Classification and Indirect Weighing of Sweet Lime Fruit through Machine Learning and Meta-heuristic Approach

Figures & data

Table 1. Different fruit mass prediction models based on manual and image processing in literature

Authors and Year	Country	Fruit	Sample size (Test)	Modeling method	R^2
Khanali et al., 2007	Iran	Tangerine	165	SLR	0.960
Sharifi et al., 2007	Iran	Orange	150	TDP	0.991
Omid et al., 2010	Iran	Sweet lime	50	SLR	0.959 0.923 0.904
		Orange	50	SLR
		Tangerine	50	SLR
Sabzi et al., 2013	Iran	Orange	100	ANFIS	0.937
Miraei Ashtiani et al., 2014	Iran	Sweet lime	120	SLR	0.99
Venkatesh et al., 2015	India	Apple	20	SLR	0.925 0.943 0.947
		Sweet lime	36	SLR
		Orange	40	SLR
Ponce et al., 2018	Spain	Olive	200 (50)	SLR	0.972
Utai et al., 2019	Thailand	Mango	61	ANN	0.990
Pathak et al., 2019	India	Dried Terminalia chebula	300 (100)	SLR and quadratic	0.970
Mahawar et al., 2019	India	kinnow mandarin	180	Quadratic	0.956

R²: Coefficient of determination, SLR: Simple linear regression, TDP: Third-degree polynomial and ANN: Artificial neural network.

Table 2. Summary of the input output features used

Features	Calibration set			Validation set
	Minimum	Maximum	Mean	Minimum	Maximum	Mean
Length (mm)	32.365	102.230	65.170	38.857	91.958	65.145
Average Width (mm)	35.950	100.001	65.363	40.262	90.844	65.466
Depth (mm)	35.950	99.129	64.963	38.663	89.633	64.936
Projected Area View1 (mm^2)	1065.042	9384.716	4095.633	1463.913	7963.252	4096.954
Projected Area View2 (mm^2)	1187.802	9257.061	4012.080	1436.622	7382.749	4011.738
Perimeter View1 (mm)	121.900	400.972	258.622	156.106	367.639	258.955
Perimeter View2 (mm)	132.365	400.391	257.507	156.881	353.491	258.051
Weight Measured (g)	30.700	316.166	148.024	45.766	261.833	148.411

Figure 1. Flow chart of preprocessing steps for image features extraction

Figure 2. Methodology adopted for calibration and validation of the models

Figure 3. Schematic of SVM type 1 classifier

Figure 4. Schematic of GA optimized ANFIS model

Figure 5. Schematic of PSO optimized ANFIS model

Table 3. Confusion matrix for different SVM classifier and support vector (SV) count

SVM Kernel	Calibration						Validation						SV (bounded) count
Linear	Predicted Class						Predicted Class
			A	B	C	D			A	B	C	D
	Observed Class	A	59	12	0	0	Observed Class	A	26	4	0	0	193 (6)
		B	1	175	5	0		B	0	79	2	0
		C	0	14	217	0		C	0	5	94	0
		D	0	0	11	59		D	0	0	2	28
Polynomial	Observed Class	A	63	8	0	0	Observed Class	A	28	2	0	0	172 (6)
		B	3	170	8	0		B	1	77	3	0
		C	0	11	220	0		C	0	3	96	0
		D	0	0	8	62		D	0	0	2	28
RBF	Observed Class	A	59	12	0	0	Observed Class	A	26	4	0	0	171(4)
		B	1	173	7	0		B	0	79	2	0
		C	0	14	217	0		C	0	5	94	0
		D	0	0	11	59		D	0	0	2	28
Sigmoidal	Observed Class	A	0	58	13	0	Observed Class	A	0	27	3	0	317(20)
		B	0	178	3	0		B	0	80	1	0
		C	0	19	212	0		C	0	6	93	0
		D	0	0	18	52		D	0	0	5	25

