Improved Generalized-Pinball-Loss-Based Laplacian Twin Support Vector Machine for Data Classification
Abstract
:1. Introduction
- We combine the twin support vector machine based on the generalized pinball loss (GPin-TSVM) with the Laplacian technique, introducing a novel semi-supervised framework named LapGPin-TSVM. Additionally, we demonstrate noise insensitivity along with a corresponding analysis.
- We evaluate the efficacy of our model through experiments on the UCI dataset, using various ratios of unlabeled data and noise, and compare the results with three state-of-the-art models. Moreover, we also investigate the application of our approach to image classification.
- To analyze the performance of LapGPin-TSVM, we employ the win/tie/loss method, average rank, and use the Wilcoxon signed-rank test to better describe the effectiveness of our proposed method.
2. Preliminaries
2.1. Twin Support Vector Machine (TSVM)
2.2. Twin Support Vector Machine with Generalized Pinball Loss (GPin-TSVM)
2.3. Laplacian Twin Support Vector Machine
3. Proposed Work
3.1. Primal Problem
3.2. Dual Problem
Algorithm 1 LapGPin-TSVM |
|
3.3. Property of the Lap-GPTSVM
Noise Insensitivity
4. Comparison of the Models
4.1. LapGPin-TSVM vs. GPin-TSVM
4.2. LapGPin-TSVM vs. Lap-TSVM
4.3. LapGPin-TSVM vs. Lap-PTSVM
5. Numerical Experiments
5.1. Evaluation Metrics
5.2. Variation in Ratio of Unlabeled Data
Computational Efficiency of Model
5.3. Ablation Study
5.4. Variation in Ratio of Noise
5.5. Experiment on an Image Dataset
6. Discussion
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Datasets | No. of Samples | No. of Features |
---|---|---|
Ionosphere | 351 | 33 |
Bupa | 345 | 6 |
Fertility | 100 | 10 |
Pima | 768 | 8 |
Banknote | 1372 | 4 |
Monk-2 | 432 | 7 |
Sonar | 208 | 60 |
Diabetes | 769 | 9 |
Spambase | 4601 | 57 |
WDBC | 569 | 30 |
Australian | 690 | 14 |
Heart | 303 | 13 |
Specf heart | 267 | 22 |
GPin-TSVM | Lap-TSVM | Lap-PTSVM | LapGPin-TSVM | ||
---|---|---|---|---|---|
Datasets | Acc (%) | Acc (%) | Acc (%) | Acc (%) | |
MCC | MCC | MCC | MCC | ||
Time (s) | Time (s) | Time (s) | Time (s) | ||
Fertility | Linear | 88.00 ± 5.10 | 88.00 ± 5.10 | 88.00 ± 5.10 | 88.00 ± 5.10 |
0.0500 | 0.000 | 0.000 | 0.000 | ||
0.0352 | 0.0361 | 0.0397 | 0.0404 | ||
RBF | 88.00 ± 4.00 | 88.00 ± 4.00 | 88.00 ± 4.00 | 88.00 ± 4.00 | |
0.0000 | 0.000 | 0.000 | 0.000 | ||
0.0469 | 0.0421 | 0.0521 | 0.0570 | ||
Banknote | Linear | 93.88 ± 1.97 | 98.98 ± 0.63 | 97.52 ± 1.43 | 98.03 ± 0.94 |
0.8804 | 0.9793 | 0.9516 | 0.9607 | ||
2.1492 | 0.6919 | 0.9516 | 0.9607 | ||
RBF | 100.00 ± 0.00 | 99.78 ± 0.18 | 99.85 ± 0.29 | 100.00 ± 0.00 | |
1.000 | 0.9956 | 0.9971 | 1.000 | ||
2.2177 | 0.6225 | 2.6625 | 2.1435 | ||
Bupa | Linear | 60.00 ± 3.85 | 68.41 ± 4.80 | 67.53 ± 3.50 | 67.25 ± 3.73 |
0.8804 | 0.9793 | 0.9516 | 0.9607 | ||
2.1492 | 0.6919 | 0.9516 | 0.9607 | ||
RBF | 68.69 ± 7.25 | 66.67 ± 4.80 | 67.53 ± 3.50 | 67.25 ± 3.73 | |
0.8804 | 0.9793 | 0.9516 | 0.9607 | ||
2.1492 | 0.6919 | 0.9516 | 0.9607 | ||
Ionosphere | Linear | 81.48 ± 3.75 | 88.03 ± 2.51 | 87.74 ± 2.35 | 90.88 ± 2.66 |
0.6207 | 0.7419 | 0.7365 | 0.8040 | ||
0.3662 | 0.1751 | 0.1499 | 0.1080 | ||
RBF | 89.19 ± 3.94 | 92.89 ± 4.21 | 91.18 ± 3.11 | 91.18 ± 2.74 | |
0.7709 | 0.8443 | 0.8065 | 0.8068 | ||
0.1506 | 0.0732 | 0.1158 | 0.1205 | ||
Monk-2 | Linear | 79.17 ± 3.74 | 83.81 ± 1.98 | 86.35 ± 2.04 | 80.55 ± 2.25 |
0.5914 | 0.6769 | 0.7278 | 0.6264 | ||
0.1253 | 0.0956 | 0.1670 | 0.1221 | ||
RBF | 96.29 ± 3.71 | 97.22 ± 3.33 | 97.22 ± 3.33 | 97.22 ± 3.33 | |
0.9272 | 0.9464 | 0.9464 | 0.9464 | ||
0.1726 | 0.0986 | 0.1809 | 0.1586 | ||
Pima | Linear | 68.36 ± 2.76 | 75.39 ± 1.41 | 75.39 ± 1.41 | 76.95 ± 1.06 |
0.2343 | 0.4251 | 0.4251 | 0.4687 | ||
0.5448 | 0.1411 | 0.6538 | 0.4987 | ||
RBF | 72.67 ± 4.82 | 75.79 ± 3.06 | 79.97 ± 4.15 | 76.05 ± 4.01 | |
0.3663 | 0.4424 | 0.4716 | 0.4499 | ||
0.5341 | 0.1874 | 0.4813 | 0.5510 | ||
Sonar | Linear | 75.45 ± 9.58 | 77.86 ± 6.07 | 78.36 ± 6.25 | 77.86 ± 6.54 |
0.5380 | 0.5585 | 0.5723 | 0.5605 | ||
