<b>Leaf area estimation in <i>Coffea canephora</i> genotypes by neural networks and multiple regression</b>

Vitória, Edney L. da; Nardotto Júnior, André O.; Ribeiro, Luis F. O.; Dubberstein, Danielly; Partelli, Fábio L.

doi:10.1590/1807-1929/agriambi.v28n9e279246

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Original Article • Rev. bras. eng. agríc. ambient. 28 (9) • Sept 2024 • https://doi.org/10.1590/1807-1929/agriambi.v28n9e279246 copy

**Leaf area estimation in Coffea canephora genotypes by neural networks and multiple regression** ¹ 1 Research developed at Universidade Federal do Espírito Santo, São Mateus, ES, Brazil

Estimativa da área foliar de genótipos de Coffea canephora por meio de redes neurais e regressão múltipla

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Leaf area data from coffee plants are important for studies and analyses of grain yield, physiology, adaptation to environmental conditions, and cultural management. The objective of this study was to predict leaf area of coffee plants using artificial neural networks and compare the efficiency of this methodology with multiple regression models. Forty-three genotypes of similar reproduction and age were evaluated, testing 14 types of multiple regression equations from combinations of leaf length and width. The backpropagation algorithm was used to develop multilayer perceptron neural networks; several combinations were tested between two activation functions of the intermediate layer (hidden layer) and the number of neurons in this layer. The best fitting results in the artificial neural network modeling were found with the sigmoid activation function and three neurons in the hidden layer (R² = 0.990 and RMSE = 2.855 in the training phase). Considering the errors (RMSE, MAE, and MAPE) and the coefficient of determination as criteria for best fit, the artificial neural network models better estimated the leaf area in the training and validation phases. Therefore, the artificial neural network methodology can be used as alternative for estimating leaf area of coffee plants.

Key words:
statistical models; artificial intelligence; backpropagation; leaf length and width

HIGHLIGHTS:

Backpropagation neural networks can be used to estimate leaf area of Coffea caneph-ora.

The use of non-destructive methods is a viable alternative for determining leaf area of C. canephora.

Multiple regression can be replaced by artificial neural network models for estimating leaf area.

Identification	Genotype	Identification	Genotype
1	Verdim R	23	Z18
2	B01	24	Z37
3	Bicudo	25	Z21
4	Alecrin	26	Z36
5	700	27	Ouro Negro
6	CH1	28	18
7	Imbigudinho	29	Tardio C
8	AD1	30	A1
9	Graudão HP	31	Cheique
10	Valcir	32	P2
11	Beira Rio 8	33	Emcapa 02
12	Late V	34	Emcapa 153
13	AP	35	P1
14	L80	36	LB1
15	Bamburral	37	122
16	Pirata	38	Verdim D
17	Peneirão	39	Seed
18	Z39	40	Emcapa 143
19	Z35	41	Ouro Negro 1
20	Z40	42	Ouro Negro 2
21	Z29	43	Clementino
22	Z38

Equation	Multiple regression models
1	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L$
2	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} W$
3	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{3} W$
4	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} L^{2} + {\hat{β}}_{3} W$
5	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} W + {\hat{β}}_{3} W^{2}$
6	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} L^{2} + {\hat{β}}_{3} W + {\hat{β}}_{4} W^{2}$
7	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} W + {\hat{β}}_{4} L W$
8	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} L^{2} + {\hat{β}}_{3} W + {\hat{β}}_{4} W L$
9	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} W + {\hat{β}}_{3} W^{2} + {\hat{β}}_{4} W L$
10	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} L^{2} + {\hat{β}}_{4} W + {\hat{β}}_{5} W^{2} + {\hat{β}}_{6} W L$
11	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} L^{2} + {\hat{β}}_{4} W + {\hat{β}}_{5} W^{2} + {\hat{β}}_{6} W L + {\hat{β}}_{7} L^{2} W$
12	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} L^{2} + {\hat{β}}_{4} W + {\hat{β}}_{5} W^{2} + {\hat{β}}_{6} W L + {\hat{β}}_{7} L W^{2}$
13	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} L^{2} + {\hat{β}}_{3} W + {\hat{β}}_{4} W^{2} + {\hat{β}}_{5} W L + {\hat{β}}_{6} L^{2} W + {\hat{β}}_{7} L W^{2}$
14	$L^A = {\hat{β}}_{0} + {\hat{β}}_{1} L + {\hat{β}}_{2} L^{2} + {\hat{β}}_{3} W + {\hat{β}}_{4} W^{2} + {\hat{β}}_{5} W L + {\hat{β}}_{6} L^{2} W + {\hat{β}}_{7} L W^{2} + {\hat{β}}_{8} L^{2} W^{2}$

Parameters	Leaf length (cm)	Leaf width (cm)	Leaf area (cm²)
	Descriptive statistics
Minimum	9.00	3.80	20.63
Maximum	19.00	9.70	101.61
Mean	13.97	5.79	51.08
Standard deviation	1.71	0.98	14.20
Coefficient of variation	12.24%	16.93%	27.80%
	Pearson correlation coefficients (r)
Leaf length	1.000
Leaf width	0.643*	1.000
Leaf area	0.921*	0.823*	1.000
	VIF (T)
Leaf length	-
Leaf width	1.703 (0.587)	-
Leaf area	6.579 (0.152)	3.096 (0.323)	-

