## 4 Discussion  
### Accuracy Assessment  
In order to evaluate the accuracy of the findings from satellite imagery, a total of 78 samples were selected from the entire study area based on the stratified random sampling technique: 25 for the double crop, 35 for the Kharif crop, and 18 for the Rabi crop (Figure 12). A confusion matrix was built in the Python programming language for the purpose of performing an accuracy evaluation. The confusion matrix (Table 2) demonstrated that the suggested model accurately recognized 19 points for the double crop. However, 1 sample point was incorrectly categorized as Kharif crop, and 5 samples were incorrectly categorized as Rabi crop. In the same manner, out of a total of 35 Kharif sample points, 32 were correctly classified, while one sample was incorrectly labeled as a double crop, and two samples were incorrectly classed as a Rabi crop. In the case of the Rabi crop, only two of the samples were incorrectly identified as the double crop, while the remaining 16 samples were correctly classified. Once the operation was done, physical verification of the locations was conducted along with GPS location marking and field photographs (Figures 13-15).  
Figure 11: Cropping intensity map (Datum: WGS84).  
Figure 12: Ground validation points (Datum: WGS84).  
Figure 13: Kharif crop ground validation point example with photograph (Datum: WGS84).  
Figure 14: Rabi crop ground validation point example with photograph (Datum: WGS84).  
Figure 15: Double crop ground validation point example with photograph (Datum: WGS84).  
The following indices were taken into consideration for the validation.  
\[\text{Accuracy }(\text{A})=\frac{(\text{TP}+\text{TN})}{(\text{TP}+\text{FP}+ \text{TN}+\text{FN})} \tag{4}\]  
\[\text{Precision }(\text{Pc})=\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{5}\]  
\[\text{Recall }(\text{Rc})=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{6}\]  
\[\text{F1 Score}=\frac{P_{c}-R_{c}}{P_{c}+R_{c}} \tag{7}\]  
\[\text{Kappa Coefficient }(\kappa_{\text{c}})=\frac{N\sum_{i=1}^{n}q_{ii} \smallsetminus\sum_{i=1}^{n}(q_{i+}\;X\;q_{+i})}{N^{2}-\sum_{i=1}^{n}(q_{i+}\;X \;q_{+i})} \tag{8}\]  
\[\text{User Accuracy }(\%)\;(\text{Ua})=\frac{q_{ii}}{q_{i+}}\times 100 \tag{9}\]  
\[\text{Producers Accuracy }(\%)\;(\text{Pa})=\frac{q_{ii}}{q_{i+}}\times 100 \tag{10}\]  
\[\text{Overall Accuracy }(\text{Oa})\;(\%)=\frac{\sum_{i=1}^{n}q_{ii}}{V} \times 100 \tag{11}\]  
where TP--True Positive, TN--True Negative, FP--False Positive, FN--False Negative, \(n\) is the total number of columns of the confusion matrix; \(q_{ii}\) is the number of correct classifications of the upper crop-type sample in the \(i\) row and \(i\) column of the confusion matrix, \(q_{i+}\) and \(q_{+i}\) are the total number of crop-type samples in row \(i\) and column \(i\), and \(V\) is the total number of samples used for verification.  
The overall accuracy of all the different crops was 0.90, equivalent to 90%. The Kharif crop showed the highest observed level of precision. In order to illustrate the positive predicted value, precision was determined, and the result was that the overall precision was 0.84, which is equivalent to 84% (Table 3). The precision was found to be highest in the Kharif crop, while it was found to be lowest in the Rabi crop. When attempting to portray sensitivity or the rate of true positives, the recall measure of the confusion matrix is beneficial.  
The overall recall value was 0.85, equivalent to 85%, with the Kharif crop having the highest recall and the double crop having the lowest. The F1 score was taken into consideration to consider both the precision and recall metrics together. The overall recall value was 0.84, equivalent to 84%, and the Kharif crop had the greatest F1 score. The kappa coefficient (\(\kappa_{\text{c}}\)) of the confusion matrix was 0.784, which can be considered significant.