Table 8.

Performance comparison of RHN-TSVR with SVR, TSVR, $\epsilon$-AHSVR, $\epsilon$-SVQR and HN-TSVR using Gaussian kernel with noise 0% on real world datasets

Dataset (Train size, Test size)	SVR RMSE $(C,\epsilon ,\mu )$ Time	TSVR RMSE $(C_1=C_2,$ $\epsilon ,\mu )$ Time	$\epsilon$-AHSVR RMSE $(C,{\epsilon }_{\alpha }={\epsilon }_{\beta },{\zeta }_{\alpha },$ ${\zeta }_{\beta },\mu )$ Time	$\epsilon$-SVQR RMSE $(C,\epsilon ,$ $\theta ,\mu )$ Time	HN-TSVR RMSE $(C_1=C_2,{\epsilon }_1={\epsilon }_2,$${\epsilon }_1^{\ast }={\epsilon }_2^{\ast },\mu )$ Time	RHN-TSVR RMSE $(C_1=C_2,{\epsilon }_1={\epsilon }_2,$ ${\epsilon }_1^{\ast }={\epsilon }_2^{\ast },\mu )$ Time
Forestfires (150X13,367X13)	0.07059 (10−3, 0.1,25) 0.55583	0.07058 (10−4,0.1,25) 0.063014	0.070592 (10−5,10−3, 0.1, 0.1, 21) 0.09428	0.070476 (101,0.1, 0.1, 2−5) 0.02012	0.07058 (10−5, 0.5, 0.5, 25) 0.25727	0.07059 (105,105, 0.3, 0.3, 2−5) 0.0125241
Machine CPU (100X8,109X8)	0.03506 (104, 0.1,2−2) 0.24525	0.02102 (103,0.9,2−2) 0.041461	0.050225 (105,10−1, 0.1, 0.1, 2−3) 0.332	0.036146 (101,0.1, 0.7, 2−5) 0.00977	0.03035 (103, 0.9, 0.5, 2−1) 0.20161	0.01579 (103,10−5, 0.9, 0.3, 2−3) 0.0107687
Auto-original (100X8,292X8)	0.33338 (100, 0.1,21) 0.2708	0.29912 (10−2,0.1,20) 0.033108	0.171313 (101,10−1, 0.1, 1, 2−5) 0.06359	0.260394 (101,0.1, 0.7, 2−1) 0.01014	0.29899 (10−1, 0.1, 0.1, 20) 0.04945	0.29899 (10−1,10−3, 0.1, 0.1, 20) 0.0126264
Winequality (500X12,4398X12)	0.13377 (102, 0.1,2−3) 6.31838	0.13437 (10−5,0.7,2−1) 0.719632	0.130454 (105,10−1, 0.1, 1, 2−3) 0.13756	0.132434 (103,0.1, 0.5, 2−5) 0.47543	0.135 (100, 0.1, 0.1, 2−1) 0.61889	0.13486 (100,10−5, 0.1, 0.1, 2−3) 0.0832587
SantafeA (500X6,495X6)	0.05654 (100, 0.1,22) 5.59668	0.03811 (10−1,0.9,23) 0.758993	0.081809 (103,10−2, 0.1, 1, 21) 0.1015	0.039983 (103,0.1, 0.5, 2−1) 0.86175	0.03922 (100, 0.9, 0.1, 23) 0.64863	0.0375 (105,10−5, 0.1, 0.7, 23) 0.113057
Gas_furnace (150X7,143X7)	0.07154 (105, 0.1,2−5) 0.47456	0.04394 (102,0.1,2−4) 0.068103	0.084165 (101,10−1, 0.1, 1, 2−3) 0.05107	0.05659 (103,0.1, 0.2, 2−3) 0.0444	0.04158 (101, 0.1, 0.1, 2−3) 0.08725	0.0383 (100,10−5, 0.1, 0.3, 2−5) 0.0174328
