## 3 Performance Analysis
Here the land cover changes in a watershed area obtained using Landsat 2 FTM+ images of 2007 and 2018 are presented in Reference [89]. The matrix is developed for land cover change detection problem where there are six types of land cover classes identified namely--forest, water body, agricultural land, grassland, bare land and urban. Suppose that we need to assess the number of pixels that are correctly and incorrectly classified under each category. On classifying 1470 pixels, water body is correctly classified for 60 pixels, forest is correctly classified for 20 pixels, agricultural land correctly classified for 20 pixels, grass land correctly classified for 290 pixels, urban area correctly classified for 90 pixels and barren land is correctly classified for 750 pixels. Remaining pixels are incorrectly classified and responsible for the misclassification errors associated with the accuracy of land cover classification. In the case of water body, _TP_ contains cases with water body correctly classified as water body, _TN_ contains cases with all other classes correctly classified, _FP_ contains cases with all other classes incorrectly classified as water body and _FN_ contains cases with water body incorrectly classified as other categories. The example can be represented in a confusion matrix as shown in Table 7.  
Overall accuracy can be obtained by dividing the total number of correct pixels (diagonal elements in the matrix) by the total number of pixels in the confusion matrix. To compare two classified data products, the observed frequencies in a confusion matrix are assumed to be multinomial distribution with the complete random nature of the elements in the confusion matrix [90]. With the availability of true data reference, the randomness within fails. If the reference data are found along column and this data is considered as truth, the elements which belong to a particular type can be correctly classified or confused with other types and they will be located in same column but never in different columns. The randomness within the multinomial is not at all possible. For this, Quality Control Column Set (QCCS) is developed. The main advantage is that it enables to state quality specifications for each category and test if they are satisfied [91]. Accuracy, Recall, precision and F-measure are also derived from the confusion matrix [92]. Accuracy is measured as the ratio of the correctly predicted observations to the total ones. It is an efficient parameter mainly when the dataset is symmetric. _Recall_ is a measure of the number of positive class predictions out of all positive examples in the database. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline  & \multicolumn{6}{c}{**Actual Class**} \\ \cline{2-7}  & **Water** & **Forest** & **Agriculture** & **Grass** & **Urban** & **Bareland** & **Total** \\ \hline Water & 60 & 0 & 0 & 0 & 0 & 0 & 60 \\ \hline Forest & 0 & 20 & 0 & 0 & 0 & 0 & 20 \\ \hline Agriculture & 0 & 0 & 20 & 0 & 0 & 0 & 20 \\ \hline Grass & 30 & 0 & 10 & 290 & 10 & 0 & 340 \\ \hline Urban & 0 & 0 & 0 & 0 & 90 & 0 & 90 \\ \hline Bareland & 10 & 20 & 60 & 50 & 50 & 750 & 940 \\ \hline Total & 100 & 40 & 90 & 340 & 150 & 750 & 1470 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Confusion matrix example. For an imbalanced classification problem having just two classes, recall is the ratio of the number of true positives to the total number of true positives and false negatives. In an imbalanced classification problem with multiple classes, recall is computed as the ratio of sum of true positives across all classes to the sum of true positives and false negatives across all classes. Its value ranges between 0 and 1 with the best value considered to be 1. _Precision_ is a measure of the number of positive class predictions that actually belong to the positive class. For an imbalanced classification problem having two classes, precision is the ratio of the number of true positives to the total number of true positives and false positives.