0.0632 | 0.0688 | 0.0710 | 0.0704 | ||
RBF | 75.45 ± 3.08 | 77.92 ± 6.17 | 79.83 ± 2.28 | 77.91 ± 4.79 | |
0.5185 | 0.5605 | 0.5955 | 0.5642 | ||
0.0552 | 0.0546 | 0.0779 | 0.0661 | ||
Diabetes | Linear | 75.39 ± 1.62 | 74.48 ± 2.19 | 77.73 ± 1.95 | 76.82 ± 2.11 |
0.4350 | 0.4093 | 0.4928 | 0.4722 | ||
0.4728 | 0.1441 | 0.6376 | 0.5980 | ||
RBF | 75.77 ± 2.03 | 76.43 ± 1.47 | 76.82 ± 1.63 | 76.95 ± 1.13 | |
0.4433 | 0.4611 | 0.4715 | 0.4744 | ||
0.5273 | 0.2047 | 0.6880 | 0.5473 | ||
Spambase | Linear | 84.08 ± 1.01 | 90.45 ± 0.91 | 91.32 ± 1.11 | 91.12 ± 0.95 |
0.7106 | 0.8000 | 0.8177 | 0.8135 | ||
50.0703 | 16.4100 | 61.5567 | 42.6016 | ||
RBF | 88.41 ± 0.97 | 90.30 ± 1.09 | 91.28 ± 0.57 | 91.41 ± 0.51 | |
0.7569 | 0.7971 | 0.8186 | 0.8194 | ||
41.5564 | 17.3560 | 79.4900 | 70.7805 | ||
WDBC | linear | 88.93 ± 1.17 | 92.96 ± 1.86 | 94.90 ± 1.52 | 95.78 ± 1.41 |
0.7729 | 0.8594 | 0.8927 | 0.9106 | ||
0.2742 | 0.1037 | 0.3075 | 0.2995 | ||
RBF | 93.15 ± 1.02 | 95.26 ± 2.57 | 95.26 ± 2.63 | 95.43 ± 2.79 | |
0.8597 | 0.8992 | 0.8991 | 0.9051 | ||
0.2595 | 0.1216 | 0.3249 | 0.3304 | ||
Australian | linear | 64.35 ± 3.79 | 85.65 ± 4.21 | 85.94 ± 4.36 | 86.09 ± 3.95 |
0.3319 | 0.7192 | 0.7272 | 0.7265 | ||
0.3362 | 0.1195 | 0.3587 | 0.3109 | ||
RBF | 67.68 ± 2.08 | 76.81 ± 3.67 | 84.20 ± 4.00 | 76.23 ± 1.96 | |
0.3676 | 0.5298 | 0.6865 | 0.5216 | ||
0.3553 | 0.1410 | 0.4298 | 0.5042 | ||
Heart | linear | 75.56 ± 5.90 | 81.85 ± 4.59 | 84.07 ± 3.01 | 84.81 ± 2.16 |
0.5169 | 0.6301 | 0.6756 | 0.6905 | ||
0.0691 | 0.0630 | 0.0919 | 0.0879 | ||
RBF | 79.62 ± 1.17 | 83.70 ± 2.46 | 81.48 ± 3.70 | 81.48 ± 4.05 | |
0.5923 | 0.6664 | 0.6317 | 0.6279 | ||
0.1039 | 0.0735 | 0.1030 | 0.0836 | ||
Spect heart | linear | 77.16 ± 3.16 | 77.53 ± 3.90 | 79.03 ± 3.78 | 79.41 ± 3.91 |
0.1456 | 0.0212 | 0.0107 | 0.000 | ||
0.0691 | 0.0630 | 0.0919 | 0.0879 | ||
RBF | 76.42 ± 4.45 | 77.19 ± 5.04 | 81.62 ± 3.92 | 82.01 ± 4.84 | |
0.0981 | 0.0547 | 0.2136 | 0.2701 | ||
0.0817 | 0.0651 | 0.1078 | 0.1036 | ||
Win/tile/loss | 22/3/1 | 15/4/7 | 13/4/9 |
GPin-TSVM | Lap-TSVM | Lap-PTSVM | LapGPin-TSVM | ||
---|---|---|---|---|---|
Datasets | Acc (%) | Acc (%) | Acc (%) | Acc (%) | |
MCC | MCC | MCC | MCC | ||
Time (s) | Time (s) | Time (s) | Time (s) | ||
Fertility | Linear | 79.00 ± 11.58 | 85.00 ± 7.75 | 88.00 ± 5.10 | 88.00 ± 5.10 |
0.0111 | −0.0439 | 0.000 | 0.000 | ||
0.0339 | 0.0303 | 0.0365 | 0.0441 | ||
RBF | 88.00 ± 4.00 | 88.00 ± 4.00 | 88.00 ± 4.00 | 88.00 ± 4.00 | |
0.0000 | 0.000 | 0.000 | 0.000 | ||
0.0376 | 0.0521 | 0.0472 | 0.0427 | ||
Banknote | Linear | 94.31 ± 1.74 | 98.76 ± 0.68 | 97.45 ± 1.36 | 98.17 ± 0.73 |
0.8880 | 0.9749 | 0.9502 | 0.9635 | ||
1.1178 | 0.3627 | 1.1045 | 1.1202 | ||
RBF | 99.78 ± 0.43 | 99.78 ± 0.29 | 99.56 ± 0.42 | 99.85 ± 0.42 | |
0.9956 | 0.9956 | 0.9912 | 0.9971 | ||
1.0669 | 0.4062 | 1.4074 | 1.1707 | ||
Bupa | Linear | 62.60 ± 5.53 | 65.21 ± 5.50 | 65.22 ± 6.28 | 64.93 ± 6.18 |
0.2042 | 0.2718 | 0.2701 | 0.2636 | ||
0.0587 | 0.0572 | 0.0712 | 0.0680 | ||
RBF | 64.93 ± 6.82 | 65.70 ± 6.12 | 67.25 ± 5.91 | 66.96 ± 6.69 | |
0.2809 | 0.2990 | 0.3407 | 0.3362 | ||
0.0694 | 0.0520 | 0.0876 | 0.0795 | ||
Ionosphere | Linear | 82.04 ± 2.82 | 86.60 ± 3.36 | 88.03 ± 2.17 | 89.17 ± 4.30 |
0.6305 | 0.7067 | 0.7467 | 0.7660 | ||
0.1310 | 0.0682 | 0.1060 | 0.0849 | ||
RBF | 88.05 ± 4.60 | 90.04 ± 3.47 | 90.62 ± 3.37 | 88.89 ± 3.97 | |
0.7402 | 0.7798 | 0.7904 | 0.7554 | ||
0.0838 | 0.0567 | 0.0895 | 0.0954 | ||
Monk-2 | Linear | 80.57 ± 3.85 | 84.73 ± 1.31 | 84.27 ± 2.74 | 84.24 ± 4.66 |
0.6198 | 0.6928 | 0.6880 | 0.6954 | ||
0.0999 | 0.0587 | 0.1280 | 0.1051 | ||
RBF | 96.75 ± 2.88 | 97.21 ± 3.34 | 97.22 ± 3.34 | 97.22 ± 3.34 | |
0.9331 | 0.9461 | 0.9464 | 0.9464 | ||
0.0935 | 0.0848 | 0.1213 | 0.1084 | ||
Pima | Linear | 68.23 ± 2.72 | 75.65 ± 1.16 | 75.91 ± 1.09 | 76.95 ± 1.24 |
0.2272 | 0.4303 | 0.4375 | 0.4695 | ||
0.2582 | 0.1118 | 0.3220 | 0.2599 | ||
RBF | 72.41 ± 4.14 | 75.66 ± 3.24 | 75.66 ± 4.13 | 75.92 ± 3.77 | |
0.3505 | 0.4328 | 0.4344 | 0.4429 | ||
