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Selected attributes_
| Selected Features | Max-Q | Std-a6 | Std- a5 | Std- a7 | Std- a4 | Std- a3 | Std- a2 | Std-a1 | std- a8 | Moy-d8 |
|---|---|---|---|---|---|---|---|---|---|---|
| Correlation rank | 0.350 | 0.326 | 0.318 | 0.314 | 0.311 | 0.310 | 0.307 | 0.306 | 0.304 | 0.300 |
RBF performance using different spread values_
| Basic function | Spread | ACC(%) | Test_time(s) | Time_response (s) | MSE |
|---|---|---|---|---|---|
| Inverse_multiquadric | 10 | 99.9 | 0.121 | 0.643 | 0.250 e-30 |
| 1 | 99.9 | 0.128 | 0.668 | 0.250 e-30 | |
| 0.1 | 99.9 | 0.140 | 0.676 | 0.250 e-30 |
MLP, RBF, and PNN Feed_Forward neural networks_
| Criteria types | Criterion | MLP | RBF | PNN |
|---|---|---|---|---|
| Structural | Architecture | An input layer, one or more hidden layer and an output layer | An input layer, one hidden layer and an output layer | An input layer, one hidden layer, a summation layer and an output layer |
| Activation function | The activation function is non-linear (sigmoid, log-sigmoid, tan-sigmoid.) | The activation function is a radial basis function which computes the Euclidian distance of the input vector and its weights | The activation function is based on the probability density function | |
| Number of hidden neurons | no defined principle for determining the number of neurons | no defined principle for determining the number of neurons | The number is equal to the number of instance | |
| Output layer | The final layer uses the activation function before linearly combining it | The final layer doesn’t use activation function, it rather linearly combines the output of the previous neuron | The final layer is a competitive output layer. It picks the maximum of the computed probabilities | |
| Training Process | Backpropagation training algorithms | Backpropagation or clustering algorithms | There is no computation of weights. The Bayesian decision rule | |
| Parametric | Parameters | Momentum factor, learning rate, parameters according to the training algorithm | Number of centers, spread of radial function | Spread value of the probability density function |
Performances of the PNN network according to the spread parameter_
| Spread | ACC(%) | Test_time(s) | Time_response (s) | MSE |
|---|---|---|---|---|
| 0.1 | 79.5 | 0.081 | 0.218 | 0.162 |
| 1 | 79.5 | 0.070 | 0.218 | 0.162 |
| 10 | 79.5 | 0.074 | 0.218 | 0.162 |
ANNs Performances_
| ANN | N0/HL | ACC(%) | Tr_time(s) | Test_time(s) | Time_response (s) | MSE |
|---|---|---|---|---|---|---|
| MLP_opt | 10 | 86.4 | 0.294 | 0.096 | 0.390 | 0.064 |
| RBF_opt | 20 | 99.9 | 0.755 | 0.121 | 0.876 | 0.250 e-30 |
| PNN_opt | 22 | 79.5 | 0.070 | 0.218 | 0.288 | 0.162 |
Comparative study with related works_
| ANN | Pre-processing | Test conditions | Division Datasets | ACC(%) |
|---|---|---|---|---|
| (Abhinav-Vishwa et al., 2011) | R peak | MIT_BIH database of 48 signals of 30 min | 50% for training and 50% for testing | 96.8 |
| (Rai et al., 2013) | Morphological and DWT coefficients | 45 ECG signal of 1 min from MIT-BIH database | 26 signals for training and 19 for testing | 97.8 |
