.14  0.55  62.78  77.66  0.55  
IWO  SVM  89.56  10.44  89.27  0.79  80.61  89.66  0.79 
KNN  84.50  15.51  84.19  0.69  72.70  84.54  0.69  
Random Forest  89.76  10.24  89.80  0.80  81.49  89.76  0.80  
Decision Tree  90.07  9.93  90.29  0.80  81.30  90.13  0.80  
Softmax Discriminant  84.13  15.87  84.75  0.68  73.54  84.31  0.68  
Multilayer Perceptron  83.21  16.79  84.00  0.67  72.42  83.47  0.66  
Bayesian LDC  87.27  12.73  88.19  0.75  78.88  88.00  0.75 
S No  Feature Extraction  Feature Selection  Classifiers  Accuracy (%) 

1  PSO    Bayesian LDC  83.42 % 
2  GWO    Decision Tree  85.01 % 
3  PSO  KL Divergence  Softmax Discriminant  83.47 % 
4  PSO  IWO  KNN  74.74 % 
5  GWO  KL Divergence  KNN  79.36 % 
6  GWO  IWO  SVM  76.63 % 
7  PSO  KL Divergence  KNN with Adam  86.70 % 
8  PSO  IWO  MLP with Adam  85.64 % 
9  PSO  KL Divergence  KNN with RAdam  87.45 % 
10  PSO  IWO  MLP with RAdam  86.32 % 
11  GWO  KL Divergence  KNN with Adam  90.87 % 
12  GWO  IWO  Decision Tree with Adam  90.07 % 
13  GWO  KL Divergence  KNN with RAdam  91.07 % 
14  GWO  IWO  Decision Tree with RAdam  91.57 % 
S No  Classifiers  Without Feature Extraction 
With Feature Extraction  With Feature Selection  With Hyperparameter Tuning of IWO Feature Selection Method 


PSO  GWO  KL Divergence 
IWO  Adam  RAdam  
1  SVM  $O\left({2n}^{2}\right)$  $O\left({2n}^{5}\right)$  $O\left({2n}^{5}\right)$  $O\left({2n}^{6}\right)$  $O\left({2n}^{6}\mathrm{log}n\right)$  $O\left({2n}^{2}\mathrm{log}n\right)$  $O\left({4n}^{7}\mathrm{log}5n\right)$ 
2  KNN  $O\left({n}^{2}\right)$  $O\left({n}^{5}\right)$  $O\left({n}^{5}\right)$  $O\left({n}^{6}\right)$  $O\left({n}^{6}\mathrm{log}n\right)$  $O\left({2n}^{7}\mathrm{log}2n\right)$  $O\left({2n}^{7}\mathrm{log}5n\right)$ 
3  RF  $O\left(n\mathrm{log}n\right)$  $O\left({n}^{4}\mathrm{log}n\right)$  $O\left({n}^{4}\mathrm{log}n\right)$  $O\left({n}^{5}\mathrm{log}n\right)$  $O\left({n}^{5}\mathrm{log}2n\right)$  $O\left({2n}^{6}\mathrm{log}3n\right)$  $O\left({2n}^{6}\mathrm{log}6n\right)$ 
4  DT  $O\left(\mathrm{log}n\right)$  $O\left({n}^{3}\mathrm{log}n\right)$  $O\left({n}^{3}\mathrm{log}n\right)$  $O\left({n}^{4}\mathrm{log}n\right)$  $O\left({n}^{4}\mathrm{log}2n\right)$  $O\left({2n}^{5}\mathrm{log}3n\right)$  $O\left({2n}^{5}\mathrm{log}6n\right)$ 
5  SDC  $O\left({n}^{2}\right)$  $O\left({n}^{5}\right)$  $O\left({n}^{5}\right)$  $O\left({n}^{6}\right)$  $O\left({n}^{6}\mathrm{log}n\right)$  $O\left({2n}^{7}\mathrm{log}2n\right)$  $O\left({2n}^{7}\mathrm{log}5n\right)$ 
6  MLP  $O\left({n}^{5}\right)$  $O\left({n}^{8}\right)$  $O\left({n}^{8}\right)$  $O\left({n}^{9}\right)$  $O\left({n}^{9}\mathrm{log}n\right)$  $O\left({2n}^{10}\mathrm{log}2n\right)$  $O\left({2n}^{10}\mathrm{log}5n\right)$ 
7  BLDC  $O\left({n}^{2}\right)$  $O\left({n}^{5}\right)$  $O\left({n}^{5}\right)$  $O\left({n}^{6}\right)$  $O\left({n}^{6}\mathrm{log}n\right)$  $O\left({2n}^{7}\mathrm{log}2n\right)$  $O\left({2n}^{7}\mathrm{log}5n\right)$ 
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Karthikeyan Shanmugam
et al.
,
2023
Nelson Filipe Miranda Faria
et al.
,
2022
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