0.2719 | 0.1302 | 0.2659 | 0.2874 | ||
Sonar | Linear | 72.62 ± 8.57 | 76.96 ± 10.079 | 79.35 ± 7.86 | 77.91 ± 8.48 |
0.4729 | 0.5431 | 0.6057 | 0.5743 | ||
0.0542 | 0.0434 | 0.0577 | 0.0595 | ||
RBF | 73.53 ± 7.69 | 75.53 ± 4.40 | 73.10 ± 5.53 | 75.47 ± 4.67 | |
0.4680 | 0.5192 | 0.4635 | 0.5154 | ||
0.0497 | 0.0543 | 0.0677 | 0.0586 | ||
Diabetes | Linear | 73.57 ± 1.92 | 73.83 ± 2.41 | 76.69 ± 1.37 | 77.08 ± 1.76 |
0.3883 | 0.3966 | 0.4736 | 0.4801 | ||
0.2361 | 0.1030 | 0.3358 | 0.3023 | ||
RBF | 74.99 ± 2.24 | 75.78 ± 1.98 | 76.30 ± 1.69 | 77.60 ± 2.21 | |
0.4218 | 0.4445 | 0.4599 | 0.4877 | ||
0.2482 | 0.1479 | 0.3597 | 0.2975 | ||
Spambase | Linear | 84.10 ± 1.36 | 88.82 ± 0.36 | 90.86 ± 1.17 | 90.78 ± 1.05 |
0.7113 | 0.7656 | 0.8081 | 0.8062 | ||
23.1552 | 7.7955 | 26.8444 | 20.8474 | ||
RBF | 88.21 ± 0.84 | 89.97 ± 0.95 | 91.12 ± 0.77 | 91.15 ± 0.69 | |
0.7534 | 0.7901 | 0.8135 | 0.8138 | ||
20.1447 | 8.5742 | 38.3108 | 38.6832 | ||
WDBC | Linear | 88.40 ± 2.02 | 93.84 ± 2.69 | 94.72 ± 1.48 | 95.78 ± 1.03 |
0.7616 | 0.8734 | 0.8890 | 0.9099 | ||
0.1466 | 0.0845 | 0.1730 | 0.1735 | ||
RBF | 93.32 ± 0.88 | 94.38 ± 3.53 | 94.38 ± 2.63 | 95.08 ± 2.25 | |
0.8627 | 0.8796 | 0.8794 | 0.8966 | ||
0.1378 | 0.1044 | 0.1781 | 0.0065 | ||
Australian | linear | 64.49 ± 3.58 | 85.36 ± 4.45 | 85.80 ± 3.57 | 86.09 ± 3.38 |
0.3435 | 0.7098 | 0.7211 | 0.7217 | ||
0.1923 | 0.0912 | 0.1931 | 0.2084 | ||
RBF | 69.57 ± 4.69 | 74.92 ± 3.26 | 81.88 ± 4.74 | 75.51 ± 1.41 | |
0.3791 | 0.4920 | 0.6426 | 0.5080 | ||
0.1821 | 0.1089 | 0.2568 | 0.2597 | ||
Heart | linear | 74.81 ± 8.65 | 80.74 ± 5.93 | 83.33 ± 5.10 | 83.33 ± 4.96 |
0.5050 | 0.6071 | 0.6597 | 0.6610 | ||
0.0520 | 0.0493 | 0.0818 | 0.0719 | ||
RBF | 77.41 ± 3.59 | 78.89 ± 3.43 | 80.37 ± 3.43 | 81.85 ± 2.16 | |
0.5667 | 0.5689 | 0.6072 | 0.6312 | ||
0.0777 | 0.0687 | 0.0886 | 0.0817 | ||
Spect heart | linear | 78.27 ± 2.26 | 80.16 ± 2.38 | 79.02 ± 4.49 | 79.03 ± 3.22 |
0.2266 | 0.1670 | 0.0390 | 0.0231 | ||
0.0604 | 0.0521 | 0.0756 | 0.0707 | ||
RBF | 76.43 ± 6.79 | 75.66 ± 4.87 | 80.51 ± 4.27 | 80.89 ± 5.62 | |
0.1111 | −0.0399 | 0.2659 | 0.2863 | ||
0.0638 | 0.0537 | 0.0734 | 0.0787 | ||
Win/tile/loss | 25/1/0 | 19/1/6 | 15/3/8 |
GPin-TSVM | Lap-TSVM | Lap-PTSVM | LapGPin-TSVM | ||
---|---|---|---|---|---|
Datasets | Acc (%) | Acc (%) | Acc (%) | Acc (%) | |
MCC | MCC | MCC | MCC | ||
Time (s) | Time (s) | Time (s) | Time (s) | ||
Fertility | Linear | 75.00 ± 10.95 | 85.00 ± 8.94 | 86.00 ± 4.90 | 88.00 ± 5.10 |
0.0709 | 0.0882 | −0.0306 | 0.000 | ||
0.0228 | 0.0355 | 0.0372 | 0.0347 | ||
RBF | 88.00 ± 4.00 | 88.00 ± 4.00 | 89.00 ± 3.74 | 88.00 ± 4.00 | |
0.0000 | 0.000 | 0.1092 | 0.000 | ||
0.0277 | 0.0382 | 0.0399 | 0.0467 | ||
Banknote | Linear | 94.31 ± 2.45 | 98.47 ± 0.78 | 97.45 ± 1.51 | 97.96 ± 0.94 |
0.888 | 0.9690 | 0.9502 | 0.9591 | ||
0.3644 | 0.2067 | 0.4249 | 0.4271 | ||
RBF | 99.19 ± 0.74 | 99.13 ± 0.91 | 99.71 ± 0.27 | 99.85 ± 0.18 | |
0.9838 | 0.9823 | 0.9941 | 0.9971 | ||
0.3521 | 0.2644 | 0.5851 | 0.4778 | ||
Bupa | Linear | 60.28 ± 5.53 | 65.21 ± 5.50 | 65.22 ± 6.28 | 64.93 ± 6.18 |
0.2042 | 0.2718 | 0.2701 | 0.2636 | ||
0.0587 | 0.0572 | 0.0712 | 0.0680 | ||
RBF | 64.64 ± 3.85 | 66.96 ± 2.95 | 67.83 ± 7.52 | 68.12 ± 6.54 | |
0.2566 | 0.3162 | 0.3405 | 0.3512 | ||
0.0657 | 0.0506 | 0.0608 | 0.0658 | ||
Ionosphere | Linear | 79.77 ± 3.57 | 86.61 ± 1.47 | 87.45 ± 3.57 | 87.75 ± 5.00 |
0.5971 | 0.7098 | 0.7323 | 0.7385 | ||
0.2376 | 0.0538 | 0.0722 | 0.0612 | ||
RBF | 86.05 ± 5.25 | 86.35 ± 6.12 | 86.62 ± 2.27 | 87.20 ± 5.83 | |
0.7010 | 0.6965 | 0.7054 | 0.7202 | ||
0.0653 | 0.0560 | 0.0627 | 0.0599 | ||
Monk-2 | Linear | 78.71 ± 3.02 | 78.25 ± 3.10 | 78.95 ± 2.12 | 84.04 ± 3.13 |
0.5904 | 0.5601 | 0.5752 | 0.6840 | ||
0.0548 | 0.0504 | 0.0784 | 0.0755 | ||
RBF | 95.60 ± 2.69 | 97.22 ± 3.33 | 96.75 ± 3.24 | 97.22 ± 3.33 | |
0.9102 | 0.9464 | 0.9373 | 0.9464 | ||
0.0617 | 0.0657 | 0.0878 | 0.0799 | ||
Pima | Linear | 69.27 ± 2.35 | 74.99 ± 1.73 | 75.00 ± 1.73 | 77.08 ± 1.03 |
0.2693 | 0.4188 | 0.4188 | 0.4703 | ||
