## 5 Results  
We present the results of various experiments we have conducted in this study. To evaluate the performance of our proposed ensemble architecture, individual baseline models were trained first that would serve as a basis for comparison of our eventual method and also to discover which DCNN architectures performed best. Out of the eight models, the four best-performing baseline models were selected to evaluate the performance of our ensemble architecture. Table 7 shows the performance of the baseline models. Only baseline models with accuracy above 90% were selected, which include ResNet50, ResNet18, DenseNet201, and EfficientNetb0. The selected models were pre-trained models using the hyperparameter values presented in Table 8. We trained the MPIFR by first combining the selected baseline models in pairs, in threes, and all four selected models. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Models** & **Accuracy** & **Sensitivity** & **Precision** & **Specificity** & **F1-Score** & **AUC** \\ \hline K-Nearest & & & & & & \\ Neighbor & 95.85 & 97.48 & 92.85 & 98.84 & 94.91 & 97.52 \\ (KNN) & & & & & & \\ \hline Generalized & & & & & \\ Additive & 94.45 & 92.50 & 96.17 & 99.02 & 92.69 & 95.25 \\ Model & & & & & & \\ \hline Naive Bayes & 95.15 & 98.80 & 91.18 & 97.98 & 93.83 & 96.89 \\ \hline Gradient & & & & & & \\ Boosted & 96.55 & 95.73 & 97.17 & 98.64 & 95.91 & 97.61 \\ (GBM) & & & & & & \\ \hline MPIFR & 97.77 & 97.48 & 98.45 & 99.57 & 97.92 & 99.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of classifying the MPIFR with various machine learning (ML) classifiers. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Models** &
\begin{tabular}{c} **Accuracy of the Pre-Trained** \\ **Baseline Models (\%)** \\ \end{tabular} & **Elapsed Training Time (Hours)** \\ \hline Efficientnetb0 & 92.08 & 8.89 \\ \hline ResNet50 & 92.84 & 5.9 \\ \hline Inceptionresnetv2 & 90.43 & 33.46 \\ \hline Inceptionv3 & 90.73 & 0.71 \\ \hline ResNet18 & 91.32 & 2.33 \\ \hline DenseNet201 & 93.34 & 33.95 \\ \hline Squeezenet & 85.92 & 1.47 \\ \hline Shufflenet & 90.60 & 3.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance of the eight pre-trained models. \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline Train-Test ratio & 70.30 \\ \hline Activation function & ReLU \\ \hline Mini Batch Size & 20 \\ \hline Max Epochs & 30 \\ \hline Initial Learn Rate & 0.00125 \\ \hline Learn-Rate Drop Factor & 0.1 \\ \hline Learn-Rate Drop Period & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Set of hyper-parameters for training baseline models using transfer learning. The result of combining the selected baseline models are presented in Table 9. The result shows significant improvement from a combined pair of baseline models in comparison to all four selected baseline models. However, model training takes more time when a large number of models are combined as indicated by the training time in hours presented in Table 9. The ensemble model took more than two (2) days to train because the final training time was that combined training time for all four models utilized in our MPIFR method. Further, we note that while the MPIFR model training time is large in some cases, training time is incurred once during model development. Test time is typically faster and is more important when the model is deployed and operationalized. We believe that it is reasonable to trade off higher training time to achieve higher performance. The ensemble model in Table 9 combines the four selected baseline models namely ResNet50, DenseNet201, ResNet18, and EfficientNetb0. The resulting performance is the best of the state-of-the-art multi-class models of the histopathological breast cancer classification based on BreakHis images. Confusion Matrix: In order to determine which classes were confounded by other classes, we analyzed the confusion matrix. Figure 17 shows the confusion matrix of the top-performing technique.