Table 4. SVM classifier performance measure

SVM Kernel	Calibration					Validation
Linear		Class					Class
		A	B	C	D		A	B	C	D
	TP	59	175	217	59	TP	26	79	94	28
	TN	481	346	306	483	TN	210	150	137	210
	FP	1	26	16	0	FP	0	9	4	0
	FN	12	6	14	11	FN	4	2	5	2
	Acc	0.9765	0.9421	0.9458	0.9801	Acc	0.9833	0.9542	0.9625	0.9917
Polynomial	TP	63	170	220	62	TP	28	77	96	28
	TN	479	353	306	483	TN	209	154	136	210
	FP	3	19	16	0	FP	1	5	5	0
	FN	8	11	11	8	FN	2	4	3	2
	Acc	0.9801	0.9458	0.9512	0.9855	Acc	0.9875	0.9625	0.9667	0.9917
RBF	TP	59	173	217	59	TP	26	79	94	28
	TN	481	346	304	483	TN	210	150	137	210
	FP	1	26	18	0	FP	0	9	4	0
	FN	12	8	14	11	FN	4	2	5	2
	Acc	0.9765	0.9385	0.9421	0.9801	Acc	0.9833	0.9542	0.9625	0.9917
Sigmoidal	TP	0	178	212	52	TP	0	80	93	25
	TN	482	295	288	483	TN	210	126	132	210
	FP	0	77	34	0	FP	0	33	9	0
	FN	71	3	19	18	FN	30	1	6	5
	Acc	0.8716	0.8553	0.9042	0.9675	Acc	0.875	0.8583	0.9375	0.9792

Note: TP: True Positive, TN: True Negative, FP: False Positive, FN: False Negative, Acc: Accuracy

Table 5. Analysis of population size and ranking of GA–ANFIS models

Population Size	Network result						Ranking						Total Rank
	Calibration			Validation			Calibration			Validation
	dr	RMSE	VAF	dr	RMSE	VAF	dr	RMSE	VAF	dr	RMSE	VAF
25	0.942	5.793	98.505	0.955	4.186	99.133	2	2	2	6	4	4	20
50	0.942	5.833	98.484	0.954	4.253	99.110	3	1	1	1	1	1	8
75	0.944	5.588	98.609	0.955	4.158	99.141	14	14	14	12	14	14	82
100	0.942	5.786	98.510	0.955	4.187	99.133	1	5	5	3	2	8	24
150	0.942	5.787	98.508	0.955	4.186	99.133	5	4	4	5	6	7	31
200	0.943	5.622	98.592	0.955	4.186	99.133	11	10	10	8	8	10	57
250	0.943	5.597	98.606	0.955	4.182	99.137	13	13	13	13	11	12	75
300	0.942	5.789	98.507	0.955	4.178	99.133	7	3	3	4	12	2	31
350	0.942	5.704	98.551	0.955	4.184	99.134	8	6	6	9	9	11	49
400	0.943	5.622	98.593	0.955	4.186	99.133	10	11	11	11	3	9	55
450	0.943	5.619	98.594	0.955	4.186	99.133	12	12	12	10	5	3	54
500	0.942	5.689	98.558	0.955	4.184	99.133	6	7	7	2	10	5	37
550	0.942	5.682	98.562	0.955	4.176	99.137	4	8	8	14	13	13	60
600	0.943	5.636	98.586	0.955	4.186	99.133	9	9	9	7	7	6	47

Figure 6. Performance of GA optimized ANFIS model for different population size

Figure 7. Proposed GA-ANFIS model validation. (a) Predicted and actual weight. (b) Error percentage. (c) Error histogram

Table 6. Analysis of population size and ranking of PSO–ANFIS models

Population Size	Network result						Ranking						Total Rank
	Calibration			Validation			Calibration			Validation
	dr	RMSE	VAF	dr	RMSE	VAF	dr	RMSE	VAF	dr	RMSE	VAF
25	0.946	5.409	98.696	0.951	4.558	98.967	1	1	1	8	11	11	33
50	0.948	5.207	98.792	0.951	4.544	98.976	2	3	3	11	12	12	43
75	0.949	5.104	98.839	0.952	4.667	98.917	4	7	7	12	7	7	44
100	0.948	5.270	98.763	0.950	5.200	98.655	3	2	2	6	3	3	19
150	0.949	5.134	98.826	0.950	4.577	98.959	6	5	5	7	10	10	43
200	0.950	4.93	98.918	0.950	4.783	98.863	11	11	11	5	6	6	50
250	0.950	4.999	98.887	0.948	4.963	98.776	8	10	10	3	4	4	39
300	0.950	4.927	98.919	0.954	4.311	99.076	9	12	12	14	14	14	75
350	0.950	5.070	98.855	0.953	4.505	98.991	10	8	8	13	13	13	65
400	0.951	4.915	98.924	0.948	4.844	98.834	13	13	13	4	5	5	53
450	0.950	5.121	98.832	0.946	6.059	98.187	7	6	6	2	1	1	23
500	0.952	4.886	98.936	0.945	5.367	98.569	14	14	14	1	2	2	47
550	0.949	5.158	98.815	0.951	4.616	98.942	5	4	4	10	9	9	41
600	0.951	5.017	98.879	0.951	4.621	98.938	12	9	9	9	8	8	55