0.1095 | 0.0741 | 0.1552 | 0.1421 | ||
RBF | 73.32 ± 5.46 | 75.14 ± 3.78 | 75.66 ± 3.54 | 75.92 ± 4.19 | |
0.3803 | 0.4232 | 0.4336 | 0.4423 | ||
0.1224 | 0.1209 | 0.1507 | 0.1578 | ||
Sonar | Linear | 66.91 ± 12.22 | 74.56 ± 5.99 | 71.72 ± 8.78 | 72.68 ± 9.93 |
0.3398 | 0.5016 | 0.4567 | 0.4740 | ||
0.0399 | 0.0543 | 0.0481 | 0.0452 | ||
RBF | 66.36 ± 3.54 | 71.65 ± 2.61 | 68.75 ± 4.78 | 69.24 ± 8.48 | |
0.3353 | 0.4334 | 0.3879 | 0.3932 | ||
0.0350 | 0.0402 | 0.0469 | 0.0461 | ||
Diabetes | Linear | 73.96 ± 2.18 | 73.83 ± 2.18 | 76.17 ± 1.89 | 76.56 ± 2.28 |
0.3983 | 0.3938 | 0.4572 | 0.4685 | ||
0.1118 | 0.0800 | 0.1773 | 0.1562 | ||
RBF | 76.30 ± 1.99 | 76.69 ± 1.25 | 76.95 ± 2.50 | 77.08 ± 1.79 | |
0.4556 | 0.4695 | 0.4770 | 0.4823 | ||
0.1293 | 0.1041 | 0.1670 | 0.1552 | ||
Spambase | Linear | 84.60 ± 1.15 | 88.77 ± 1.47 | 90.82 ± 1.13 | 90.88 ± 1.01 |
0.7177 | 0.7645 | 0.8069 | 0.8084 | ||
7.8185 | 3.3341 | 9.7254 | 7.8930 | ||
RBF | 87.32 ± 0.90 | 89.45 ± 1.28 | 91.28 ± 0.71 | 91.02 ± 0.93 | |
0.7347 | 0.7792 | 0.8168 | 0.8113 | ||
7.2114 | 3.4492 | 12.8823 | 11.6014 | ||
WDBC | Linear | 85.94 ± 2.02 | 94.19 ± 0.89 | 94.73 ± 2.15 | 95.43 ± 1.69 |
0.7110 | 0.8783 | 0.8892 | 0.9023 | ||
0.1014 | 0.0632 | 0.1276 | 0.1188 | ||
RBF | 93.49 ± 1.05 | 94.38 ± 2.51 | 94.20 ± 2.45 | 94.03 ± 2.30 | |
0.8666 | 0.8806 | 0.8761 | 0.8750 | ||
0.0735 | 0.0836 | 0.1322 | 0.1245 | ||
Australian | linear | 65.07 ± 4.48 | 84.05 ± 4.85 | 85.22 ± 4.24 | 85.94 ± 4.04 |
0.3513 | 0.6841 | 0.7110 | 0.7216 | ||
0.1013 | 0.0742 | 0.1169 | 0.1065 | ||
RBF | 69.27 ± 4.68 | 74.78 ± 2.56 | 78.12 ± 4.62 | 73.48 ± 2.85 | |
0.3754 | 0.4888 | 0.5657 | 0.4656 | ||
0.1071 | 0.0860 | 0.1388 | 0.1552 | ||
Heart | linear | 72.96 ± 5.32 | 81.11 ± 5.90 | 82.96 ± 4.28 | 82.22 ± 5.19 |
0.4608 | 0.6166 | 0.6534 | 0.6396 | ||
0.0572 | 0.0556 | 0.0638 | 0.0525 | ||
RBF | 76.67 ± 2.51 | 80.00 ± 1.39 | 80.00 ± 0.74 | 80.00 ± 3.59 | |
0.5680 | 0.5952 | 0.6002 | 0.6034 | ||
0.0587 | 0.0540 | 0.0685 | 0.0645 | ||
Spect heart | linear | 74.89 ± 3.92 | 77.54 ± 2.23 | 78.65 ± 4.02 | 78.65 ± 3.47 |
0.2415 | 0.1317 | 0.0952 | 0.0139 | ||
0.0394 | 0.0378 | 0.0685 | 0.0584 | ||
RBF | 75.65 ± 3.52 | 77.51 ± 4.68 | 79.43 ± 3.94 | 77.18 ± 4.46 | |
0.0578 | 0.1535 | 0.2400 | 0.2137 | ||
0.0648 | 0.0439 | 0.0552 | 0.0544 | ||
Win/tile/loss | 25/1/0 | 17/2/7 | 18/0/8 |
GPin-TSVM | Lap-TSVM | Lap-PTSVM | LapGPin-TSVM | ||
---|---|---|---|---|---|
Datasets | Acc (%) | Acc (%) | Acc (%) | Acc (%) | |
MCC | MCC | MCC | MCC | ||
Time (s) | Time (s) | Time (s) | Time (s) | ||
Fertility | Linear | 50.00 ± 15.17 | 78.00 ± 12.08 | 85.00 ± 8.37 | 89.00 ± 4.90 |
0.0140 | 0.0926 | 0.0453 | 0.1092 | ||
0.0256 | 0.0926 | 0.0366 | 0.0274 | ||
RBF | 88.00 ± 4.00 | 87.00 ± 4.00 | 86.00 ± 5.83 | 88.00 ± 4.00 | |
0.0000 | −0.0153 | 0.0677 | 0.000 | ||
0.0268 | 0.0346 | 0.0364 | 0.0320 | ||
Banknote | Linear | 93.88 ± 2.36 | 97.45 ± 0.8 | 97.38 ± 1.16 | 98.54 ± 0.73 |
0.8803 | 0.9485 | 0.9487 | 0.9704 | ||
0.2019 | 0.1419 | 0.1605 | 0.1552 | ||
RBF | 97.38 ± 1.95 | 98.32 ± 1.18 | 98.69 ± 1.56 | 98.84 ± 1.47 | |
0.9473 | 0.9661 | 0.9739 | 0.9768 | ||
0.1054 | 0.1865 | 0.2345 | 0.2183 | ||
Bupa | Linear | 63.77 ± 3.89 | 63.76 ± 6.01 | 68.12 ± 4.10 | 67.25 ± 2.98 |
0.2306 | 0.2474 | 0.3315 | 0.3129 | ||
0.0274 | 0.0403 | 0.0463 | 0.0411 | ||
RBF | 62.61 ± 4.79 | 62.90 ± 4.16 | 65.80 ± 4.20 | 66.09 ± 4.81 | |
0.2228 | 0.2718 | 0.3221 | 0.3300 | ||
0.0270 | 0.0517 | 0.0495 | 0.0514 | ||
Ionosphere | Linear | 78.89 ± 4.25 | 83.18 ± 1.95 | 82.89 ± 4.38 | 84.32 ± 5.12 |
0.5896 | 0.6360 | 0.6283 | 0.6576 | ||
0.0334 | 0.0506 | 0.0500 | 0.0377 | ||
RBF | 84.60 ± 2.95 | 86.34 ± 3.58 | 84.62 ± 2.91 | 88.05 ± 3.61 | |
0.6584 | 0.7010 | 0.6611 | 0.7438 | ||
0.0378 | 0.0490 | 0.0512 | 0.0492 | ||
Monk-2 | Linear | 73.40 ± 3.79 | 69.93 ± 6.92 | 77.57 ± 5.45 | 79.17 ± 1.53 |
0.4962 | 0.3903 | 0.5516 | 0.5878 | ||
0.0377 | 0.0385 | 0.0560 | 0.0480 | ||
RBF | 92.60 ± 2.14 | 94.90 ± 3.34 | 94.90 ± 3.34 | 97.21 ± 3.86 | |
0.8542 | 0.8986 | 0.8993 | 0.9470 | ||
