## 4 Experiment Results and Discussions  
In our study, the experiments were carried out in a MATLAB_R2016b environment using an Intel(R) Core (TM) i7 CPU 3.40-3.70 GHz personal computer and Microsoft Windows 7, 64-bit operating system. The study is based on a local dataset containing 124 CPE images. The main contribution of the study is the development of an effective algorithm that can accurately determine the presence of overlapping nuclei in CPE images. The first step of the proposed algorithm was to deal with image quality. Histogram stretching and CLAHE image enhancement methods were utilized in order to enhance the contrast of cell nuclei. Then, maximum entropy thresholding based nuclei segmentation was employed to extract candidate nuclei regions from surrounding objects in the image. The segmentation performance of maximum entropy based nuclei segmentation was evaluated in the test images and yielded a 92% detection accuracy. After the nuclei were detected, an overlapping nuclei detection scheme was developed. A new combination of 16 geometrical and 10 textural features was extracted from 4000 nuclei containing single and overlapping nuclei. Thus, our dataset is made up of 4000 \(\times\) 26-dimensional datasets. It is partitioned into training and testing sets in an 80/20 ratio, as given in Table 4.  
Then, double-strategy RF was utilized to select the most important features and classify single and overlapping nuclei using selected high-ranking features. One of the important parameters that we needed to adjust while constructing RF was the number of decision trees to be grown. The optimal number of decision trees was obtained through empirical tuning. OBB errors using a different number of decision trees are illustrated in Figure 13. From the graph, it can be seen that OOB errors decrease at above 250 decision trees, and start to stabilize from 300 trees. Thus, we grew 400 decision trees in order to maintain classification stability and keep the computation cost low. Once a random forest was constructed with 400 decision trees, feature selection was performed by scoring OOB permutation errors using each feature. The importance of features ranked by RF is given in Figure 14. To select the most significant features, we experimentally tested the different feature numbers in ascending rank order and examined their training accuracy as given in Figure 15. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Observational Data** & **Training** & **Testing** & **Total** \\ \hline Single Nuclei & 2692 & 683 & 3375 \\ Overlapped Nuclei & 508 & 117 & 625 \\ Total & 3200 & 800 & 4000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The number of observations used in the training and testing stage. Figure 13: Out-of-bag (OOB) error of RF using different number of decision trees. The chart shows that the first eight ranked features achieved the highest training accuracy, and those features are described in Table 5. We fed those selected features as input to train the RF ensemble classifier. The trained RF classifier was used to validate the testing dataset. The classification accuracy of using RF's selected features was compared to the accuracy of using all features. In addition, we also examined four alternative classifiers: NB [40], SVM [41], KNN [42], and DT [43] by coupling with all features and RF's selected features. The classification accuracies of using all features and RF selected features blending with five classifiers are presented in Tables 6 and 7, respectively. From the experiment results, it is shown that using RF selected features provides better accuracy compared to using all features for most classifiers except NB. The results also reveal that the RF ensemble classifier yields preferable accuracy compared to NB, SVM, KNN, and DT classifiers. The synergy between RF's selected features and the