Table 7. Analysis of personal and global learning coefficients and ranking of PSO–ANFIS models

Learning coefficients		Network result						Ranking						Total Rank
		Calibration			Validation			Calibration			Validation
C1	C2	dr	RMSE	VAF	dr	RMSE	VAF	dr	RMSE	VAF	dr	RMSE	VAF
0.67	3.33	0.942	5.723	98.541	0.955	4.182	99.134	3	7	7	18	17	17	69
1.33	2.67	0.941	5.852	98.491	0.954	4.252	99.134	1	1	1	15	14	18	50
1.0	2.0	0.950	4.927	98.919	0.954	4.311	99.076	15	18	18	12	10	10	83
3.33	0.67	0.942	5.802	98.501	0.955	4.181	99.131	2	3	4	17	18	16	60
1.0	0.75	0.943	5.741	98.532	0.953	4.264	99.098	7	6	6	11	13	13	56
1.0	1.25	0.946	5.312	98.743	0.951	4.632	98.934	9	9	9	4	6	6	43
1.0	1.5	0.947	5.273	98.761	0.952	4.748	98.883	11	10	10	7	4	4	46
1.0	1.75	0.948	5.163	98.812	0.953	4.394	99.040	12	13	13	8	9	9	64
1.0	2.25	0.950	4.994	98.889	0.947	4.823	98.850	16	16	16	1	3	3	55
1.0	2.5	0.947	5.252	98.771	0.952	4.500	98.994	10	11	11	6	8	8	54
0.25	2.0	0.949	5.158	98.815	0.954	4.501	98.992	13	14	14	16	7	7	71
0.5	2.0	0.951	4.942	98.912	0.950	4.971	98.771	17	17	17	3	2	2	58
0.6	2.0	0.949	5.211	98.790	0.949	5.089	98.713	14	12	12	2	1	1	42
0.75	2.0	0.951	5.081	98.850	0.951	4.717	98.895	18	15	15	5	5	5	63
1.0	1.0	0.945	5.489	98.658	0.953	4.280	99.090	8	8	8	10	12	12	58
0.75	0.75	0.942	5.777	98.513	0.953	4.287	99.088	4	5	5	9	11	11	45
0.5	0.5	0.943	5.802	98.500	0.954	4.240	99.107	6	4	3	13	16	15	57
0.25	0.25	0.942	5.810	98.496	0.954	4.242	99.107	5	2	2	14	15	14	52

Table 8. Analysis of inertia weight and ranking of PSO–ANFIS models

Inertia Weight	Network result						Ranking							Total Rank
	Calibration			Validation			Calibration				Validation
	dr	RMSE	VAF	dr	RMSE	VAF	dr	RMSE	VAF	dr		RMSE	VAF
0.2	0.9498	5.0662	98.8565	0.9479	5.1763	98.6705	3	2	2	2		3	3	15
0.4	0.9513	4.9035	98.9287	0.9468	5.4013	98.55	5	5	5	1		2	2	20
0.6	0.9496	5.0436	98.8667	0.9518	4.4719	99.006	2	3	3	4		4	4	20
0.8	0.9496	5.114	98.8348	0.9503	6.1999	98.0881	1	1	1	3		1	1	8
1.0	0.950	4.9265	98.9187	0.9536	4.3113	99.0755	4	4	4	5		5	5	27

Figure 8. Performance of PSO optimized ANFIS model for different population size

Figure 9. Performance of PSO optimized ANFIS model for different personal and global learning coefficients

Figure 10. Performance of PSO optimized ANFIS model for different inertia weight

Figure 11. Proposed PSO-ANFIS model validation. (a) Predicted and actual weight. (b) Error percentage. (c) Error histogram

Table 9. Comparison of the different sweet lime weighing models

Model	dr	RMSE	Ref.	Eq.
$M_{est}=1.002V_{psp}-1.094$	0.7466	26.4108	Miraei Ashtiani et al., 2014	8
$M_{est}=0.7925V+21.502$	0.9460	5.0210	Venkatesh et al., 2015	9
$\begin{array}{c}{W}_{est}=26.0089-1.41238L-0.86038D_{1avg}\\ +1.2961D_2+0.057225P{A}_1-0.00594P{A}_2\\ +0.028537Per{i}_{Hori}-0.10904Per{i}_{Ver}\end{array}$	0.9260	7.9774	Phate et al., 2019a	10
FCM clustered ANFIS model	0.9536	4.2439	Phate et al., 2019b	-
GA-ANFIS model	0.9548	4.1581	Present work	-

Figure 12. Comparison of the optimized ANFIS models for validation samples

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