Table 10.

Performance comparison of SVR, TSVR, $\epsilon$-AHSVR, $\epsilon$-SVQR, HN-TSVR and RHN-TSVR using Gaussian kernel with noise 5% 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)	0.070592 (10−5, 0.1,25) 0.229976	0.0842079 (10−4, 0.9, 25) 0.09435	0.070588 (10−5,10−3, 0.1, 0.1, 25) 0.0112	0.069557 (10−1,0.9, 0.1, 25) 0.08134	0.08422 (103, 0.9, 0.1, 25) 0.22418	0.07057 (10−5,105, 0.9, 0.1, 25) 0.012158
Machine CPU (100X8,109X8)	0.052104 (105, 0.1,2−5) 0.11723	0.0485319 (10−1, 0.1, 2−2) 0.04732	0.07941 (105,10−3, 0.1, 0.1, 2−3) 0.0042	0.072152 (105,0.1, 0.5, 2−5) 0.04398	0.05934 (100,0.1, 0.1, 2−1) 0.05237	0.04173 (100,10−5, 0.1, 0.1, 2−3) 0.0118531
Auto-original (100X8,292X8)	0.155361 (103, 0.1,2−5) 0.100113	0.16358 (10−2, 0.9, 2−1) 0.04578	0.156916 (103,10−1, 0.1, 1, 2−1) 0.01078	0.157831 (101,0.1, 0.5, 2−3) 0.04071	0.1639 (10−1, 0.1, 0.5, 2−1) 0.13337	0.15585 (100,10−5, 0.1, 0.1, 2−3) 0.0137573
Winequality (500X12,4398X12)	0.158162 (100, 0.1,2−1) 2.7085	0.181833 (10−1, 0.9, 2−2) 0.92887	0.160284 (103,10−1, 0.1, 0.1, 2−3) 0.1069	0.225503 (103,0.1, 0.5, 2−5) 1.41081	0.17557 (100, 0.9, 0.3, 2−3) 0.991	0.1538 (100,10−1, 0.9, 0.1, 20) 0.0646298
SantafeA (500X6,495X6)	0.10608 (100, 0.1,23) 3.07441	0.0665399 (10−1, 0.9, 22) 0.84628	0.061044 (105,10−2, 0.1, 1, 21) 0.13854	0.082625 (101,0.1, 0.4, 23) 1.50956	0.06684 (10−1, 0.9, 0.1, 23) 0.97786	0.06568 (100,10−5, 0.9, 0.1, 21) 0.0511625
Gas_furnace (150X7,143X7)	0.094555 (100, 0.1,2−3) 0.228517	0.0603093 (10−1, 0.7, 2−4) 0.09493	0.061808 (105,10−3, 0.1, 1, 2−5) 0.01632	0.080781 (101,0.1, 0.1, 2−5) 0.09148	0.05582 (100, 0.1, 0.1, 2−3) 0.11075	0.04891 (100,10−5, 0.1, 0.1, 2−5) 0.0181955
Quake (500X4,1678X4)	0.186957 (10−1, 0.1,2−1) 2.76314	0.185072 (100, 0.9, 2−5) 0.82747	0.185139 (10−1,10−1, 0.1, 0.1, 2−3) 0.15029	0.19368 (10−1,0.5, 0.1, 2−5) 1.63681	0.1851 (100, 0.9, 0.3, 2−5) 0.91814	0.18506 (100,101, 0.1, 0.3, 2−5) 0.0648712
Flex_robotarm (500X10,519X10)	0.044356 (103, 0.1,2−5) 2.91903	0.0455536 (10−1, 0.9, 2−1) 0.88575	0.056341 (105,10−1, 0.1, 0.1, 2−5) 0.11533	0.029939 (103,0.1, 0.1, 2−5) 1.56187	0.04608 (100, 0.9, 0.1, 2−1) 0.92991	0.02582 (100,10−5, 0.9, 0.1, 2−1) 0.0688442
