. 2021 Jan 3;53(1):459–515. doi: 10.1007/s11063-020-10380-y

Table 6.

Performance comparison of RHN-TSVR with SVR, TSVR, $ε$ -AHSVR, $ε$ -SVQR and HN-TSVR using Gaussian kernel on synthetic data sets with Laplacian noise

Dataset (Train size, Test size)	SVR RMSE $(C, ε, μ)$ Time	TSVR RMSE $(C_{1} = C_{2}, ε, μ)$ Time	$ε$ -AHSVR RMSE $(C, ε_{α} = ε_{β}, ζ_{α},$ $ζ_{β}, μ)$ Time	$ε$ -SVQR RMSE $(C, ε, θ, μ)$ Time	HN-TSVR RMSE $(C_{1} = C_{2}, ε_{1} = ε_{2},$ $ε_{1}^{} = ε_{2}^{}, μ)$ Time	RHN-TSVR RMSE $(C_{1} = C_{2}, ε_{1} = ε_{2},$ $ε_{1}^{} = ε_{2}^{}, μ)$ Time
Function19 (150X2,500X2)	0.416258 (10²,0.1,2⁻¹) 0.55812	0.404259 (10⁰,0.9,2⁻¹) 0.03316	0.40645 (10³,10⁻¹, 1, 1, 2⁻¹) 0.00513	0.47416 (10³,0.7,0.5,2⁻¹) 0.02272	0.404141 (10¹, 0.9, 0.1, 2⁻¹) 0.02615	0.404141 (10¹,10⁻³, 0.9, 0.1, 2⁻¹) 0.0083096
Function20 (150X3,500X3)	0.146758 (10⁰,0.1,2⁰) 0.47995	0.217388 (10⁰,0.9,2⁻¹) 0.02454	0.252318 (10⁻²,10⁻¹, 0.1, 1, 2⁴) 0.01452	0.21538 (10¹,0.5,0.5,2¹) 0.02619	0.217806 (10¹, 0.9, 0.1, 2⁻¹) 0.02312	0.138944 (10¹,10², 0.5, 0.1, 2³) 0.0125658
Function21 (150X3,500X3)	0.193024 (10⁵,0.1,2⁻⁵) 0.46148	0.215517 (10⁰,0.9,2⁻³) 0.02405	0.213251 (10⁻¹,10⁻¹, 1, 1.345, 2⁰) 0.01195	0.24943 (10⁻¹,0.1,0.8,2⁵) 0.03729	0.215388 (10¹, 0.9, 0.1, 2⁻³) 0.02207	0.188105 (10¹,10¹, 0.9, 0.1, 2⁰) 0.0189023
Function22 (150X2,500X2)	0.107321 (10⁰,0.1,2⁴) 0.43419	0.116748 (10⁰,0.9,2²) 0.03422	0.081983 (10⁰,10⁻¹, 0.1, 0.1, 2⁵) 0.00426	0.11815 (10⁵,0.3,0.4,2⁻¹) 0.0151	0.118841 (10¹, 0.1, 0.1, 2³) 0.02572	0.104688 (10¹,10¹, 0.1, 0.1, 2⁵) 0.0133986
Function23 (150X6,500X6)	0.190689 (10²,0.1,2¹) 0.38126	0.240025 (10⁰,0.1,2¹) 0.02595	0.24585 (10⁰,10⁻¹, 1, 1, 2²) 0.01102	0.28425 (10¹,0.3,0.3,2³) 0.0199	0.244521 (10⁰, 0.1, 0.7, 2¹) 0.02311	0.18934 (10¹,10⁻¹, 0.9, 0.1, 2¹) 0.0136633
Function24 (200X2,500X2)	0.026582 (10²,0.1,2¹) 0.89983	0.021008 (10⁰,0.9,2¹) 0.06646	0.027998 (10⁴,10⁻¹, 0.1, 0.1, 2²) 0.00481	0.01086 (10³,0.1,0.4,2¹) 0.02411	0.019294 (10¹, 0.1, 0.1, 2¹) 0.08291	0.012581 (10⁰,10⁻⁴, 0.9, 0.3, 2¹) 0.0169828