0.0362 | 0.0502 | 0.0541 | 0.0591 | ||
Pima | Linear | 68.36 ± 2.00 | 74.74 ± 3.09 | 75.13 ± 3.19 | 76.43 ± 1.27 |
0.2287 | 0.4141 | 0.4251 | 0.4556 | ||
0.0534 | 0.0570 | 0.0791 | 0.0822 | ||
RBF | 73.45 ± 4.57 | 75.27 ± 3.04 | 75.14 ± 3.08 | 76.18 ± 3.03 | |
0.3814 | 0.4227 | 0.4237 | 0.4487 | ||
0.0553 | 0.0840 | 0.0970 | 0.0982 | ||
Sonar | Linear | 65.38 ± 6.91 | 68.79 ± 4.80 | 67.31 ± 5.41 | 67.31 ± 5.58 |
0.3085 | 0.3804 | 0.3613 | 0.3613 | ||
0.0313 | 0.0463 | 0.0401 | 0.0396 | ||
RBF | 61.56 ± 4.83 | 66.89 ± 6.01 | 61.61 ± 7.61 | 68.39 ± 10.48 | |
0.2221 | 0.3369 | 0.2459 | 0.3813 | ||
0.0301 | 0.0522 | 0.0418 | 0.0399 | ||
Diabetes | Linear | 73.18 ± 3.03 | 74.74 ± 1.88 | 77.47 ± 2.63 | 77.21 ± 2.76 |
0.3766 | 0.4123 | 0.4829 | 0.4801 | ||
0.0540 | 0.0817 | 0.0895 | 0.0881 | ||
RBF | 74.22 ± 1.74 | 75.40 ± 3.41 | 74.48 ± 2.61 | 75.66 ± 3.61 | |
0.4023 | 0.4462 | 0.4327 | 0.4449 | ||
0.0606 | 0.0843 | 0.1097 | 0.0968 | ||
Spambase | Linear | 85.25 ± 1.74 | 88.54 ± 1.58 | 91.16 ± 1.35 | 91.28 ± 1.21 |
0.7233 | 0.7598 | 0.8142 | 0.8165 | ||
1.1479 | 1.2968 | 2.3394 | 2.1206 | ||
RBF | 86.12 ± 1.70 | 88.17 ± 1.46 | 90.38 ± 1.23 | 90.58 ± 1.07 | |
0.7104 | 0.7510 | 0.7980 | 0.8020 | ||
1.3286 | 1.3474 | 2.7166 | 2.6171 | ||
WDBC | Linear | 81.55 ± 3.44 | 83.13 ± 7.10 | 93.32 ± 1.07 | 94.02 ± 1.71 |
0.6239 | 0.6379 | 0.8574 | 0.8727 | ||
0.0446 | 0.0541 | 0.0696 | 0.0700 | ||
RBF | 91.73 ± 3.27 | 92.80 ± 2.67 | 91.57 ± 2.10 | 92.97 ± 2.47 | |
0.8373 | 0.8495 | 0.8221 | 0.8501 | ||
0.0595 | 0.0636 | 0.0850 | 0.0752 | ||
Australian | linear | 63.91 ± 1.41 | 84.20 ± 3.34 | 85.22 ± 4.04 | 85.80 ± 3.54 |
0.3266 | 0.6861 | 0.7056 | 0.7132 | ||
0.0516 | 0.0556 | 0.0841 | 0.0782 | ||
RBF | 64.05 ± 3.02 | 71.45 ± 2.65 | 68.41 ± 3.85 | 70.00 ± 3.32 | |
0.2872 | 0.4249 | 0.3608 | 0.3944 | ||
0.0514 | 0.0701 | 0.0926 | 0.0932 | ||
Heart | linear | 62.22 ± 10.70 | 75.19 ± 7.64 | 73.33 ± 8.96 | 76.30 ± 6.13 |
0.2552 | 0.5033 | 0.4636 | 0.5198 | ||
0.0341 | 0.0432 | 0.0458 | 0.0492 | ||
RBF | 70.37 ± 5.61 | 78.15 ± 1.38 | 80.00 ± 2.15 | 80.74 ± 2.77 | |
0.4747 | 0.5570 | 0.5981 | 0.6141 | ||
0.0458 | 0.0553 | 0.0569 | 0.0553 | ||
Spect heart | linear | 62.94 ± 7.16 | 65.51 ± 5.16 | 77.15 ± 4.36 | 79.04 ± 4.45 |
0.1669 | 0.1130 | 0.0525 | 0.0792 | ||
0.0373 | 0.0412 | 0.0503 | 0.0518 | ||
RBF | 64.88 ± 10.93 | 58.43 ± 6.85 | 70.04 ± 2.59 | 69.66 ± 3.21 | |
0.1066 | 0.1136 | 0.2132 | 0.2100 | ||
0.0290 | 0.0411 | 0.0455 | 0.0384 | ||
Win/tile/loss | 25/1/0 | 24/0/2 | 23/0/3 |
Model | Mean Rank of Accuracy | Mean Rank of MCC | ||
---|---|---|---|---|
Linear | Nonlinear | Linear | Nonlinear | |
GPin-TSVM | 1.44 | 1.37 | 1.31 | 1.30 |
Lap-TSVM | 2.38 | 2.43 | 2.44 | 2.42 |
Lap-PTSVM | 3.05 | 2.85 | 2.84 | 2.89 |
LapGPin-TSVM | 3.45 | 3.38 | 3.28 | 3.38 |
Model | Percentage of Unlabeled Data | ||
---|---|---|---|
30% | 50% | 70% | |
LapGPin-TSVM | 89.74 ± 2.11 | 88.04 ± 2.91 | 82.91 ± 1.94 |
LapGPin-TSVM without Laplacian term | 89.74 ± 2.12 | 86.62 ± 4.25 | 80.91 ± 2.93 |
GPin-TSVM | Lap-TSVM | Lap-PTSVM | LapGPin-TSVM | ||
---|---|---|---|---|---|
Datasets | r | Acc (%) | Acc (%) | Acc (%) | Acc (%) |
MCC | MCC | MCC | MCC | ||
Time (s) | Time (s) | Time (s) | Time (s) | ||
Fertility | 0 | 88.00 ± 2.45 | 87.00 ± 2.45 | 88.00 ± 2.45 | 88.00 ± 2.45 |
0.0000 | −0.0153 | 0.0939 | 0.000 | ||
0.0242 | 0.0297 | 0.0361 | 0.0292 | ||
0.05 | 88.00 ± 2.45 | 88.00 ± 2.45 | 88.00 ± 2.45 | 88.00 ± 2.45 | |
0.0000 | 0.0000 | 0.000 | 0.000 | ||
0.0233 | 0.0325 | 0.0220 | 0.0352 | ||
0.1 | 88.00 ± 2.45 | 88.00 ± 2.45 | 88.00 ± 2.45 | 88.00 ± 2.45 | |
0.0000 | 0.0000 | 0.0658 | 0.000 | ||
0.0206 | 0.0280 | 0.0311 | 0.0303 | ||
Banknote | 0 | 94.39 ± 1.97 | 98.24 ± 1.09 | 98.25 ± 0.70 | 98.40 ± 1.04 |
0.8916 | 0.9654 | 0.9650 | 0.9675 | ||
0.1121 | 0.1076 | 0.1505 | 0.1667 | ||
0.05 | 94.32 ± 1.95 | 98.24 ± 1.90 | 98.47 ± 0.70 | 98.54 ± 1.03 | |
0.8903 | 0.9654 | 0.9694 | 0.9706 | ||
0.1027 | 0.1073 | 0.1612 | 0.1706 | ||
0.1 | 94.46 ± 2.24 | 98.25 ± 1.09 | 98.32 ± 0.67 | 98.54 ± 0.46 | |
0.8933 | 0.9654 | 0.9664 | 0.9705 | ||