S&P500 (200X6,550X6)	0.039455 (101, 0.1,2−5) 0.413842	0.0264072 (10−1, 0.9, 2−5) 0.15642	0.045908 (105,10−1, 0.1, 1, 2−5) 0.02588	0.027269 (103,0.1, 0.4, 2−5) 0.191	0.02683 (100, 0.1, 0.1, 2−5) 0.17724	0.02663 (10−1,10−5, 0.1, 0.1, 2−5) 0.0197694
Space-Ga (500X7,2607X7)	0.29754 (100, 0.1,2−5) 2.78144	0.327565 (100, 0.1, 25) 1.01007	0.292501 (101,10−1, 1, 0.1, 2−5) 0.12059	0.273409 (10−1,0.1, 0.6, 2−1) 1.32311	0.33016 (100, 0.1, 0.1, 25) 0.97394	0.28284 (100,10−1, 0.9, 0.1, 25) 0.0719253
Gauss1 (75X2,175X2)	0.399263 (101, 0.1,2−5) 0.062618	0.391528 (103, 0.9, 20) 0.01613	0.414253 (103,10−1, 0.1, 1.345, 2−5) 0.0006	0.409457 (101,0.5, 0.7, 21) 0.01021	0.391532 (105, 0.9, 0.1, 20) 0.02981	0.389198 (103,10 −1, 0.1, 0.3, 21) 0.0072498
Chwirut2 (17X2,37X2)	0.097839 (103, 0.1,23) 0.005741	0.116295 (10−1, 0.9, 2−3) 0.01351	0.093916 (101,10−3, 0.1, 1, 25) 0.0002	0.087731 (105,0.3, 0.3, 23) 0.00406	0.114574 (100, 0.9, 0.3, 2−3) 0.02547	0.108905 (101,10 −5, 0.1, 0.1, 23) 0.004341
Roszman1 (8X2,17X2)	0.079154 (102, 0.0001,23) 0.002892	0.049779 (10−1, 1, 20) 0.01399	0.212352 (102,10−3, 0.1, 1, 25) 0.00008	0.292596 (105,0.3, 0.3, 23) 0.00387	0.047258 (100, 1, 0.3, 20) 0.02349	0.048173 (101,10−5, 1, 0.1, 20) 0.004168
INFY (226X6,525X6)	0.048422 (103, 0.1,2−5) 0.512362	0.044445 (100, 0.3, 2−5) 0.06776	0.050969 (105,10−1, 0.1, 1, 2−5) 0.02874	0.046417 (103,0.1, 0.6, 2−3) 0.05323	0.043197 (100, 0.9, 0.1, 2−5) 0.05714	0.043197 (100,10−3, 0.9, 0.1, 2−5) 0.0147357
ONGC_NS (221X6,514X6)	0.040992 (103, 0.1,2−5) 0.545728	0.036287 (100, 0.1, 2−5) 0.05809	0.045566 (105,10−1, 0.1, 0.1, 2−5) 0.02695	0.035167 (103,0.1, 0.4, 2−5) 0.05503	0.036136 (101, 0.9, 0.1, 2−5) 0.06659	0.035021 (100,10−5, 0.9, 0.1, 2−5) 0.0200796
XOM (226X6,525X6)	0.044282 (101, 0.1,2−3) 0.52792	0.040461 (10−3, 0.9, 2−3) 0.05028	0.046998 (103,10−1, 0.1, 0.1, 2−3) 0.01829	0.040378 (101,0.1, 0.5, 2−3) 0.05652	0.040412 (10−1, 0.1, 0.1, 2−3) 0.10638	0.040412 (10−1,10−3, 0.1, 0.1, 2−3) 0.0254784
ATX (222X6,515X6)	0.027291 (101, 0.1,2−3) 0.512387	0.025448 (100, 0.9, 2−5) 0.05701	0.037052 (103,10−1, 0.1, 1, 2−3) 0.03231	0.02157 (103,0.1, 0.4, 2−3) 0.04981	0.023878 (100, 0.5, 0.1, 2−5) 0.06775	0.024036 (100,10−5, 0.9, 0.1, 2−5) 0.020381