Quake (500X4,1678X4)	0.17349 (10−1, 0.1,2−2) 9.48833	0.17227 (100,0.9,2−5) 0.758743	0.17214 (10−1,10−1, 0.1, 0.1, 2−3) 0.14973	0.172642 (10−3,0.1, 0.7, 2−3) 0.36931	0.17219 (100, 0.9, 0.3, 2−5) 0.82559	0.17224 (100,101, 0.9, 0.3, 2−5) 0.0794874
Flex_robotarm (500X10,519X10)	0.04337 (103, 0.1,2−5) 9.5114	0.03595 (101,0.1,2−1) 0.795891	0.056807 (105,10−1, 0.1, 0.1, 2−5) 0.0878	0.025886 (105,0.1, 0.4, 2−5) 0.24667	0.03595 (103, 0.1, 0.9, 2−1) 1.20655	0.02046 (103,10−5, 0.9, 0.7, 2−1) 0.10096
S&P500 (200X6,550X6)	0.19605 (105, 0.1,2−1) 1.41245	0.13739 (10−1,0.9,21) 0.113956	0.255194 (10−1,10−1, 0.1, 1, 2−1) 0.02659	0.095518 (103,0.1, 0.8, 2−3) 0.04174	0.13983 (101, 0.9, 0.1, 21) 0.33202	0.13355 (100,10−5, 0.1, 0.3, 2−1) 0.0243076
Space-Ga (500X7,2607X7)	0.30306 (10−1, 0.1,2−1) 9.72392	0.29628 (10−3,0.1,25) 0.697419	0.30902 (101,10−1, 0.1, 1, 25) 0.09576	0.285357 (10−1,0.1, 0.6, 2−1) 0.39695	0.29628 (10−5, 0.1, 0.1, 25) 0.92673	0.29306 (100,10−1, 0.9, 0.1, 25) 0.107667
Gauss1 (75X2,175X2)	0.738274 (105,0.1,2−5) 0.12142	0.479003 (103, 0.9, 23) 0.01401	0.738025 (103,10−1, 0.1, 0.1, 23) 0.00066	0.645752 (105,0.1, 0.8, 2−5) 0.00861	0.478936 (105, 0.9, 0.5, 23) 0.02833	0.619614 (101,101, 0.9, 0.9, 23) 0.0061953
Chwirut2 (17X2,37X2)	0.120144 (100,0.1,25) 0.00941	0.078331 (10−5, 0.5, 25) 0.01558	0.131455 (101,10−1, 0.1, 1, 25) 0.00014	0.10763 (101,0.1, 0.3, 25) 0.00408	0.078332 (10−5, 0.3, 0.7, 25) 0.02219	0.101378 (103,10−5, 0.9, 0.7, 23) 0.0053057
Roszman1 (8X2,17X2)	0.833004 (102,0.1,25) 0.00441	0.147794 (10−5, 1, 20) 0.01062	0.704285 (102,10−1, 0.1, 1, 25) 0.00009	0.774556 (101,0.1, 0.3, 25) 0.00621	0.147779 (10−5, 1, 0.7, 20) 0.02386	0.955187 (103,10−5, 1, 0.7, 20) 0.0039767
INFY (226X6,525X6)	0.061211 (103,0.1,2−5) 0.98812	0.040511 (10−1, 0.9, 2−3) 0.0482	0.047693 (105,10−1, 0.1, 1, 2−5) 0.02781	0.041628 (103,0.1, 0.5, 2−5) 0.05389	0.040633 (100, 0.9, 0.1, 2−3) 0.06636	0.040282 (10−1,10−5, 0.9, 0.1, 2−5) 0.0205775
ONGC_NS (221X6,514X6)	0.029434 (101,0.1,2−5) 0.91666	0.028493 (100, 0.1, 2−3) 0.05983	0.044317 (103,10−1, 0.1, 1, 2−5) 0.02583	0.02502 (103,0.1, 0.5, 2−5) 0.05644	0.029634 (101, 0.9, 0.1, 2−3) 0.06879	0.023333 (101,10−5, 0.1, 0.1, 2−5) 0.0232562
