## 4 Results and Discussion  
Quantitative analysis was performed on each cancerous image based on the four prostate cancer tissue groups (Grade 3, Grade 4, Grade 5, and Benign). We implemented the proposed method using MATLAB R2018a. We performed data analysis to analyze the components of the nuclei, which were segmented from prostate tissue images. In this paper, 400 images were used in total. Of these, 240 were used for training and 160 were used for testing. The number of images considered for each group was 100, and these were classified as malignant vs. benign, Grade 3 vs. Grade 4+5, and Grade 4 vs. Grade 5. Each image was 24-bits/pixel with a size of \(512\times 512\) pixels. All of the possible results are shown in Tables 2-4, where we show the confusion matrices of SVM binary classification for training and testing separately. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Training: 99.2\%**} & \multicolumn{3}{c}{**Testing: 88.7\%**} \\ \hline
**Train** & **Malignant** & **Benign** & **Data** & **Test** & **Malignant** & **Benign** & **Data** \\ \hline Malignant & 60 & 0 & 60 & Malignant & 34 & 6 & 40 \\ \hline Benign & 1 & 59 & 60 & Benign & 3 & 37 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Confusion matrix of SVM binary classification—Malignant vs. Benign. Figure 6: Proposed binary method for support vector machine (SVM) classification. Three different classifiers have been used here for binary classification and each group is classified independently and separately. Tables 2-4 show the confusion matrices used to evaluate the performance of machine learning algorithms and the classifiers on a set of train and test data. We have shown these confusion matrix tables to get a better idea about the errors of a classification model. Each one of these tables is divided into two parts to show the correctly classified and misclassified data with respect to the training and testing process respectively. In Table 5, we used four types of performance metrics, namely, accuracy, sensitivity, specificity, and Matthews's correlation coefficient (MCC). These metrics were calculated using our confusion matrices, i.e., true positive (TP), true negative (TN), false positive (FP), and false negative (FN). We multiplied the accuracy by 100% to normalize it with respect to the other measurements. The four types of performance metrics used in Table 5 are explained as follow,  
1. Accuracy is measure of the proportion of correctly classified samples. \[Accuracy=\frac{TP+TN}{TP+TN+FP+FN}\times 100\] (12)
2. Sensitivity is a measure of the proportion of positive correctly classified samples. \[Sensitivity=\frac{TP}{TP+FN}\times 100\] (13)
3. Specificity is a measure of the proportion of negative correctly classified samples. \[Specificity=\frac{TN}{TN+FP}\times 100\] (14)
4. [PERSON]'s correlation coefficient (MCC) is the eminence of binary class classification. It is a correlation coefficient between target and predictions. \[MCC=\frac{TP\times TN-FP\times FN}{\sqrt{((TP+FN)(TP+FP)(TN+FN)(TN+FP))}}\times 100\] (15)  
Table 5 shows the classification results of the proposed method for three different groups. The SVM binary classification accuracy, sensitivity, specificity, and MCC for malignant vs. benign are 88.7%, 91.8%, 86.0%, and 70.2%, respectively. For Grade 3 vs. Grade 4+5, the classification accuracy, sensitivity, specificity, and MCC are 85.0%, 81.8%, 88.8%, and 70.3, respectively. For Grade 4 vs. Grade 5, the classification accuracy, sensitivity, specificity, and MCC are 92.5%, 94.7%, 95.0%, and 85.1, respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Training: 95.0\%**} & \multicolumn{3}{c}{**Testing: 92.5\%**} \\ \hline
**Train** & **Grade 4** & **Grade 5** & **Data** & **Test** & **Grade 4** & **Grade 5** & **Data** \\ \hline Grade 4 & 54 & 6 & 60 & Grade 4 & 36 & 4 & 40 \\ \hline Grade 5 & 0 & 60 & 60 & Grade 5 & 2 & 38 & 40 \\ \hline \hline \end{tabular}
\end{table}