Adaptive Linear and Normalized Combination of Radial Basis Function Networks for Function Approximation and Regression

Table 3

Results of function approximation experiments in terms of mean-squared error (MSE), normalized correlation coefficient (NCC), and computation time consumption (CTC in ms).

Function name	Evaluation	RBFN	SA	WA	ALNC
Zigzag	MSE	0.0295 ± 0.0735	0.0062 ± 0.0164	0.0007 ± 0.0049	0.0004 ± 0.0011
	NCC (%)	96.3055 ± 9.6683	99.4763 ± 9.3546	99.9250 ± 6.3702	99.9571 ± 4.2214
	CTC (ms)		7.42 ± 1.89	8.84 ± 0.92	7.28 ± 0.95
Rhythm	MSE	0.0029 ± 0.0010	0.0024 ± 0.0013	0.0023 ± 0.0012	0.0020 ± 0.0009
	NCC (%)	87.5134 ± 5.0192	89.7075 ± 3.2103	90.1384 ± 2.8523	91.5593 ± 1.8064
	CTC (ms)		8.71 ± 1.12	9.33 ± 1.74	8.54 ± 1.03
SinCos	MSE	0.0634 ± 0.2023	0.0055 ± 0.0047	0.0000 ± 0.0002	0.0000 ± 0.0002
	NCC (%)	97.7722 ± 7.2694	99.9010 ± 5.3231	100.0000 ± 2.0012	100.0000 ± 2.0012
	CTC (ms)		9.01 ± 1.24	9.24 ± 1.01	8.52 ± 1.36
ExpSin	MSE	2.6070 ± 5.9641	0.5745 ± 0.2563	0.2246 ± 0.1094	0.1793 ± 0.0521
	NCC (%)	98.9156 ± 2.5046	99.7826 ± 1.3005	99.9097 ± 0.7421	99.9992 ± 0.5096
	CTC (ms)		8.42 ± 1.88	9.12 ± 3.65	9.07 ± 2.09
3-D Mexican Hat	MSE	0.0056 ± 0.0092	0.0016 ± 0.0022	0.0001 ± 0.0003	0.0001 ± 0.0003
	NCC (%)	96.7638 ± 5.4163	99.2510 ± 2.3316	99.9973 ± 0.05433	99.9992 ± 0.0097
	CTC (ms)		12.67 ± 1.04	13.69 ± 1.06	11.15 ± 0.98
Gabor	MSE	0.0526 ± 0.0591	0.0284 ± 0.0087	0.0044 ± 0.0027	0.0030 ± 0.0015
	NCC (%)	85.9035 ± 19.5016	94.5788 ± 12.0816	99.1086 ± 7.3341	99.4828 ± 4.2035
	CTC (ms)		12.41 ± 1.35	12.97 ± 1.39	11.79 ± 1.19
SwingCos	MSE	0.6108 ± 0.2585	0.4614 ± 0.2448	0.3663 ± 0.1802	0.2018 ± 0.0097
	NCC (%)	79.6648 ± 9.7284	86.2856 ± 7.0205	89.2254 ± 6.6522	94.3319 ± 4.3316
	CTC (ms)		11.38 ± 0.74	13.03 ± 0.89	11.65 ± 0.81
Exponential	MSE	0.0016 ± 0.0022	0.0007 ± 0.0003	0.0004 ± 0.0001	0.0001 ± 0.0001
	NCC (%)	96.3979 ± 5.2557	98.5697 ± 3.4681	99.2090 ± 1.0506	99.7315 ± 0.6233
	CTC (ms)		12.46 ± 1.52	13.18 ± 2.13	11.53 ± 1.08