XOM (226X6,525X6)	0.03609 (101,0.1,2−3) 0.97152	0.033274 (10−1, 0.1, 2−3) 0.04656	0.05045 (105,10−1, 0.1, 1, 2−3) 0.034	0.033264 (101,0.1, 0.5, 2−3) 0.05051	0.033344 (10−1, 0.1, 0.7, 2−3) 0.05523	0.032806 (10−3,10−5, 0.1, 0.1, 2−5) 0.0252035
ATX (222X6,515X6)	0.413258 (10−1,0.1,20) 0.93081	0.155567 (10−1, 0.1, 2−1) 0.04733	0.475983 (10−1,10−1, 0.1, 1, 21) 0.03145	0.129202 (103,0.1, 0.2, 2−3) 0.05126	0.161982 (100, 0.1, 0.3, 2−1) 0.09139	0.067275 (10−1,10−5, 0.9, 0.7, 2−3) 0.0260819
BSESN (220X6,513X6)	0.197459 (100,0.1,2−1) 0.92109	0.080313 (10−1, 0.1, 2−1) 0.05851	0.117697 (101,10−1, 0.1, 1, 2−3) 0.0298	0.034469 (103,0.1, 0.7, 2−5) 0.04303	0.08503 (100, 0.1, 0.3, 2−1) 0.0663	0.04276 (10−1,10−5, 0.1, 0.1, 2−3) 0.0254383
DJI (226X6,525X6)	0.437188 (10−1,0.1,21) 0.98217	0.252219 (10−1, 0.1, 2−1) 0.05257	0.445899 (10−1,10−1, 0.1, 0.1, 21) 0.02312	0.134225 (101,0.1, 0.8, 2−5) 0.04319	0.304002 (10−1, 0.1, 0.1, 20) 0.06687	0.106785 (100,10−5, 0.1, 0.1, 2−3) 0.0278918
GDAXI (227X6,528X6)	0.033826 (105,0.1,2−5) 1.00256	0.032456 (100, 0.9, 2−3) 0.06494	0.059894 (103,10-1, 0.1, 1, 2−5) 0.03418	0.050758 (101,0.1, 0.6, 2−1) 0.05458	0.036447 (101, 0.9, 0.3, 2−3) 0.07007	0.028567 (10−1,10−5, 0.9, 0.1, 2−5) 0.0259832
MXX (225X6,525X6)	0.096186 (105,0.1,2−5) 0.98059	0.207771 (10−3, 0.9, 2−1) 0.0454	0.15942 (105,10−1, 0.1, 1, 2−3) 0.02529	0.170982 (103,0.1, 0.5, 2−3) 0.05175	0.208147 (10−1, 0.1, 0.1, 2−1) 0.07338	0.070677 (10−1,10−5, 0.1, 0.1, 2−3) 0.0260515
N225 (220X6,512X6)	0.100205 (105,0.1,2−3) 0.94593	0.0391 (10−1, 0.9, 2−3) 0.04503	0.215338 (10−1,10−1, 0.1, 1, 21) 0.01587	0.032827 (103,0.1, 0.7, 2−5) 0.04882	0.040257 (100, 0.1, 0.1, 2−3) 0.07263	0.032986 (10−1,10−5, 0.1, 0.1, 2−5) 0.0236554
Wankara (97X10,224X10)	0.056582 (103,0.1,20) 0.18213	0.025151 (10−1, 0.9, 2−3) 0.02217	0.059292 (103,10−1, 0.1, 0.1, 2−5) 0.00379	0.031492 (103,0.1, 0.2, 2−3) 0.01671	0.025243 (101, 0.9, 0.7, 2−3) 0.03012	0.024392 (101,10−5, 0.1, 0.1, 2−3) 0.014395
Laser (298X5,695X5)	0.057145 (103,0.1,2−3) 1.72804	0.036527 (10−1, 0.9, 23) 0.08	0.076187 (105,10−2, 0.1, 0.1, 2−3) 0.04045	0.039881 (101,0.1, 0.4, 21) 0.18004	0.037124 (103, 0.9, 0.1, 23) 0.14206	0.037946 (103,10−5, 0.1, 0.9, 23) 0.0432735