Id	Regression model	R²	RMSE	F Value
1	$L A = - 44.94 + 6.87 * L$	0.823	7.989	2,778.0
2	$L A = - 25.98 + 13.30 * W$	0.921	5.527	7,209.3
3	$L A = - 50.89 + 3 . 32^{n s} L + 9.59 * W$	0.970	3.419	10,448.5
4	$L A = - 14.63 - 1.91 * L + 0 . 18^{n s} L^{2} + 9.58 * W$	0.972	3.574	7,308.9
5	$L A = - 33.97 + 3.42 * L + 3.46 * W + 0.49 * W^{2}$	0.972	3.371	7,235.1
6	$L A = - 8.61 - 0.87 * L + 0 . 15^{n s} L^{2} + 5.01 * W + 0.37 * W^{2}$	0.972	3.326	5,591.2
7	$L A = - 9.63 + 0.42 * L + 2 . 26^{n s} W + 0.51 * L W$	0.973	3.303	7,492.6
8	$L A = - 7.28 - 0.31 * L + 0 . 004^{n s} L^{2} + 3.19 * W + 0.44 * L W$	0.973	3.314	5,620.7
9	$L A = - 10.10 + 0 . 70^{n s} L + 1.76 * W + 0.09 * W^{2} + 0.46 * L W$	0.973	3.322	5,619.8
10	$L A = - 6.63 - 0 . 28^{n s} L + 0.06 * L^{2} + 2.92 * W + 0.16 * W^{2} + 0.32 * L W$	0.972	3.469	4,502.4
11	$L A = 39.94 - 6 . 99^{n s} L + 0.30 * L^{2} - 5.46 * W + 0.16 * W^{2} + 1.52 * L W - 0.04 L^{2} W$	0.973	3.980	3,760.7
12	$L A = 42.14 - 3 . 42^{n s} L + 0.04 * L^{2} - 15.05 * W + 1.66 * W^{2} + 1.57 * L W - 0.10 L W^{2}$	0.972	3.377	3,767.9
13	$L A = 43.43 - 3 . 78^{n s} L + 0.06 * L^{2^{n s}} - 14.87 * W + 1.59 * W^{2} + 1.60 * L W - 0.01 L^{2} W - 0.09 * L W^{2}$	0.972	4.949	3,227.2
14	$L A = 50.72 - 4 . 83^{n s} L + 0 . 10^{n s} L^{2} - 17.51 * W + 1.82 * W^{2} + 1.98 * L W - 0 . 02^{n s} L^{2} W - 0.13 * L W^{2} + 0.001 * L^{2} W^{2}$	0.973	6.283	2,821.6

Activation function	Number of neurons in the hidden layer	Training		Validation
Activation function	Number of neurons in the hidden layer	RMSE	R²	RMSE	R²
Sigmoid	1	5.559	0.967	5.853	0.958
	2	4.771	0.978	4.831	0.974
	3	2.853	0.990	2.862	0.989
	4	2.866	0.990	2.874	0.989
	5	2.968	0.990	2.980	0.989
	6	2.909	0.990	2.945	0.989
	7	2.895	0.990	2.921	0.989
	8	2.919	0.990	2.945	0.989
	9	3.289	0.988	3.349	0.986
	10	3.170	0.988	3.219	0.986
Hyperbolic tangent	1	56.680	0.923	55.222	0.915
	2	52.680	0.870	55.221	0.785
	3	52740	0.820	55.665	0.797
	4	52.890	0.693	55.222	0.656
	5	56.648	0.804	55.225	0.777
	6	55.611	0.931	55.150	0.920
	7	56.672	0.935	55.213	0.927
	8	56.684	0.879	55.225	0.870
	9	56.684	0.740	55.225	0.697
	10	56.674	0.710	55.217	0.671

		Artificial neural network
		Training	Validation
R²	0.973	0.990	0.989
RMSE	3.303	2.853	2.862

Unidade Acadêmica de Engenharia Agrícola Unidade Acadêmica de Engenharia Agrícola, UFCG, Av. Aprígio Veloso 882, Bodocongó, Bloco CM, 1º andar, CEP 58429-140, Campina Grande, PB, Brasil, Tel. +55 83 2101 1056 - Campina Grande - PB - Brazil
E-mail: revistagriambi@gmail.com

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[1] * Corresponding author - E-mail: vitoria.edney@gmail.com

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Leaf area estimation in Coffea canephora genotypes by neural networks and multiple regression 1 1 Research developed at Universidade Federal do Espírito Santo, São Mateus, ES, Brazil

Estimativa da área foliar de genótipos de Coffea canephora por meio de redes neurais e regressão múltipla

ABSTRACT

HIGHLIGHTS:

**Leaf area estimation in Coffea canephora genotypes by neural networks and multiple regression** ¹ 1 Research developed at Universidade Federal do Espírito Santo, São Mateus, ES, Brazil