Dataset
(Train size, Test size)

SVR
RMSE

(C, ε, μ)

Time

TSVR
RMSE

(C_{1} = C_{2}, ε, μ)

Time

ε

-AHSVR
RMSE

(C, ε_{α} = ε_{β}, ζ_{α},

ζ_{β}, μ)

Time

ε

-SVQR
RMSE

(C, ε, θ, μ)

Time

HN-TSVR
RMSE

(C_{1} = C_{2}, ε_{1} = ε_{2},

ε_{1}^{*} = ε_{2}^{*}, μ)

Time

RHN-TSVR
RMSE

(C_{1} = C_{2}, ε_{1} = ε_{2},

ε_{1}^{*} = ε_{2}^{*}, μ)

Time

Function19

(150X2,500X2)

0.416258

(10²,0.1,2⁻¹)

0.55812

0.404259

(10⁰,0.9,2⁻¹)

0.03316

0.40645

(10³,10⁻¹, 1, 1, 2⁻¹)

0.00513

0.47416

(10³,0.7,0.5,2⁻¹)

0.02272

0.404141

(10¹, 0.9, 0.1, 2⁻¹)

0.02615

0.404141

(10¹,10⁻³, 0.9, 0.1, 2⁻¹)

0.0083096

Function20

(150X3,500X3)

0.146758

(10⁰,0.1,2⁰)

0.47995

0.217388

(10⁰,0.9,2⁻¹)

0.02454

0.252318

(10⁻²,10⁻¹, 0.1, 1, 2⁴)

0.01452

0.21538

(10¹,0.5,0.5,2¹)

0.02619

0.217806

(10¹, 0.9, 0.1, 2⁻¹)

0.02312

0.138944

(10¹,10², 0.5, 0.1, 2³)

0.0125658

Function21

(150X3,500X3)

0.193024

(10⁵,0.1,2⁻⁵)

0.46148

0.215517

(10⁰,0.9,2⁻³)

0.02405

0.213251

(10⁻¹,10⁻¹, 1, 1.345, 2⁰)

0.01195

0.24943

(10⁻¹,0.1,0.8,2⁵)

0.03729

0.215388

(10¹, 0.9, 0.1, 2⁻³)

0.02207

0.188105

(10¹,10¹, 0.9, 0.1, 2⁰)

0.0189023

Function22

(150X2,500X2)

0.107321

(10⁰,0.1,2⁴)

0.43419

0.116748

(10⁰,0.9,2²)

0.03422

0.081983

(10⁰,10⁻¹, 0.1, 0.1, 2⁵)

0.00426

0.11815

(10⁵,0.3,0.4,2⁻¹)

0.0151

0.118841

(10¹, 0.1, 0.1, 2³)

0.02572

0.104688

(10¹,10¹, 0.1, 0.1, 2⁵)

0.0133986

Function23

(150X6,500X6)

0.190689

(10²,0.1,2¹)

0.38126

0.240025

(10⁰,0.1,2¹)

0.02595

0.24585

(10⁰,10⁻¹, 1, 1, 2²)

0.01102

0.28425

(10¹,0.3,0.3,2³)

0.0199

0.244521

(10⁰, 0.1, 0.7, 2¹)

0.02311

0.18934

(10¹,10⁻¹, 0.9, 0.1, 2¹)

0.0136633

Function24

(200X2,500X2)

0.026582

(10²,0.1,2¹)

0.89983

0.021008

(10⁰,0.9,2¹)

0.06646

0.027998

(10⁴,10⁻¹, 0.1, 0.1, 2²)

0.00481

0.01086

(10³,0.1,0.4,2¹)

0.02411

0.019294

(10¹, 0.1, 0.1, 2¹)

0.08291

0.012581

(10⁰,10⁻⁴, 0.9, 0.3, 2¹)

0.0169828

The best result is shown as boldface