A Novel Robust Principal Component Analysis Algorithm of Nonconvex Rank Approximation

Table 4

The algorithm’s quantity indexes for Wallflower experiment.

Algorithms	Evaluation indexes	BS	CF	LS	WT	TOD	MO	FA
GoDec [38]	RE	2.325e − 03	3.625e − 03	2.402e − 05	1.0996e − 04	2.5267e − 03	6.7650e − 04	8.2345e − 03
	Iteration	20	22	43	12	89	30	21
	Rank ()	13	3	4	8	16	7	5
	RMSE	0.6213	0.7112	0.6322	0.5546	0.7032	0.6505	0.5890
	CPU time(s)	28.6702	3.5344	19.2457	0.66918	15.4668	4.3642	6.2168
ALM	RE	3.5567e − 04	3.5567e − 06	1.4453e − 05	2.2310e − 06	2.2121e − 04	2.2223e − 05	2.3512e − 05
	Iteration	178	149	154	23	204	56	104
	Rank ()	663	42	26	8	32	13	56
	RMSE	0.6534	0.7243	0.6231	0.5043	0.6439	0.7230	0.5546
	CPU time(s)	241.5925	34.5612	46.7471	18.5634	568.3478	167.2456	356.2323
RegL1-ALM [24]	RE	2.426e − 05	1.390e − 05	1.255e − 05	3.5624e − 07	3.4011e − 04	2.5144e − 07	2.8995e − 07
	Iteration	144	147	154	55	240	40	48
	Rank ()	589	237	16	4	98	983	1153
	RMSE	0.5937	0.6894	0.6025	0.5523	0.5722	0.6332	0.6534
	CPU time(s)	231.5002	28.2874	24.64	20.5867	430.5623	205.8264	284.3467
NCRPCA	RE	1.0996e − 07	1.2994e − 07	2.1757e − 07	3.6489e − 08	5.3841e − 07	2.3394e − 07	2.2697e − 07
	Iteration	36	23	30	20	48	36	40
	Rank ()	8	3	4	1	2	3	4
	RMSE	0.5546	0.6943	0.6001	0.5014	0.5421	0.6522	0.5867
	CPU time(s)	83.8376	1.4279	39.7935	1.0232	128.5847	22.719	54.980
GOSUS [19]	RE	7.2312e − 02	5.2562e − 03	4.2231e − 02	3.231e − 01	3.2548e − 00	4.4423e − 03	2.4323e − 02
	Iteration	10	10	10	7	12	10	10
	Rank ()	6	5	6	3	18	5	6
	RMSE	0.5134	0.7356	0.6654	0.6732	0.7622	0.5821	0.6521
	CPU time(s)	2.2312	2.8270	1.2432	1.4058	13.7578	4.6285	5.1747
SLM [22]	RE	9.6320e − 08	6.2156e − 08	7.5632e − 09	6.5432e − 08	4.5621e − 08	7.3230e − 08	2.3120e − 08
	Iteration	27	16	38	14	45	17	32
	Rank ()	14	5	8	2	3	2	2
	RMSE	0.5015	0.7283	0.5213	0.5523	0.5018	0.5689	0.5590
	CPU time(s)	29.2312	2.3210	10.2354	3.3421	38.2654	13.6218	24.6654
NNCRPCA	RE	9.990e − 08	7.6623e − 07	3.2243e − 09	2.5643e − 08	3.5478e − 09	2.7865e − 08	3.6542e − 09
	Iteration	24	16	28	6	22	10	14
	Rank ()	6	4	3	1	2	2	3
	RMSE	0.5032	0.6650	0.5976	0.5000	0.5032	0.5034	0.5530
	CPU time(s)	51.4532	2.5426	14.6745	4.2214	48.5523	23.2246	35.6240

BS: Bootstrap; CF: Camouflage; LS: LightSwitch; WT: Waving Trees; TOD: Time of Day; MO: Moved Object; FA: Foreground Aperture. The bold represents the minimum value of the same index in the same subject experiment, and the underline represents the maximum value.