Dee (110X7,255X7)	0.104984 (100,0.1,2−3) 0.22914	0.142128 (100, 0.1, 2−5) 0.02127	0.129019 (101,10−1, 1, 0.1, 2−3) 0.00309	0.101998 (101,0.1, 0.7, 2−5) 0.02589	0.145534 (101, 0.1, 0.1, 2−5) 0.03195	0.102515 (101,10−1, 0.9, 0.1, 2−3) 0.0154981
Friedman (360X6,840X6)	0.058623 (103,0.1,2−1) 2.57757	0.044491 (10−5, 0.1, 20) 0.12724	0.067515 (103,10−1, 0.1, 1, 2−1) 0.08704	0.045422 (105,0.1, 0.5, 2−5) 0.24806	0.044433 (100, 0.1, 0.5, 20) 0.18492	0.043238 (10−5,10−5, 0.1, 0.3, 2−1) 0.0423292
Mortgage (315X16,734X16)	0.047516 (103,0.1,2−1) 1.97172	0.007537 (103, 0.9, 20) 0.11881	0.061293 (101,10−1, 0.1, 0.1, 2-5) 0.05237	0.024022 (101,0.1, 0.8, 2−3) 0.2937	0.007581 (101, 0.9, 0.1, 20) 0.21581	0.00775 (10−1,10−5, 0.9, 0.3, 21) 0.0464666
NNGC1_dataset_E1_V1_001 (111X5,259X5)	0.182661 (101,0.1,21) 0.2343	0.180173 (10−1, 0.9, 21) 0.01953	0.172927 (101,10−1, 0.1, 1, 23) 0.00626	0.181204 (101,0.1, 0.6, 21) 0.01454	0.180518 (100, 0.1, 0.1, 21) 0.02345	0.17386 (100,100, 0.9, 0.1, 23) 0.0142513
NNGC1_dataset_F1_V1_008 (269X5,626X5)	0.123395 (101,0.1,25) 1.41931	0.073928 (103, 0.1, 25) 0.13796	0.114369 (101,10−1, 0.1, 1, 25) 0.02353	0.104162 (101,0.1, 0.5, 25) 0.07411	0.073928 (105, 0.1, 0.5, 25) 0.10784	0.073928 (105,10−3, 0.1, 0.5, 25) 0.0428835
NNGC1_dataset_F1_V1_009 (269X5,626X5)	0.092724 (105,0.1,21) 1.44621	0.06457 (10−3, 0.9, 25) 0.07942	0.092574 (105,10−1, 0.1, 1, 21) 0.02105	0.076728 (101,0.1, 0.7, 23) 0.0875	0.064281 (10−1, 0.9, 0.1, 25) 0.08413	0.064281 (10−1,10−3, 0.9, 0.1, 25) 0.0320651
NNGC1_dataset_F1_V1_010 (269X5,626X5)	0.086069 (105,0.1,2−3) 1.41684	0.044163 (10−3, 0.9, 25) 0.10058	0.084937 (105,10−1, 0.1, 1, 21) 0.01928	0.06221 (101,0.1, 0.7, 23) 0.07695	0.04426 (100, 0.1, 0.1, 25) 0.0761	0.04426 (100,10−3, 0.1, 0.1, 25) 0.0402401
NNGC1_dataset_F1_V1_006 (521X5,1214X5)	0.060847 (105,0.1,2−1) 5.75965	0.037313 (10−1, 0.9, 25) 0.31331	0.065632 (105,10−1, 0.1, 1, 21) 0.08754	0.045866 (101,0.1, 0.6, 23) 0.3148	0.037242 (100, 0.9, 0.1, 25) 0.28168	0.037242 (100,10−3, 0.9, 0.1, 25) 0.10657
NN5_Complete_109 (237X5,550X5)	0.109583 (100,0.1,23) 1.09254	0.107237 (10−1, 0.9, 23) 0.06317	0.110924 (101,10−1, 0.1, 0.1, 23) 0.01518	0.102385 (101,0.1, 0.6, 23) 0.05181	0.106897 (100, 0.1, 0.1, 23) 0.07392	0.095636 (100,100, 0.3, 0.1, 25) 0.026553
