Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Final confusion matrix of HGA-FLVQ model after a re-examination by ZN staining_
| n = 50 | Predicted: No | Predicted: Yes | |
| ZN Staining: No | TN = 22 | FP = 1 | 23 |
| ZN Staining: Yes | FN = 1 | TP = 26 | 27 |
| 23 | 27 |
Confusion matrix of HGA-FLVQ model using ZN staining method_
| n = 50 | Predicted: No | Predicted: Yes | |
| ZN staining: No | TN = 22 | FP = 4 | 26 |
| ZN staining: Yes | FN = 1 | TP = 23 | 24 |
| 23 | 27 |
Confusion matrix of FLVQ method using ZN staining as Gold standard_
| n = 50 | Predicted : No | Predicted: Yes | |
| ZN Staining: No | TN=25 | FP=1 | 26 |
| ZN Staining: Yes | FN=7 | TP=17 | 24 |
| 32 | 18 |
Results of weight calculation and revision of LVQ training_
| TGS813 Sensor | TGS822 Sensor | TGS2611 Sensor | |
| 1st Iteration | |||
| The weight of the negative class | −0.051673025 | 0.26946884 | −0.003179715 |
| The weight of the positive class | −0.002036426 | 0.1985224 | 0.21423542 |
| 2nd Iteration | |||
| The weight of the negative class | −0.0356808 | 0.28372976 | −3.8830974E-4 |
| The weight of the positive class | 0.028204879 | 0.14191468 | 0.16531087 |
| 3rd Iteration | |||
| The weight of the negative class | −0.0029952978 | 0.3213401 | 0.00271485 |
| The weight of the positive class | 0.052159406 | 0.10385808 | 0.13945574 |
| 4th Iteration | |||
| The weight of the negative class | 0.03716613 | 0.37145796 | 0.0097912615 |
| The weight of the positive class | 0.062625006 | 0.088705875 | 0.1361857 |
| 5th Iteration | |||
| The weight of the negative class | 0.07502196 | 0.407575 | 0.017326174 |
| The weight of the positive class | 0.06537599 | 0.080875896 | 0.12186478 |
| 6th Iteration | |||
| The weight of the negative class | 0.09876694 | 0.42662817 | 0.02240251 |
| The weight of the positive class | 0.06590489 | 0.07604013 | 0.1046309 |
| 7th Iteration | |||
| The weight of the negative class | 0.11628124 | 0.44089812 | 0.026141549 |
| The weight of the positive class | 0.06780671 | 0.074578255 | 0.09289357 |
| 8th Iteration | |||
| The weight of the negative class | 0.12786691 | 0.44939327 | 0.02856244 |
| The weight of the positive class | 0.06953817 | 0.07365509 | 0.08497784 |
| 9th Iteration | |||
| The weight of the negative class | 0.13485843 | 0.45396066 | 0.029982805 |
| The weight of the positive class | 0.07066574 | 0.07268719 | 0.08011716 |
| 10th Iteration | |||
| The weight of the negative class | 0.13828559 | 0.4564701 | 0.030701837 |
| The weight of the positive class | 0.07150341 | 0.072542615 | 0.07794089 |
Performance rates of HGA-FLVQ model_
| Performance rate | Formula | Result |
|---|---|---|
| Accuracy | (TP+TN)/n | (23+22)/50 × 100% = 90.00% |
| Error rate | (FP+FN)/n | (4+1)/50 × 100% = 10.00% |
| Sensitivity (true positive rate) | TP/ZN Staining Yes | 23/24 × 100% = 95.83% |
| False positive rate | FP/ZN Staining No | 4/26 × 100% = 15.38% |
| Specificity (true negative rate) | TN/ZN Staining No | 22/26 × 100% = 84.62% |
| Precision | TP/Predictive Yes | 23/27 × 100% = 85.19% |
| Prevalence | TP/n | 23/50 ×100% = 46.00% |