0.111 | 0.1230 | 0.1597 | 0.1648 | ||
Bupa | 0 | 63.48 ± 3.23 | 66.09 ± 4.36 | 67.25 ± 4.82 | 67.54 ± 4.45 |
0.2176 | 0.2774 | 0.3014 | 0.3193 | ||
0.0346 | 0.0365 | 0.0509 | 0.0433 | ||
0.05 | 64.35 ± 2.68 | 66.09 ± 3.50 | 67.54 ± 4.73 | 68.41 ± 4.88 | |
0.2387 | 0.2796 | 0.3080 | 0.3409 | ||
0.0260 | 0.0372 | 0.0505 | 0.0439 | ||
0.1 | 64.05 ± 2.65 | 66.09 ± 3.95 | 66.67 ± 4.93 | 68.12 ± 4.39 | |
0.2322 | 0.2779 | 0.2896 | 0.3341 | ||
0.0531 | 0.0406 | 0.0516 | 0.0424 | ||
Ionosphere | 0 | 84.03 ± 8.07 | 86.03 ± 2.34 | 85.74 ± 5.29 | 83.75 ± 2.82 |
0.6499 | 0.7039 | 0.6901 | 0.6510 | ||
0.0352 | 0.0402 | 0.0546 | 0.0515 | ||
0.05 | 81.18 ± 4.77 | 84.33 ± 0.91 | 84.33 ± 1.60 | 85.76 ± 1.23 | |
0.5865 | 0.6603 | 0.6608 | 0.6962 | ||
0.0381 | 0.0494 | 0.0510 | 0.0540 | ||
0.1 | 79.49 ± 4.99 | 84.33 ± 1.80 | 84.33 ± 1.60 | 85.75 ± 1.59 | |
0.5515 | 0.6542 | 0.6612 | 0.6909 | ||
0.0383 | 0.0404 | 0.0520 | 0.0437 | ||
Monk-2 | 0 | 79.19 ± 6.15 | 78.95 ± 4.38 | 78.50 ± 6.45 | 80.11 ± 5.23 |
0.5845 | 0.5771 | 0.5712 | 0.5987 | ||
0.0413 | 0.0507 | 0.0828 | 0.0962 | ||
0.05 | 78.96 ± 5.39 | 79.18 ± 4.71 | 79.43 ± 6.36 | 80.34 ± 4.93 | |
0.5788 | 0.5798 | 0.5894 | 0.6044 | ||
0.0443 | 0.0473 | 0.0880 | 0.0663 | ||
0.1 | 78.26 ± 6.22 | 78.72 ± 4.55 | 78.96 ± 6.41 | 79.41 ± 5.01 | |
0.5613 | 0.5702 | 0.5812 | 0.5860 | ||
0.0347 | 0.0503 | 0.0566 | 0.0705 | ||
Pima | 0 | 75.78 ± 1.29 | 77.60 ± 1.48 | 77.73 ± 0.77 | 77.60 ± 1.58 |
0.4385 | 0.4821 | 0.4867 | 0.4843 | ||
0.0699 | 0.0796 | 0.0970 | 0.0863 | ||
0.05 | 76.30 ± 1.48 | 77.99 ± 1.78 | 78.38 ± 1.27 | 77.60 ± 1.96 | |
0.4535 | 0.4923 | 0.5026 | 0.4831 | ||
0.0624 | 0.0671 | 0.0908 | 0.0920 | ||
0.1 | 76.18 ± 1.92 | 76.82 ± 1.46 | 77.73 ± 1.28 | 78.00 ± 1.11 | |
0.4501 | 0.4644 | 0.4844 | 0.4929 | ||
0.0609 | 0.0679 | 0.1022 | 0.0910 | ||
Sonar | 0 | 66.40 ± 5.56 | 70.66 ± 2.92 | 74.02 ± 7.29 | 73.05 ± 4.79 |
0.3387 | 0.4221 | 0.4811 | 0.4678 | ||
0.0340 | 0.0461 | 0.0429 | 0.0419 | ||
0.05 | 64.38 ± 7.85 | 71.14 ± 4.61 | 71.13 ± 5.66 | 69.71 ± 3.27 | |
0.3085 | 0.4247 | 0.4258 | 0.4043 | ||
0.0267 | 0.0424 | 0.0385 | 0.0404 | ||
0.1 | 62.49 ± 6.59 | 68.75 ± 3.03 | 68.77 ± 2.36 | 70.21 ± 4.79 | |
0.2653 | 0.3741 | 0.3811 | 0.4041 | ||
0.0278 | 0.0421 | 0.0430 | 0.0332 | ||
Diabetes | 0 | 75.27 ± 4.29 | 76.30 ± 4.66 | 77.22 ± 2.34 | 77.48 ± 2.96 |
0.4240 | 0.4520 | 0.4770 | 0.4849 | ||
0.0902 | 0.0693 | 0.0971 | 0.0985 | ||
0.05 | 76.05 ± 4.03 | 76.56 ± 4.60 | 77.48 ± 3.07 | 78.13 ± 2.87 | |
0.4444 | 0.4584 | 0.4817 | 0.4980 | ||
0.0681 | 0.0570 | 0.1013 | 0.1179 | ||
0.1 | 76.31 ± 4.53 | 76.43 ± 4.06 | 76.83 ± 3.46 | 77.48 ± 2.88 | |
0.4534 | 0.4528 | 0.4679 | 0.4832 | ||
0.111 | 0.1230 | 0.1597 | 0.1648 | ||
Spambase | 0 | 90.36 ± 1.55 | 91.58 ± 1.07 | 90.67 ± 1.08 | 91.39 ± 1.32 |
0.8019 | 0.8231 | 0.8039 | 0.8188 | ||
2.2855 | 1.4991 | 2.6345 | 3.1632 | ||
0.05 | 89.19 ± 1.93 | 91.34 ± 0.95 | 90.82 ± 1.10 | 90.47 ± 1.15 | |
0.7794 | 0.8181 | 0.8073 | 0.7999 | ||
2.3051 | 1.4790 | 2.632 | 2.9123 | ||
0.1 | 88.97 ± 1.51 | 90.30 ± 0.70 | 90.47 ± 0.52 | 89.75 ± 0.86 | |
0.7729 | 0.7961 | 0.8000 | 0.7848 | ||
2.2058 | 1.4714 | 2.7201 | 2.8718 | ||
WDBC | 0 | 85.77 ± 3.43 | 95.78 ± 1.29 | 95.95 ± 1.21 | 94.37 ± 1.82 |
0.7086 | 0.9092 | 0.9135 | 0.8799 | ||
0.0586 | 0.0684 | 0.0789 | 0.0738 | ||
0.05 | 83.13 ± 1.48 | 93.15 ± 1.87 | 94.02 ± 2.58 | 94.03 ± 1.15 | |
0.6475 | 0.8525 | 0.8716 | 0.8729 | ||
0.0539 | 0.0698 | 0.0818 | 0.0731 | ||
0.1 | 84.01 ± 3.86 | 93.50 ± 2.04 | 94.37 ± 2.13 | 94.38 ± 2.12 | |
0.6686 | 0.8615 | 0.8804 | 0.8787 | ||
0.0609 | 0.0679 | 0.0984 | 0.1074 | ||
win/tile/loss | 26/3/1 | 21/2/7 | 19/3/8 |
GPin-TSVM | Lap-TSVM | Lap-PTSVM | LapGPin-TSVM | ||
---|---|---|---|---|---|
Datasets | r | Acc (%) | Acc (%) | Acc (%) | Acc (%) |
MCC | MCC | MCC | MCC | ||
Time (s) | Time (s) | Time (s) | Time (s) | ||
Fertility | 0 | 88.00 ± 2.45 | 87.00 ± 2.45 | 87.00 ± 2.45 | 88.00 ± 2.45 |
0.0000 | −0.0153 | 0.1593 | 0.000 | ||
0.0243 | 0.0331 | 0.0327 | 0.0334 | ||
0.05 | 88.00 ± 2.45 | 88.00 ± 2.45 | 88.00 ± 2.45 | 88.00 ± 2.45 | |