NN5_Complete_104 (237X5,550X5)	0.174167 (10−1,0.1,23) 1.07709	0.144628 (10−3, 0.1, 23) 0.05759	0.153973 (101,10−1, 0.1, 1, 25) 0.01743	0.154479 (101,0.1, 0.8, 23) 0.05446	0.143688 (100, 0.9, 0.1, 23) 0.06773	0.142988 (100,100, 0.1, 0.1, 25) 0.030209
NN5_Complete_106 (237X5,550X5)	0.189308 (100,0.1,23) 1.10129	0.174154 (10−1, 0.1, 23) 0.06459	0.165296 (101,10−1, 0.1, 1, 25) 0.01407	0.187904 (101,0.1, 0.6, 23) 0.05242	0.171795 (10−1, 0.1, 0.1, 23) 0.06597	0.15994 (100,100, 0.9, 0.1, 25) 0.0335387
NN5_Complete_103 (237X5,550X5)	0.128696 (100,0.1,2−1) 1.08169	0.130192 (100, 0.1, 2−1) 0.06974	0.131486 (101,10−1, 0.1, 0.1, 21) 0.02025	0.128318 (101,0.1, 0.4, 2−3) 0.06604	0.129899 (10−5, 0.1, 0.3, 2−1) 0.06392	0.129068 (100,10−1, 0.1, 0.3, 20) 0.027654
NN5_Complete_101 (237X5,550X5)	0.149576 (100,0.1,21) 1.08068	0.154734 (100, 0.9, 20) 0.06989	0.150469 (101,10−1, 0.1, 0.1, 23) 0.01455	0.14708 (101,0.1, 0.6, 21) 0.05376	0.155191 (101, 0.1, 0.1, 20) 0.06886	0.144747 (100,100, 0.9, 0.1, 23) 0.0264708
NN5_Complete_105 (237X5,550X5)	0.127845 (100,0.1,21) 1.08763	0.13341 (10−1, 0.9, 21) 0.04819	0.130747 (101,10−1, 1, 0.1, 23) 0.0148	0.129324 (101,0.1, 0.4, 21) 0.0635	0.134297 (100, 0.1, 0.1, 21) 0.09553	0.126683 (100,100, 0.9, 0.1, 25) 0.031413
NN5_Complete_111 (237X5,550X5)	0.089431 (100,0.1,23) 1.09501	0.092115 (10−5, 0.9, 23) 0.07277	0.087204 (101,10−1, 0.1, 0.1,25) 0.0199	0.094835 (101,0.1, 0.2, 23) 0.0468	0.092115 (10−5, 0.1, 0.1, 23) 0.06021	0.08508 (10−1,100, 0.1, 0.1, 25) 0.0297235
D1dat_1_2000 (599X5,1396X5)	0.091946 (103,0.1,2−1) 7.51017	0.135055 (10−1, 0.9, 23) 0.51861	0.10349 (103,10−1, 0.1, 1, 2−3) 0.10285	0.115531 (103,0.1, 0.4, 21) 0.39425	0.145437 (100, 0.1, 0.9, 23) 0.32529	0.121417 (10−1,10−5, 0.1, 0.1, 21) 0.117241
Vineyard (16X4,36X4)	0.141193 (100,0.1,20) 0.00798	0.298839 (100, 0.9, 2−1) 0.01456	0.234064 (101,10−1, 0.1, 0.1, 21) 0.00015	0.188534 (101,0.1, 0.1, 21) 0.00692	0.241009 (101, 0.9, 0.3, 2−3) 0.01197	0.240423 (100,101, 0.9, 0.5, 21) 0.0103753
COVID-19_spain (251X5,585X5)	0.167119 (103,0.1,21) 1.21284	0.154007 (10−3, 0.5, 25) 0.07972	0.167119 (10−5,10−3, 0.1, 0.1, 2−5) 0.01419	0.156555 (105,0.1, 0.7, 25) 0.04876	0.154173 (10−1, 0.1, 0.9, 25) 0.04778	0.154061 (10−5,10-5, 0.9, 0.1, 25) 0.024674

The best result is shown as boldface