Improving the Solution of Least Squares Support Vector Machines with Application to a Blast Furnace System

Table 1

Experimental results of three methods on Boston data set.

	Boston data set, 506 samples, 13-d inputs, 𝜎^2 equals 13
log2𝐶	Conjugate gradient method			Null space method			MINRES method
	Cond^†	CPU^‡	MSE*	Cond	CPU	MSE	Cond	CPU	MSE
−5	4	0.3281	49.1027	366.9451	0.8438	49.1027	45.6283	0.2500	49.1027
−4	8	0.4688	39.4132	369.0926	0.6250	39.4132	31.6150	0.3438	39.4132
−3	15	0.3438	29.7686	388.1770	0.7656	29.7686	26.3388	0.3125	29.7686
−2	28	0.4531	24.2532	460.1920	0.7656	24.2532	29.2813	0.3281	24.2532
−1	60	0.2500	21.0322	474.6254	1.0625	21.0322	61.3493	0.4219	21.0322
0	116	0.3438	15.5875	566.2504	1.2500	15.5875	119.071	0.1875	15.5875
1	234	0.7188	13.6449	946.4564	1.1250	13.6449	239.374	0.4375	13.6449
2	472	0.9531	13.0252	1945.300	1.0625	13.0252	482.447	0.6875	13.0252
3	924	0.9375	10.9810	2244.342	1.4063	10.9810	944.042	0.6406	10.9810
4	1734	1.3594	10.3168	5229.460	1.2500	10.3168	1776.31	0.8906	10.3168
5	3801	1.5469	10.2063	10785.92	1.4844	10.2063	3876.97	1.1406	10.2063
6	7530	2.0469	11.3937	24998.71	1.9063	11.3937	7682.07	1.2969	11.3937
7	14618	2.4531	11.7750	47781.41	2.2188	11.7750	14932.2	1.6875	11.7750
8	29769	3.0625	12.9925	61351.85	2.9844	12.9925	30382.8	2.3750	12.9925
9	58387	3.4063	14.0194	101181.8	3.5938	14.0194	59619.0	2.6875	14.0194
10	119285	4.0313	17.2330	285440.0	4.8281	17.2330	121708	3.5313	17.2330

Cond^† denotes the condition number, CPU^‡ stands for running time, MSE* is mean square error.