Confusion matrix of HGA-FLVQ model using ZN staining re-examination_
| n = 4 | Re-Examination ZN Staining: No | Re-Examination ZN Staining: Yes | |
| ZN Staining: No | TN = 1 | FP = 3 | 4 |
| ZN Staining: Yes | FN = 0 | TP = 0 | 0 |
| 1 | 3 |
Results of cluster center revisions of FLVQ training_
| TGS813 Sensor data | ||||||
| Iteration | Fuzziness parameter | Learning rate | Cluster-Center | Error | ||
| 1 | 1.100590 | 0.001075 | 0.001401 | 0.073105 | 0.072574 | 0.004639 |
| 2 | 1.101180 | 0.001309 | 0.001160 | 0.079481 | 0.068403 | 0.000058 |
| TGS822 Sensor data | ||||||
| 1 | 1.100590 | 0.001113 | 0.001346 | 0.160899 | 0.142446 | 0.004211 |
| 2 | 1.101180 | 0.001361 | 0.001012 | 0.218137 | 0.103790 | 0.004771 |
| 3 | 1.101770 | 0.001516 | 0.000935 | 0.236398 | 0.101749 | 0.000338 |
| 4 | 1.102360 | 0.001731 | 0.000869 | 0.246578 | 0.106190 | 0.000123 |
| 5 | 1.102950 | 0.001982 | 0.000817 | 0.257252 | 0.110136 | 0.000129 |
| 6 | 1.103540 | 0.002266 | 0.000776 | 0.268349 | 0.113576 | 0.000135 |
| 7 | 1.104130 | 0.002558 | 0.000747 | 0.278854 | 0.116367 | 0.000118 |
| 8 | 1.104720 | 0.002829 | 0.000726 | 0.287788 | 0.118478 | 0.000084 |
| TGS2611 Sensor data | ||||||
| 1 | 1.100590 | 0.003575 | 0.000705 | 0.040732 | 0.029254 | 0.001988 |
| 2 | 1.101180 | 0.002175 | 0.000788 | 0.074589 | 0.016031 | 0.001321 |
| 3 | 1.101770 | 0.002993 | 0.000715 | 0.092969 | 0.017238 | 0.000339 |
| 4 | 1.102360 | 0.003588 | 0.000688 | 0.101591 | 0.018471 | 0.000076 |
Final confusion matrix of LVQ method after a re-examination by ZN staining_
| n = 50 | Predicted : No | Predicted: Yes | |
| ZN Staining: No | TN=22 | FP=4 | 26 |
| ZN Staining: Yes | FN=3 | TP=21 | 24 |
| 25 | 25 |
Final results of HGA-FLVQ model performance_
| Performance rates | Formulation | Performance of HGA-FLVQ model | Performance of LVQ method | Performance of FLVQ method |
|---|---|---|---|---|
| Accuracy | (TP+TN)/n | (26+22)/50 ×100% = 96.00% | (21+25)/50 ×100% = 92.00% | (17+25)/50 ×100% = 84.00% |
| Error rate | (FP+FN)/n | (1+1)/50 ×100% = 4.00% | (1+3)/50 ×100% = 8.00% | (1+7)/40 ×100% = 16.00% |
| Sensitivity (true positive rate) | TP/(ZN Staining Yes) | 26/27 ×100% = 96.30% | 21/24 ×100% = 87.50% | 17/24 ×100% = 70.83% |
| False positive rate | FP/(ZN Staining No) | 1/23 ×100% =4.35% | 1/26 ×100% = 3.85% | 1/26 ×100% = 3.85% |
| Specificity (true negative rate) | TN/(ZN Staining No) | 22/23 ×100% = 95.65% | 25/26 ×100% = 96.15% | 25/26 ×100% = 96.15% |
| Precision | TP/Predictive Yes | 26/27 ×100% = 96.30% | 21/22 ×100% = 95.45% | 17/18 ×100% = 94.44% |
| Prevalence | TP/n | 26/50 ×100% = 52.00% | 21/50 ×100% = 42.00% | 17/50 ×100% = 34.00% |
Results of HGA-FLVQ model training_
| TGS813 Sensor data | ||||||
| Iteration | Fuzziness parameter | Learning rate | Cluster center | Error | ||
| 1 | 1.100590 | 0.000987 | 0.001400 | 0.108494 | 0.024354 | 0.0014483775 |
| 2 | 1.101180 | 0.001541 | 0.000924 | 0.140709 | 0.033404 | 0.00111976 |
| 3 | 1.101770 | 0.002089 | 0.000798 | 0.163612 | 0.039210 | 5.5822276E-4 |
| 4 | 1.102360 | 0.002508 | 0.000750 | 0.177564 | 0.042487 | 2.0541892E-4 |