BSESN (220X6,513X6)	0.027462 (101, 0.1,2−3) 0.529594	0.02329 (10−1, 0.9, 2−5) 0.05242	0.030826 (105,10−1, 0.1, 1, 2−5) 0.01959	0.025185 (101,0.1, 0.6, 2−5) 0.04508	0.023207 (100, 0.9, 0.1, 2−5) 0.06566	0.022333 (100,10−5, 0.9, 0.1, 2−5) 0.0285901
DJI (226X6,525X6)	0.024042 (101, 0.1,2−5) 0.541827	0.02023 (10−1, 0.9, 2−5) 0.04965	0.021978 (103,10−1, 0.1, 1, 2−3) 0.01969	0.040544 (101,0.1, 0.7, 2−3) 0.0463	0.019661 (100, 0.1, 0.1, 2−5) 0.06078	0.019661 (100,10−3, 0.1, 0.1, 2−5) 0.0217884
GDAXI (227X6,528X6)	0.029271 (101, 0.1,2−5) 0.615071	0.028296 (10−1, 0.1, 2−5) 0.05101	0.032066 (103,10−1, 1, 1, 2−5) 0.03326	0.026 (103,0.1, 0.5, 2−5) 0.05606	0.028228 (100, 0.9, 0.1, 2−5) 0.07403	0.027102 (100,10−5, 0.9, 0.1, 2−5) 0.0287863
MXX (225X6,525X6)	0.042338 (101, 0.1,2−3) 0.559407	0.03836 (10−1, 0.9, 2−3) 0.04882	0.044005 (103,10−1, 0.1, 1, 2−3) 0.01992	0.040381 (101,0.1, 0.6, 2−3) 0.0505	0.038028 (100, 0.1, 0.1, 2−3) 0.12634	0.036046 (100,10−5, 0.1, 0.1, 2−5) 0.0187388
N225 (220X6,512X6)	0.03575 (101, 0.1,2−5) 0.497952	0.033073 (10−1, 0.9, 2−5) 0.0423	0.034927 (103,10−1, 1, 1, 2−3) 0.02333	0.034832 (101,0.1, 0.5, 2−3) 0.0498	0.032898 (100, 0.1, 0.1, 2−5) 0.04164	0.033887 (100,10−5, 0.1, 0.1, 2−5) 0.0189589
Wankara (97X10,224X10)	0.064073 (105, 0.1,2−5) 0.095646	0.029472 (10−1, 0.9, 2−3) 0.01693	0.039629 (103,10−2, 0.1, 0.1, 2−5) 0.00491	0.034031 (101,0.1, 0.1, 2−1) 0.01904	0.030836 (10−1, 0.1, 0.1, 2−3) 0.02922	0.030752 (100,10−5, 0.1, 0.1, 2−5) 0.0168666
Laser (298X5,695X5)	0.081302 (100, 0.1,21) 1.08662	0.04679 (10−1, 0.1, 23) 0.10288	0.051436 (103,10−3, 1, 1, 21) 0.04178	0.058167 (105,0.1, 0.4, 2−5) 0.29224	0.042864 (100, 0.1, 0.1, 21) 0.08458	0.040318 (100,10−5, 0.1, 0.1, 21) 0.0288311
Dee (110X7,255X7)	0.107666 (100, 0.1,20) 0.12765	0.108599 (100, 0.9, 2−5) 0.01828	0.100024 (101,10−1, 1, 0.1, 2−3) 0.0039	0.107159 (101,0.1, 0.3, 2−1) 0.01765	0.109692 (101, 0.9, 0.1, 2−5) 0.02564	0.104123 (101,10−1, 0.9, 0.1, 2−5) 0.0134618
