Linear Twin Quadratic Surface Support Vector Regression

Table 1

Results of Ridge Regression (RR), Linear Regression (LR), nu-SVR, ϵ-SVR, LSSVR, TSVR, LTSVR, and LTQSSVR on benchmark data sets with RBF kernel.

Noise	Alg	RMSE	MAE	SSE/SST	SSR/SST	Time (s)	c	ϵ	σ
Type 1	RR	0.3102 ± 0.0115	0.1804 ± 0.0066	1.1385 ± 0.0163	0.1389 ± 0.0162	0.0434
	LR	0.3106 ± 0.0115	0.1805 ± 0.0066	1.1410 ± 0.0170	0.1410 ± 0.0170	0.0004
	nu-SVR	635.0782 ± 2.0081e + 03	257.3113 ± 813.5255	4.7260e + 07 ± 1.4945e + 08	4.7260e + 07 ± 1.4945e + 08	47.0139	2^2	0.001	2^–1
	ϵ-SVR	158.5021 ± 350.9712	91.1181 ± 197.1021	1.6476e + 06 ± 3.9456e + 06	1.6476e + 06 ± 3.9456e + 06	28.7549	2^2	0.001	2^–1
	LSSVR	0.6531 ± 0.0155	0.5141 ± 0.0144	4.5383 ± 0.4865	4.3325 ± 0.5131	830.3177	2^5		2^–1
	TSVR	0.6544 ± 0.0270	0.5314 ± 0.0176	4.3852 ± 0.4677	4.2048 ± 0.4878	2024.7431	2^–4	0.001	2^–1
	LTSVR	0.5870 ± 0.0372	0.4839 ± 0.0247	3.7994 ± 0.2871	3.8503 ± 0.1351	26531.2	2^2	0.01	2^2
	LTQSSVR	0.3961 ± 0.0187	0.2851 ± 0.0239	1.7631 ± 0.1997	0.3917 ± 0.1451	96.3907	2^–1	0.01
Type 2	RR	0.3432 ± 0.0102	0.2034 ± 0.0065	1.1693 ± 0.0168	0.1695 ± 0.0172	0.0027
	LR	0.3434 ± 0.0110	0.2034 ± 0.0075	1.1705 ± 0.0222	0.1705 ± 0.0222	0.0024
	nu-SVR	588.4 ± 186.1	140.7 ± 444.7	3.4195e + 07 ± 1.0814e + 08	3.4196e + 07 ± 1.0814e + 08	53.9877	2^–2	0.001	2^0
	ϵ-SVR	107.6 ± 238.9	87.9 ± 193.4	6.4387e + 05 ± 1.6125e + 06	6.4345e + 05 ± 1.6114e + 06	43.9494	2^–2	0.001	2^0
	LSSVR	0.6406 ± 0.0257	0.5193 ± 0.0233	4.3594 ± 0.4286	4.0586 ± 0.3830	959.2185	2^0		2^–2
	TSVR	0.6338 ± 0.0397	0.5123 ± 0.0321	4.1191 ± 0.6138	3.7309 ± 0.5828	5657.1416	2^–4	0.2	2^0
	LTSVR	0.6988 ± 0.1573	0.5541 ± 0.1162	4.8817 ± 1.5382	5.0229 ± 1.9708	4583.9875	2^–2	0.001	2^4
	LTQSSVR	0.3979 ± 0.0321	0.2817 ± 0.0225	1.7730 ± 0.2054	0.3920 ± 0.1574	93.6575	2^–1	0.01
Type 3	RR	0.3431 ± 0.0102	0.2033 ± 0.0068	1.1688 ± 0.0171	0.1690 ± 0.0175	0.0038
	LR	0.3431 ± 0.0107	0.2033 ± 0.0072	1.1688 ± 0.0190	0.1688 ± 0.0190	0.0003
	nu-SVR	165.9 ± 524.4	93.1 ± 293.7	2.8467e + 06 ± 9.0020e + 06	2.8464e + 06 ± 9.0012e + 06	26531.2	2^3	0.001	2^–1
	ϵ-SVR	0.1545 ± 0.0015	0.1536 ± 0.0017	0.2373 ± 0.0130	1.2355 ± 0.0176	30.5638	2^0	0.001	2^0
	LSSVR	0.6531 ± 0.0155	0.5141 ± 0.0144	4.5383 ± 0.4865	4.3325 ± 0.5131	1200.9825	2^5		2^–1
	TSVR	0.6273 ± 0.0062	0.4944 ± 0.0094	4.0209 ± 0.0178	3.6071 ± 0.0231	2887.8195	2^–4	0.1	2^0
	LTSVR	0.6852 ± 0.0327	0.5311 ± 0.0301	5.4208 ± 1.1646	5.4496 ± 1.3123	4735.0025	2^2	0.001	2^2
	LTQSSVR	0.3935 ± 0.0160	0.3310 ± 0.0148	1.7354 ± 0.1279	0.4470 ± 0.0608	100.1174	2^–2	0.01
Type 4	RR	0.3431 ± 0.0103	0.2033 ± 0.0071	1.1687 ± 0.0174	0.1687 ± 0.0175	0.0037
	LR	0.3431 ± 0.0104	0.2033 ± 0.0070	1.1687 ± 0.0183	0.1687 ± 0.0183	0.0003
	nu-SVR	542.5 ± 1429.7	235.1 ± 571.1	2.1116e + 07 ± 6.3937e + 07	2.1115e + 07 ± 6.3936e + 07	26531.2	2^3	0.001	2^–1
	ϵ-SVR	0.0811 ± 0.0070	0.0769 ± 0.0070	0.0658 ± 0.0119	0.9687 ± 0.0149	9.4324	2^3	0.001	2^–1
	LSSVR	0.6531 ± 0.0155	0.5141 ± 0.0144	4.5383 ± 0.4865	4.3325 ± 0.5131	1200.9825	2^5		2^–1
	LSSVR	0.6442 ± 0.0173	0.5121 ± 0.0142	4.4135 ± 0.4501	4.2044 ± 0.4833	12.1205	2^3		2^–2
	TSVR	0.6064 ± 0.0099	0.4784 ± 0.0060	3.7604 ± 0.2137	3.2961 ± 0.2944	737.7178	2^–4	0.2	2^0
	LTSVR	0.6426 ± 0.0481	0.5 ± 0.0140	4.1282 ± 0.3409	4.0077 ± 0.3712	9533.4572	2^2	0.01	2^–2
	LTQSSVR	0.3781 ± 0.0257	0.2980 ± 0.0298	1.6028 ± 0.1709	0.3151 ± 0.1171	113.2787	2^–1	0.01