Robust Extreme Learning Machine Using New Activation and Loss Functions Based on M-Estimation for Regression and Classification

Table 5

Testing RMSE and SD of existing and proposed weighted ELM with 20% outliers in abalone data.

Af	ELM	W1ELM	W2ELM	W3ELM; Proposed	W4ELM; Proposed	W5ELM; Proposed	W6ELM Proposed
Sigmoid	4.754750 0.06268815	3.227287 0.1091655	2.414179 0.09269088	2.287563 0.12418925	2.172357 0.038659	3.757036 0.103437	2.234866 0.06961570
Tan-sig	4.703597 0.13000821	3.132457 0.1208053	2.406314 0.01755072	2.276477 0.07965595	2.170417 0.010285181	3.615910 0.134645	2.239491 0.010221790
Sine	4.666985 0.20622199	3.060303 0.2181420	2.361913 0.06551598	2.265762 0.10267846	2.150898 0.006244196	3.528365 0.2596405	2.210075 0.033152012
Cosine	4.698598 0.20381093	3.180699 0.2577677	2.399364 0.21437287	2.308385 0.14727834	2.198570 0.0875391569	3.701441 0.2523779	2.249796 0.145378848
BentIdle	4.713415 0.13830989	3.143851 0.1155777	2.390502 0.03791609	2.287222 0.11066652	2.163265 0.0004587613	3.644029 0.1344872	2.228988 0.018264087
RAF	4.750438 0.10228568	3.196679 0.1157485	2.378543 0.09912061	2.267268 0.12104854	2.133434 0.0453002613	3.729898 0.1163393	2.204034 0.072324507
Proposed 1	4.705598 0.14179679	3.089672 0.2089739	2.378945 0.06826299	2.265295 0.09770380	2.057172 0.0025575652	3.565513 0.2448967	2.219889 0.032597902
Proposed 2	4.751669 0.14523476	3.097359 0.1859790	2.375285 0.06077762	2.276195 0.09643253	2.119978 0.00707343	4.582049 0.2195192	2.223024 0.037928300
Proposed 3	4.409515 0.66763602	3.089344 0.4398715	2.462548 0.24848033	2.350298 0.20780245	2.271832 0.0850197195	3.504199 0.5013264	2.318664 0.160961103
Proposed 4	4.754798 0.23081970	3.120053 0.2150026	2.426455 0.05665887	2.297376 0.08989809	2.205088 0.0134925439	3.583513 0.2651077	2.267244 0.036196250
Proposed 5	4.599507 0.30391626	3.074987 0.2746488	2.396853 0.10360959	2.315319 0.15672495	2.190741 0.0127734590	3.530176 0.3270949	2.247327 0.061538856
Proposed 6	4.595273 0.29349235	3.117355 0.2979396	2.435072 0.13227469	2.321735 0.17585465	2.218868 0.0340319304	3.569725 0.3348503	2.280369 0.088922964
Proposed 7	5.291630 1.54315324	3.723273 1.2721507	3.230150 1.31582437	2.554555 0.51404176	2.965076 1.1100654156	4.081953 1.2158311	3.003771 1.144834877
Proposed 8	4.733634 0.17460431	3.314672 0.1572617	2.763327 0.10634390	2.598141 0.09347673	2.501335 0.0801301294	3.696463 0.1703520	2.558568 0.099964180
Proposed 9	4.606322 0.33914493	3.073412 0.2470656	2.388054 0.09013738	2.289723 0.14496423	2.179600 0.0151039952	3.532195 0.2858742	2.237992 0.060854415
Proposed 10	4.818178 0.23783341	3.134719 0.1284443	2.378025 0.06425884	2.268276 0.08654497	2.147976 0.0408592032	3.638479 0.1393702	2.212687 0.059960084
Proposed 11	4.716515 0.12247669	3.106628 0.1597634	2.378284 0.02981345	2.274507 0.06553342	2.122296 0.0231154939	3.590920 0.1990009	2.217427 0.002427482