Friedman (360X6,840X6)	0.061985 (101, 0.1,2−1) 1.33317	0.050917 (10−1, 0.9, 2−1) 0.12606	0.070737 (103,10−1, 1, 1, 2−1) 0.05842	0.049461 (105,0.1, 0.3, 2−5) 0.42496	0.051177 (100, 0.1, 0.1, 2−1) 0.1547	0.049195 (10−5,10−5, 0.1, 0.1, 2−1) 0.0283486
Mortgage (315X16,734X16)	0.056068 (100, 0.1,2−5) 1.05694	0.018067 (10−1, 0.1, 2−1) 0.10178	0.037756 (103,10−3, 0.1, 1, 2−5) 0.05046	0.041226 (101,0.1, 0.6, 21) 0.46162	0.018797 (100, 0.1, 0.1, 2−1) 0.10658	0.01766 (100,10 -5, 0.1, 0.1, 2−3) 0.0292358
NNGC1_dataset_E1_V1_001 (111X5,259X5)	0.174273 (100, 0.1,21) 0.119395	0.180527 (10−1, 0.1, 21) 0.01801	0.174901 (101,10−1, 0.1, 1, 23) 0.00866	0.181674 (101,0.1, 0.4, 21) 0.01282	0.180662 (100, 0.9, 0.1, 21) 0.0269	0.174368 (100,100, 0.9, 0.1, 23) 0.017439
NNGC1_dataset_F1_V1_008 (269X5,626X5)	0.077357 (101, 0.1,23) 0.737512	0.057912 (10−1, 0.9, 25) 0.1161	0.069382 (101,10−2, 0.1, 1.345, 25) 0.02783	0.061483 (101,0.1, 0.4, 25) 0.07307	0.057788 (10−1, 0.9, 0.1, 25) 0.07614	0.057788 (10−1,10−3, 0.9, 0.1, 25) 0.0272107
NNGC1_dataset_F1_V1_009 (269X5,626X5)	0.077045 (103, 0.1,2−1) 0.735128	0.050753 (10−1, 0.9, 23) 0.10377	0.080904 (101,10−1, 0.1, 1, 25) 0.02837	0.055231 (101,0.1, 0.5, 23) 0.06838	0.051426 (100, 0.9, 0.1, 23) 0.09655	0.048986 (100,10−1, 0.9, 0.1, 25) 0.022648
NNGC1_dataset_F1_V1_010 (269X5,626X5)	0.073579 (103, 0.1,21) 0.745154	0.044397 (10−1, 0.9, 23) 0.12389	0.068758 (103,10−2, 0.1, 1, 23) 0.03004	0.057324 (103,0.1, 0.3, 21) 0.08042	0.045481 (100, 0.9, 0.1, 23) 0.07167	0.05176 (10−1,10−5, 0.1, 0.1, 23) 0.0318337
NNGC1_dataset_F1_V1_006 (521X5,1214X5)	0.063795 (103, 0.1,21) 3.01858	0.041367 (10−1, 0.9, 25) 0.37961	0.06495 (103,10−1, 0.1, 0.1, 23) 0.08197	0.049231 (101,0.1, 0.3, 23) 0.28967	0.042234 (10−1, 0.9, 0.1, 25) 0.24892	0.047416 (100,10−5, 0.9, 0.1, 23) 0.0936319
NN5_Complete_109 (237X5,550X5)	0.160178 (100, 0.1,21) 0.559677	0.169086 (10−1, 0.1, 21) 0.07075	0.153803 (101,10−1, 0.1, 0.1, 23) 0.0163	0.167964 (101,0.1, 0.5, 21) 0.06157	0.170163 (100, 0.1, 0.1, 21) 0.07691	0.159525 (100,100, 0.1, 0.1, 23) 0.0250756
NN5_Complete_104 (237X5,550X5)	0.25227 (100, 0.1,21) 0.557894	0.246728 (10−1, 0.9, 20) 0.08172	0.223425 (101,10−1, 0.1, 1, 25) 0.01747	0.243549 (101,0.1, 0.6, 21) 0.06105	0.245921 (100, 0.9, 0.1, 20) 0.08696	0.226614 (100,100, 0.9, 0.1, 25) 0.0190927