| (Tomar et al., 2013) | Morphological, DWT coefficients, power spectral density and Energy of Periodogram | 62 ECG signals of 10 s from MIT-BIH database and Normal Sinus Rhythm (NSR) | Cross validation division (70%, 30%) | 98.4 |
| (Savalia et al., 2017) | R peaks, the heart beats/min, the duration of complex QRS | 66 ECG signal from MIT_BIH arrhythmia database and NSR database | Cross validation division (70%, 30%). | 82.5 |
| (Dalvi et al., 2016) | QRS complex, RR interval and the beat waveform morphology. PCA for feature selection | MIT_BIH database of 48 signals of 30 min. | 18 ECG records for test dataset and 30 ECG for train dataset | 96.9 |
| Proposed work | Morphological and DWT coefficients | 44 ECG signals of 1 min. recording from MIT_BIH database | 22 signal for training and 22 for testing following the AAM.I recommendations | 99.9 |
MLP performance with different learning algorithms_
| Learning algorithms types | Learning algorithms | ACC(%) | Tr_time(s) | Test_time(s) | Time_response (s) | MSE |
|---|---|---|---|---|---|---|
| Jacobian derivatives | trainlm | 86.4 | 0.222 | 0.024 | 0.246 | 0.094 |
| trainbr | 74.5 | 0.229 | 0.031 | 0.260 | 0.124 | |
| Gradient derivatives | trainscg | 86.4 | 0.553 | 0.355 | 0.908 | 0.077 |
| traingda | 81.8 | 0.416 | 0.218 | 0.634 | 0.078 | |
| trainrp | 86.4 | 0.294 | 0.096 | 0.390 | 0.073 | |
| traingdx | 81.8 | 0.543 | 0.345 | 0.888 | 0.076 | |
| trainbfg | 86.4 | 0.330 | 0.132 | 0.462 | 0.087 | |
| traincgb | 81.8 | 0.316 | 0.118 | 0.434 | 0.070 |
MLP performance by learning rate_
| Lr | ACC(%) | Time_response (s) | MSE |
|---|---|---|---|
| 0.01 | 86.4 | 0.390 | 0.130 |
| 0.1 | 86.4 | 0.399 | 0.064 |
| 1 | 86.4 | 0.392 | 0.073 |
RBF performance using different N/HL_
| NO/HL | ACC (%) | Tr_time(s) | Test_time(s) | Time_response (s) | MSE |
|---|---|---|---|---|---|
| 5 | 54.5 | 0.380 | 0.015 | 0.395 | 0.204 |
| 10 | 59.1 | 0.436 | 0.013 | 0.449 | 0.150 |
| 15 | 81.8 | 0.501 | 0.014 | 0.515 | 0.080 |
| 20 | 99.9 | 0.640 | 0.014 | 0.654 | 1.266e-30 |
| 25 | 99.9 | 0.699 | 0.017 | 0.716 | 2.411e-30 |
PNN performance_
| NO/HL | ACC(%) | Tr_time(s) | Test_time(s) | Time_response (s) | MSE |
|---|---|---|---|---|---|
| 22 | 79.5 | 0.081 | 0.218 | 0.299 | 0.162 |
MLP performance using different number of hidden layer_
| NO/HL | |||||||
|---|---|---|---|---|---|---|---|
| N_HL | H1 | H2 | ACC(%) | Tr_time(s) | Test_time(s) | Time_response (s) | MSE |
| 5 | 0 | 72.7 | 0.221 | 0.113 | 0.334 | 0.026 | |
| 10 | 0 | 86.4 | 0.222 | 0.094 | 0.316 | 0.024 | |
| 1 | 15 | 0 | 81.8 | 0.380 | 0.099 | 0.479 | 0.021 |
| 20 | 0 | 81.8 | 0.390 | 0.073 | 0.463 | 0.016 | |
| 25 | 0 | 81.8 | 0.406 | 0.071 | 0.477 | 0.013 | |
| 10 | 5 | 81.8 | 0.315 | 0.238 | 0.553 | 0.019 | |
| 2 | 10 | 10 | 81.8 | 0.319 | 0.253 | 0.572 | 0.021 |
| 10 | 15 | 72.7 | 0.383 | 0.281 | 0.664 | 0.018 | |
| 10 | 20 | 72.7 | 0.423 | 0.317 | 0.740 | 0.017 | |
RBF performance using different basic functions_
| RBF functions | ACC(%) | Tr_time(s) | Test_time(s) | Time_response (s) | MSE |
|---|---|---|---|---|---|
| Gaussian | 99.9 | 0.380 | 0.014 | 0.654 | 1.266e-30 |
| Polyharmonic | 99.9 | 0.436 | 0.051 | 0.639 | 1.221e-30 |
| Inverse_multiquadric | 99.9 | 0.501 | 0.121 | 0.676 | 0.250e-30 |
| Multiquadric | 99.9 | 0.640 | 0.132 | 0.698 | 0.891e-30 |
| Biharmonic | 99.9 | 0.699 | 0.002 | 0.640 | 0.891e-30 |