0.0000 | 0.0000 | −0.0306 | 0.1542 | ||
0.0239 | 0.0323 | 0.0324 | 0.0421 | ||
0.1 | 88.00 ± 2.45 | 88.00 ± 2.45 | 87.00 ± 2.45 | 88.00 ± 2.45 | |
0.0000 | 0.0000 | 0.0501 | 0.000 | ||
0.0232 | 0.0332 | 0.0332 | 0.0340 | ||
Banknote | 0 | 98.90 ± 0.89 | 99.48 ± 0.72 | 99.34 ± 0.58 | 100.00 ± 0.00 |
0.9780 | 0.9898 | 0.9868 | 1.000 | ||
0.1315 | 0.1907 | 0.2853 | 0.2806 | ||
0.05 | 98.90 ± 0.89 | 99.34 ± 0.99 | 99.42 ± 0.55 | 100.00 ± 0.00 | |
0.9780 | 0.9870 | 0.9882 | 1.000 | ||
0.1447 | 0.2174 | 0.2851 | 0.2734 | ||
0.1 | 98.76 ± 1.14 | 99.34 ± 0.81 | 99.49 ± 0.50 | 100.00 ± 0.00 | |
0.9752 | 0.9869 | 0.9897 | 1.000 | ||
0.1388 | 0.2004 | 0.2735 | 0.2652 | ||
Bupa | 0 | 68.11 ± 3.77 | 70.72 ± 3.59 | 70.14 ± 5.31 | 70.72 ± 6.37 |
0.3249 | 0.3917 | 0.3823 | 0.3749 | ||
0.0357 | 0.0387 | 0.0589 | 0.0580 | ||
0.05 | 68.41 ± 4.14 | 70.14 ± 4.05 | 70.43 ± 4.98 | 71.01 ± 5.86 | |
0.3313 | 0.3787 | 0.3861 | 0.3848 | ||
0.0404 | 0.0416 | 0.0571 | 0.0612 | ||
0.1 | 68.41 ± 4.61 | 70.43 ± 3.12 | 70.72 ± 5.05 | 70.43 ± 4.72 | |
0.3312 | 0.3857 | 0.3929 | 0.3773 | ||
0.0358 | 0.0464 | 0.0560 | 0.0624 | ||
Ionosphere | 0 | 85.18 ± 4.93 | 87.47 ± 2.07 | 86.03 ± 3.58 | 87.46 ± 2.63 |
0.6781 | 0.7332 | 0.6990 | 0.7245 | ||
0.0412 | 0.0573 | 0.0525 | 0.0457 | ||
0.05 | 84.03 ± 6.50 | 86.32 ± 1.96 | 87.75 ± 1.13 | 88.88 ± 3.45 | |
0.6505 | 0.7077 | 0.7413 | 0.7613 | ||
0.0419 | 0.0502 | 0.0535 | 0.0481 | ||
0.1 | 82.32 ± 3.93 | 85.46 ± 4.49 | 87.45 ± 4.84 | 87.46 ± 1.69 | |
0.6174 | 0.6856 | 0.7305 | 0.7266 | ||
0.0382 | 0.0521 | 0.0478 | 0.0494 | ||
Monk-2 | 0 | 94.20 ± 4.53 | 96.05 ± 3.93 | 96.29 ± 3.41 | 96.99 ± 3.34 |
0.8919 | 0.9216 | 0.9281 | 0.9420 | ||
0.0404 | 0.0579 | 0.0748 | 0.0747 | ||
0.05 | 93.52 ± 4.42 | 95.59 ± 3.48 | 96.51 ± 3.60 | 96.52 ± 3.21 | |
0.8799 | 0.9138 | 0.9323 | 0.9327 | ||
0.0550 | 0.0584 | 0.0700 | 0.0726 | ||
0.1 | 91.44 ± 3.34 | 95.36 ± 2.45 | 95.36 ± 2.66 | 94.21 ± 3.75 | |
0.8409 | 0.9073 | 0.9072 | 0.8912 | ||
0.0385 | 0.0676 | 0.0715 | 0.0718 | ||
Pima | 0 | 76.04 ± 2.99 | 76.17 ± 2.65 | 77.21 ± 1.71 | 76.56 ± 2.60 |
0.4520 | 0.4545 | 0.4772 | 0.4624 | ||
0.0714 | 0.1229 | 0.1462 | 0.1324 | ||
0.05 | 76.04 ± 2.89 | 76.69 ± 2.33 | 77.21 ± 1.71 | 76.56 ± 2.83 | |
0.4526 | 0.4665 | 0.4776 | 0.4632 | ||
0.0779 | 0.1187 | 0.1450 | 0.1418 | ||
0.1 | 76.04 ± 2.71 | 76.30 ± 2.71 | 76.43 ± 1.52 | 76.69 ± 2.83 | |
0.4498 | 0.4756 | 0.4572 | 0.4662 | ||
0.0639 | 0.1137 | 0.1370 | 0.1359 | ||
Sonar | 0 | 68.32 ± 11.04 | 69.23 ± 9.27 | 71.21 ± 9.81 | 73.12 ± 6.82 |
0.3671 | 0.3852 | 0.4232 | 0.4663 | ||
0.0296 | 0.0388 | 0.0427 | 0.0405 | ||
0.05 | 69.71 ± 3.23 | 72.13 ± 2.32 | 73.03 ± 7.23 | 71.64 ± 2.77 | |
0.3972 | 0.4496 | 0.4600 | 0.4400 | ||
0.0285 | 0.0425 | 0.0370 | 0.0431 | ||
0.1 | 64.91 ± 1.69 | 65.92 ± 7.41 | 67.80 ± 8.41 | 69.72 ± 7.30 | |
0.2931 | 0.3145 | 0.3564 | 0.3876 | ||
0.0295 | 0.0427 | 0.0418 | 0.0395 | ||
Diabetes | 0 | 76.04 ± 4.75 | 76.82 ± 3.53 | 78.12 ± 3.64 | 78.39 ± 4.18 |
0.4445 | 0.4688 | 0.4939 | 0.5017 | ||
0.0645 | 0.1021 | 0.1357 | 0.1281 | ||
0.05 | 76.56 ± 4.45 | 76.69 ± 3.33 | 77.87 ± 4.10 | 78.39 ± 4.18 | |
0.4577 | 0.4632 | 0.4888 | 0.5015 | ||
0.0669 | 0.0927 | 0.1293 | 0.1216 | ||
0.1 | 76.69 ± 4.56 | 76.82 ± 3.28 | 78.13 ± 3.77 | 78.65 ± 4.70 | |
0.4593 | 0.4663 | 0.4958 | 0.5073 | ||
0.0703 | 0.0914 | 0.1279 | 0.1239 | ||
Spambase | 0 | 89.01 ± 1.38 | 90.04 ± 1.66 | 90.75 ± 1.29 | 90.91 ± 1.15 |
0.7688 | 0.7905 | 0.8057 | 0.8089 | ||
2.8210 | 3.9467 | 4.2431 | 3.9955 | ||
0.05 | 89.06 ± 1.08 | 89.88 ± 1.48 | 90.49 ± 1.01 | 90.56 ± 0.62 | |
0.7699 | 0.7873 | 0.8003 | 0.8018 | ||
2.7608 | 4.0191 | 3.9964 | 3.7862 | ||
0.1 | 88.16 ± 0.93 | 89.42 ± 1.30 | 89.58 ± 0.99 | 89.43 ± 0.82 | |
0.7513 | 0.7780 | 0.7808 | 0.7776 | ||
2.6906 | 3.9297 | 3.9392 | 3.6749 | ||
WDBC | 0 | 92.99 ± 0.96 | 93.32 ± 1.22 | 93.84 ± 2.31 | 94.72 ± 1.78 |
0.8499 | 0.8574 | 0.8680 | 0.8869 | ||
0.0588 | 0.0681 | 0.0893 | 0.0878 | ||
0.05 | 92.97 ± 0.96 | 93.49 ± 1.34 | 94.02 ± 2.34 | 94.99 ± 1.72 | |
0.8497 | 0.8614 | 0.8719 | 0.8907 | ||
