Online Regularized and Kernelized Extreme Learning Machines with Forgetting Mechanism

Table 1

RMSE comparison between the proposed ELMs and other ELMs on identification of process (20) with input (23).

𝑧		50	70	100	150	200	∞
𝐿=15	FOS-ELM (𝑝=2)	0.3474	0.0967	0.0731	0.0975	0.0817	—
	ReOS-ELM	—	—	—	—	—	0.0961
	DR-ELM	0.0681	0.0683	0.0712	0.0833	0.0671	—
	FORELM (𝑝=2)	0.0850	0.0708	0.0680	0.0816	0.0718	—
𝐿=25	FOS-ELM	0.9070	0.1808	0.1324	0.0821	0.0883	—
	ReOS-ELM	—	—	—	—	—	0.0804
	DR-ELM	0.0543	0.0670	0.0789	0.0635	0.0656	—
	FORELM	0.0578	0.0697	0.0833	0.0653	0.0600	—
𝐿=50	FOS-ELM	×	×	×	9.9541	0.4806	—
	ReOS-ELM	—	—	—	—	—	0.0529
	DR-ELM	0.0377	0.0351	0.0345	0.0425	0.0457	—
	FORELM	0.0344	0.0320	0.0324	0.0457	0.0456	—
𝐿=100	FOS-ELM	×	×	×	×	×	—
	ReOS-ELM	—	—	—	—	—	0.0359
	DR-ELM	0.0298	0.0306	0.0308	0.0391	0.0393	—
	FORELM	0.0312	0.0263	0.0288	0.0405	0.0378	—
𝐿=150	FOS-ELM	×	×	×	×	×	—
	ReOS-ELM	—	—	—	—	—	0.0351
	DR-ELM	0.0268	0.0270	0.0281	0.0417	0.0365	—
	FORELM	0.0270	0.0276	0.0284	0.0378	0.0330	—
𝐿=200	FOS-ELM	×	×	×	×	×	—
	ReOS-ELM	—	—	—	—	—	0.0344
	DR-ELM	0.0259	0.0284	0.0272	0.0363	0.0351	—
	FORELM	0.0263	0.0289	0.0274	0.0355	0.0325	—
𝐿=400	FOS-ELM	×	×	×	×	×	—
	ReOS-ELM	—	—	—	—	—	0.0296
	DR-ELM	0.0240	0.0255	0.0249	0.0362	0.0327	—
	FORELM	0.0231	0.0248	0.0256	0.0372	0.0310	—
𝐿=800	FOS-ELM	×	×	×	×	×	—
	ReOS-ELM	—	—	—	—	—	0.0292
	DR-ELM	0.0233	0.0253	0.0270	0.0374	0.0320	—
	FORELM	0.0223	0.0256	0.0252	0.0407	0.0318	—
𝐿=1000	FOS-ELM	×	×	×	×	×	—
	ReOS-ELM	—	—	—	—	—	0.0298
	DR-ELM	0.0234	0.0263	0.0278	0.0418	0.0323	—
	FORELM	0.0232	0.0238	0.0259	0.0372	0.0310	—
FOKELM		0.0236	0.0251	0.0267	0.0386	0.0331	—

“—” represents nondefinition or inexistence in the case.
“×” represents nullification owing to the too large RMSE or MAPE.