Optimized Extreme Learning Machine for Color Difference Classification Based on Improved Black-Winged Kite Algorithm

Test function	Dimension	Search scope
$f_{1} (x) = \sum_{i = 1}^{D - 1} [100 {(x_{i + 1} - x_{i}^{2})}^{2} + {(x_{i} - 1)}^{2}]$	30	［-30，30］
$f_{2} (x) = \sum_{i = 1}^{n} {\|x_{i} + 0.5\|}^{2}$	30	［-100，100］
$f_{3} (x) = - 20 e x p (- 0.2 \sqrt[]{\frac{1}{d} \sum_{i = 1}^{d} x_{i}^{2}}) - e x p [\frac{1}{d} \sum_{i}^{d} c o s (2 π x_{i})] + 20$	30	［-30，30］
$f_{4} (x) = \frac{1}{4000} \sum_{i = 1}^{n} (x_{i}^{2}) - \overset{n}{\prod_{i = 1}} c o s (\frac{x_{i}}{\sqrt[]{i}}) + 1$	30	［-500，500］

Table 2. Optimization results of the six algorithms

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Table 2. Optimization results of the six algorithms

Function	Measure	MBKA	BKA	CPO	PKO	SO	PUMA
$f_{1}$	Best	0	25.9902	29.00252	26.50928	0.00087	25.88323
$f_{1}$	Stdv	9.29×10^-28	1.03444	146.8906	202.9455	12.0794	0.349169
$f_{1}$	Ave	2.87×10^-28	28.01717	382.9408	142.3693	21.1918	26.70203
$f_{1}$	Mean	0	28.59256	606.9859	30.13644	28.7842	26.76293
$f_{1}$	Worst	4.48×10^-27	28.99413	8066276	855.0812	28.9221	27.37428
$f_{2}$	Best	0	0.343978	5.941301	0.000102	0.00368	3.2×10^-6
$f_{2}$	Stdv	8.94×10^-30	1.347039	1382.876	0.097186	0.57753	8.78×10^-5
$f_{2}$	Ave	3.41×10^-30	2.148931	918.7335	0.049211	0.82686	9.47×10^-5
$f_{2}$	Mean	0	1.699957	203.0064	0.000397	0.7616	5.9×10^-5
$f_{2}$	Worst	3.99×10^-29	6.027411	4766.345	0.366826	2.52236	0.000343
$f_{3}$	Best	0	0	0.001006	5.71×10^-5	0	0
$f_{3}$	Stdv	0	0	11.10109	0.123147	0.16729	0
$f_{3}$	Ave	0	0	6.23919	0.111835	0.06634	0
$f_{3}$	Mean	0	0	2.15118	0.063856	0	0
$f_{3}$	Worst	0	0	59.14386	0.43511	0.67774	0
$f_{4}$	Best	1.57×10^-32	0.01851	0.700922	2.3×10^-5	0.00092	3.6×10^-7
$f_{4}$	Stdv	1.66×10^-31	0.181737	1155.216	9.210266	0.10570	1.13×10^-5
$f_{4}$	Ave	7.81×10^-32	0.101794	232.7225	3.413291	0.06730	8.84×10^-6
$f_{4}$	Mean	2.27×10^-32	0.049343	4.375669	0.131785	0.01617	5.36×10^-6
$f_{4}$	Worst	4.37×10^-12	13.42474	6.72×10^-5	0.553304	35.01559	0.761368

Table 3. Comparison of color differences
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Table 3. Comparison of color differences
$Δ E$ Human eye perception Level
0‒0.5 Infinitesimal 1
0.5‒1.5 Slight 2
1.5‒3.0 Obvious 3
3.0‒6.0 Very obvious 4
>6.0 Strong 5

Table 4. Partial dataset

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Table 4. Partial dataset

Level	ΔE	ΔL	Δa	Δb	ΔH	ΔS	ΔV
1	0.376640	0.4649	0.3176	0.44590	0.070408	0.000677	0.007843
4	3.328710	0.9937	5.9825	2.39710	1.723019	0.055344	0.023529
5	8.349800	4.0287	12.9919	3.04330	6.439542	0.006196	0.019608
5	17.249500	17.8150	12.1040	11.20280	6.412319	0.084000	0.160784
1	0.469531	0.3697	0.0254	1.41780	1.008734	0.047855	0.003922
3	1.622631	0.1271	3.0882	1.04090	0.932443	0.017333	0.019608
4	4.988158	2.3428	8.6778	1.16190	2.276981	0.072235	0.019608
4	5.734576	0.7374	9.9134	1.05440	4.625556	0.002455	0.066667
1	0.417131	0.3668	0.0089	1.19110	0.832263	0.039823	0.003922
2	1.396967	1.8741	0.0111	0.52880	0.356560	0.026623	0.023529
3	2.953418	0.3229	4.4221	2.68800	3.641387	0.084000	0.019608
2	1.496266	1.7949	0.1569	2.86820	1.433127	0.072863	0.019608
2	0.787515	0.8295	1.0228	1.10260	0.508734	0.047855	0.003922
3	2.966687	0.6889	2.6690	6.33080	3.788368	0.104235	0.019608
5	8.567891	7.9078	11.9219	9.59920	2.342067	0.210118	0.019608

Table 5. Influence of hidden layer nodes on ELM

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Table 5. Influence of hidden layer nodes on ELM

Number of neurons	Average accuracy /%	Training time /ms	Prediction time /ms
5	48.96	0.99	0.91
10	59.44	13.70	1.99
15	71.08	30.96	1.51
20	75.00	50.86	1.99
25	75.84	54.27	2.01
30	79.20	69.81	2.99
35	81.96	75.79	3.98
40	82.80	92.45	2.99
45	83.32	124.66	3.98
50	85.80	131.64	4.19
100	89.40	424.13	8.99
200	92.32	812.11	9.97
300	93.55	1412.99	18.69
400	91.92	2105.65	27.92
500	92.64	3062.03	35.90

Table 6. Parameters of optimization algorithms

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Table 6. Parameters of optimization algorithms

Algorithm	Parameter	Value
MBKA， BKA	Number of populations	10
	Maximum number of iterations	30
	p	0.9
PKO	Number of populations	10
	Maximum number of iterations	30
	BF	8
	PE_min	0
	PE_max	0.5
CPO	Number of populations	10
	Maximum number of iterations	30
	α	0.2
	TF	0.8
PUMA	Number of populations	10
	Maximum number of iterations	30
	PF	［0.5 0.5 0.3］
	Mega_Explor， Mega_Exploit	0.99
SO	Number of populations	10
	Maximum number of iterations	30
	vec_flag	［-1，1］
	Threshold	0.25
	C₁	0.5
	C₂	0.05

Table 7. Comparative experiments of different algorithms
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Table 7. Comparative experiments of different algorithms
Algorithm Running time /s Accuracy /%
ELM 0.72 85.3
MBKA-ELM 3.22 98.4
BKA-ELM 4.37 95.4
PKO-ELM 3.61 96.1
CPO-ELM 1.22 94.6
PUMA-ELM 1.85 97.0
SO-ELM 2.05 92.5

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Jiale Chen, Xiaobin Li, Haiyan Sun. Optimized Extreme Learning Machine for Color Difference Classification Based on Improved Black-Winged Kite Algorithm[J]. Laser & Optoelectronics Progress, 2025, 62(12): 1237012

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