0.0544 | 0.0736 | 0.0817 | 0.0930 | ||
0.1 | 93.33 ± 1.62 | 93.66 ± 1.32 | 94.02 ± 2.27 | 94.72 ± 1.26 | |
0.8572 | 0.8655 | 0.8722 | 0.8871 | ||
0.0605 | 0.0698 | 0.0941 | 0.0885 | ||
win/tile/loss | 27/3/0 | 23/3/4 | 23/1/6 |
Model | Mean Rank of Accuracy | Mean Rank of MCC | ||
---|---|---|---|---|
Linear | Nonlinear | Linear | Nonlinear | |
GPin-TSVM | 1.27 | 1.20 | 1.23 | 1.13 |
Lap-TSVM | 2.40 | 2.28 | 2.32 | 2.45 |
Lap-PTSVM | 3.00 | 2.97 | 3.15 | 3.10 |
LapGPin-TSVM | 3.33 | 3.55 | 3.30 | 3.32 |
Compare with LapGPin-TSVM | Negative Ranks | Positive Ranks | Test Statistics | |||||
---|---|---|---|---|---|---|---|---|
n | Mean Rank | Sum of Ranks | n | Mean Rank | Sum of Ranks | Ties | p-Value | |
Linear case | ||||||||
GPin-TSVM | 0 | NaN | 0.00 | 51 | 26.00 | 1326.00 | 1 | ≤0.001 * |
Lap-TSVM | 11 | 13.73 | 151.00 | 39 | 28.82 | 1124.00 | 2 | ≤0.001 * |
Lap-PTSVM | 15 | 18.53 | 278.00 | 35 | 28.49 | 997.00 | 2 | ≤0.001 * |
Nonlinear case | ||||||||
GPin-TSVM | 1 | 11.50 | 11.50 | 46 | 24.27 | 1116.50 | 5 | ≤0.001 * |
Lap-TSVM | 11 | 22.50 | 247.50 | 36 | 24.46 | 880.50 | 5 | ≤0.001 * |
Lap-PTSVM | 13 | 30.35 | 394.50 | 34 | 21.57 | 733.50 | 5 | 0.073 |
Compare with LapGPin-TSVM | Negative Ranks | Positive Ranks | Test Statistics | |||||
---|---|---|---|---|---|---|---|---|
n | Mean Rank | Sum of Ranks | n | Mean Rank | Sum of Ranks | Ties | p-Value | |
Linear case | ||||||||
GPin-TSVM | 1 | 1.00 | 1.00 | 26 | 14.50 | 377.00 | 3 | ≤0.001 * |
Lap-TSVM | 7 | 12.86 | 90.00 | 21 | 15.05 | 361.00 | 2 | 0.010 * |
Lap-PTSVM | 8 | 17.06 | 136.50 | 19 | 12.71 | 241.50 | 3 | 0.207 |
Nonlinear case | ||||||||
GPin-TSVM | 0 | NaN | 0.00 | 27 | 14.00 | 378.00 | 3 | ≤0.001 * |
Lap-TSVM | 4 | 7.88 | 31.50 | 23 | 15.07 | 346.50 | 3 | ≤0.001 * |
Lap-PTSVM | 6 | 15.67 | 94.00 | 23 | 14.83 | 341.00 | 1 | 0.008 * |
Dataset | Model | Fold 1 | Fold 2 | Fold 3 | Fold 4 | Fold 5 | Average Accuracy |
---|---|---|---|---|---|---|---|
Airplane vs. | GPin-TSVM | 96.79 | 97.29 | 97.58 | 96.71 | 96.83 | 97.04 ± 0.34 |
Automobile | Lap-TSVM | 97.96 | 98.46 | 98.25 | 98.33 | 98.54 | 98.31 ± 0.20 |
Lap-PTSVM | 98.00 | 98.17 | 98.17 | 97.79 | 97.79 | 97.98 ± 0.17 | |
LapGPin-TSVM | 97.92 | 97.96 | 98.29 | 97.75 | 97.96 | 97.98 ± 0.18 | |
Ship vs. | GPin-TSVM | 90.50 | 91.29 | 90.46 | 89.08 | 89.38 | 90.14 ± 0.81 |
Truck | Lap-TSVM | 97.21 | 98.42 | 97.33 | 97.67 | 97.33 | 97.59 ± 0.44 |
Lap-PTSVM | 97.92 | 98.38 | 97.38 | 97.79 | 97.75 | 97.84 ± 0.32 | |
LapGPin-TSVM | 98.08 | 98.71 | 97.54 | 97.96 | 97.83 | 98.03 ± 0.39 | |
Deer vs. | GPin-TSVM | 89.92 | 91.67 | 91.54 | 91.75 | 90.88 | 91.15 ± 0.69 |
Shore | Lap-TSVM | 91.30 | 91.88 | 91.75 | 92.83 | 91.04 | 91.76 ± 0.62 |
Lap-PTSVM | 92.71 | 92.58 | 92.46 | 92.46 | 92.08 | 92.46 ± 0.21 | |
LapGPin-TSVM | 92.54 | 92.96 | 93.29 | 92.96 | 92.50 | 92.85 ± 0.29 | |
Dog vs. | GPin-TSVM | 79.30 | 78.75 | 79.17 | 79.96 | 80.88 | 79.61 ± 0.74 |
Cat | Lap-TSVM | 83.05 | 81.71 | 83.00 | 83.04 | 84.25 | 83.01 ± 0.80 |
Lap-PTSVM | 85.46 | 83.79 | 85.96 | 85.42 | 85.75 | 85.28 ± 0.77 | |
LapGPin-TSVM | 85.26 | 84.96 | 85.83 | 86.04 | 87.67 | 85.95 ± 0.94 |
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Share and Cite
Damminsed, V.; Wangkeeree, R. Improved Generalized-Pinball-Loss-Based Laplacian Twin Support Vector Machine for Data Classification. Symmetry 2024, 16, 1373. https://doi.org/10.3390/sym16101373
Damminsed V, Wangkeeree R. Improved Generalized-Pinball-Loss-Based Laplacian Twin Support Vector Machine for Data Classification. Symmetry. 2024; 16(10):1373. https://doi.org/10.3390/sym16101373
Chicago/Turabian StyleDamminsed, Vipavee, and Rabian Wangkeeree. 2024. "Improved Generalized-Pinball-Loss-Based Laplacian Twin Support Vector Machine for Data Classification" Symmetry 16, no. 10: 1373. https://doi.org/10.3390/sym16101373
APA StyleDamminsed, V., & Wangkeeree, R. (2024). Improved Generalized-Pinball-Loss-Based Laplacian Twin Support Vector Machine for Data Classification. Symmetry, 16(10), 1373. https://doi.org/10.3390/sym16101373