| 5 | 1.102950 | 0.002808 | 0.000727 | 0.186139 | 0.044436 | 7.73241E-5 |
| TGS822 Sensor data | ||||||
| 1 | 1.100590 | 0.001144 | 0.001169 | 0.093718 | 0.212932 | 0.004191581 |
| 2 | 1.101180 | 0.001008 | 0.001355 | 0.097408 | 0.228077 | 2.4299692E-4 |
| 3 | 1.101770 | 0.000919 | 0.001562 | 0.102777 | 0.238711 | 1.41901E-4 |
| 4 | 1.102360 | 0.000857 | 0.001782 | 0.107080 | 0.248823 | 1.207616E-4 |
| 5 | 1.102950 | 0.000807 | 0.002042 | 0.110949 | 0.259704 | 1.3338469E-4 |
| 6 | 1.103540 | 0.000769 | 0.002332 | 0.114258 | 0.270786 | 1.3375138E-4 |
| 7 | 1.104130 | 0.000742 | 0.002620 | 0.116887 | 0.280968 | 1.105932E-4 |
| 8 | 1.104720 | 0.000723 | 0.002887 | 0.118887 | 0.289624 | 7.890986E-5 |
| TGS2611 Sensor data | ||||||
| 1 | 1.100590 | 0.000644 | 0.005906 | 0.031570 | 0.029312 | 0.0014235964 |
| 2 | 1.101180 | 0.001916 | 0.000857 | 0.055587 | 0.020714 | 6.50747E-4 |
| 3 | 1.101770 | 0.002333 | 0.000767 | 0.081313 | 0.015552 | 6.8849424E-4 |
| 4 | 1.102360 | 0.003203 | 0.000704 | 0.096225 | 0.017693 | 2.2693272E-4 |
| 5 | 1.102950 | 0.003725 | 0.000683 | 0.103321 | 0.018730 | 5.1426956E-5 |
Confusion matrix of LVQ method using ZN staining as Gold standard_
| n = 50 | Predicted : No | Predicted: Yes | |
| ZN Staining: No | TN=25 | FP=1 | 26 |
| ZN Staining: Yes | FN=3 | TP=21 | 24 |
| 28 | 22 |
Testing result of a positive ZN staining patient using HGA-FLVQ model_
| Amplitude order | Target class | Class distance 1 | Class distance 2 | Prediction class |
|---|---|---|---|---|
| 1 | 2 | 0.369 | 0.424 | 1 |
| 2 | 2 | 0.357 | 0.392 | 1 |
| 3 | 2 | 0.285 | 0.238 | 2 |
| 4 | 2 | 0.262 | 0.177 | 2 |
| 5 | 2 | 0.337 | 0.318 | 2 |
| 6 | 2 | 0.317 | 0.150 | 2 |
| 7 | 2 | 0.321 | 0.076 | 2 |
| 8 | 2 | 0.310 | 0.087 | 2 |
| 9 | 2 | 0.307 | 0.090 | 2 |
| 10 | 2 | 0.290 | 0.107 | 2 |
| 11 | 2 | 0.286 | 0.111 | 2 |
| 12 | 2 | 0.305 | 0.092 | 2 |
| 13 | 2 | 0.286 | 0.111 | 2 |
| 14 | 2 | 0.284 | 0.113 | 2 |
| 15 | 2 | 0.2880 | 0.109 | 2 |
| 16 | 2 | 0.292 | 0.105 | 2 |
| 17 | 2 | 0.280 | 0.117 | 2 |
| 18 | 2 | 0.288 | 0.111 | 2 |
| 19 | 2 | 0.289 | 0.112 | 2 |
| 20 | 2 | 0.280 | 0.117 | 2 |
Final confusion matrix of FLVQ method after a re-examination by ZN staining_
| n = 50 | Predicted: No | Predicted: Yes | |
| ZN Staining: No | TN=22 | FP=4 | 26 |
| ZN Staining: Yes | FN=7 | TP=17 | 24 |
| 29 | 21 |
Previous researches_
| Reference | Sample type | Classification methods | Results |
|---|---|---|---|
| Fend et al. (2006) | Sputum | Back propagation artificial neural network | Sensitivity 89.09% Specificity 91.14% |
| Gibson et al. (2009) | Sputum | Linear discriminant analysis | Average Sensitivity 80% Average Specificity 75% |
| Kolk et al. (2010) | Sputum | Rob electronic-nose: Linear Discriminant Analysis Partial least square discriminant analysis | Sensitivity 57-64% Specificity 61–70% Sensitivity 42–50% Specificity 73–77% |
| Walter electronic-nose: Linear discriminant analysis Partial least square discriminant analysis | Sensitivity 56-66% Specificity 65–68% Sensitivity 37–61% Specificity 56–67% |