NN5_Complete_106 (237X5,550X5)	0.212644 (101, 0.1,21) 0.563886	0.227166 (10−3, 0.3, 21) 0.05488	0.223541 (101,10−1, 0.1, 0.1, 23) 0.01608	0.203542 (101,0.1, 0.5, 21) 0.05971	0.226991 (10−1, 0.1, 0.3, 21) 0.06767	0.207904 (100,100, 0.9, 0.1, 25) 0.0196831
NN5_Complete_103 (237X5,550X5)	0.128071 (100, 0.1,2−1) 0.55103	0.129677 (100, 0.9, 2−3) 0.06733	0.130405 (101,10−1, 1, 0.1, 2−1) 0.02415	0.129381 (101,0.3, 0.4, 2−3) 0.0482	0.129794 (101, 0.9, 0.1, 2−3) 0.09831	0.129352 (101,10−1, 0.1, 0.1, 2−1) 0.0197878
NN5_Complete_101 (237X5,550X5)	0.150229 (100, 0.1,21) 0.566503	0.154038 (10−1, 0.9, 21) 0.06516	0.154147 (101,10−1, 0.1, 0.1, 21) 0.02724	0.146225 (101,0.1, 0.5, 21) 0.05404	0.153808 (10−1, 0.9, 0.1, 21) 0.07726	0.147679 (100,100, 0.9, 0.1, 23) 0.026214
NN5_Complete_105 (237X5,550X5)	0.206735 (100, 0.1,21) 0.59797	0.20295 (10−1, 0.9, 21) 0.07722	0.212735 (101,10−1, 1, 0.1, 23) 0.01905	0.215317 (101,0.1, 0.3, 21) 0.0591	0.204263 (100, 0.9, 0.1, 21) 0.07342	0.202491 (100,100, 0.1, 0.1, 23) 0.0223573
NN5_Complete_111 (237X5,550X5)	0.18836 (100, 0.1,21) 0.555449	0.211531 (10−5, 0.7, 21) 0.06467	0.218224 (101,10−1, 1, 0.1, 23) 0.01603	0.194376 (101,0.1, 0.4, 21) 0.06702	0.211115 (10−1, 0.1, 0.1, 21) 0.06854	0.202472 (100,100, 0.1, 0.1, 23) 0.0195859
D1dat_1_2000 (599X5,1396X5)	0.056375 (103, 0.1,2−5) 3.88997	0.039592 (10−1, 0.1, 21) 0.50661	0.056756 (105,10−1, 0.1, 1, 2−3) 0.11601	0.04234 (101,0.1, 0.3, 21) 0.37059	0.039961 (100, 0.1, 0.1, 21) 0.46588	0.038144 (100,10−5, 0.9, 0.1, 20) 0.0892223
Vineyard (16X4,36X4)	0.237345 (100, 0.1,2−1) 0.004569	0.236484 (101, 0.9, 2−5) 0.01397	0.246205 (101,10−1, 0.1, 0.1, 2−1) 0.00014	0.213259 (103,0.5, 0.2, 2−1) 0.00665	0.236413 (101, 0.9, 0.7, 2−5) 0.01649	0.240828 (101,101, 0.7, 0.1, 20) 0.0119425
COVID-19_spain (251X5,585X5)	0.118454 (101, 0.1,2−5) 0.650153	0.097704 (10−1, 0.1, 21) 0.08398	0.08227 (103,10−3, 0.1, 1.345, 2−3) 0.01543	0.081305 (101,0.3, 0.3, 2−3) 0.06166	0.097513 (100, 0.1, 0.1, 21) 0.0508	0.084161 (10−1,10−5, 0.9, 0.1, 20) 0.0200923

The best result is shown as boldface