## 3 Results
### Application of Artificial Neural Networks for MWR Data  
Let us expand the combined dataset (\"REAL\"+\"SIMULATION\") from Section 3.2 with additional numerical simulation results by varying the size and location of the tumor. Table 3 contains results of binary classification of brightness temperature and IR temperature for four different neural network topologies. A significant influence of the structure of the neural network classifier on the efficiency of diagnostics is shown. The difference between the best (Topology 3) and worst (Topology 2) efficiency values reaches 21 percent. At the same time, a larger number of internal layers (Topology 1) does not give an advantage in the final results. Table 4 shows the original data in the form of confusion matrix for CNN. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Topology 1** & **Topology 2** & **Topology 3** & **Topology 4** \\ \hline Number of layers & 8 & 6 & 5 & 4 \\ Number of neurons on the 1 st layer & 20 & 20 & 20 & 20 \\ Number of neurons on the 2 nd layer & 20 & 20 & 20 & 10 \\ Number of neurons on the 3 rd layer & 20 & 10 & 14 & 3 \\ Number of neurons on the 4 th layer & 20 & 6 & 3 & 2 \\ Number of neurons on the 5 th layer & 20 & 4 & 2 & – \\ Number of neurons on the 6 th layer & 20 & 2 & – & – \\ Number of neurons on the 7 th layer & 20 & – & – & – \\ _sens_ & 0.74 & 0.66 & 0.86 & 0.81 \\ _spec_ & 0.67 & 0.61 & 0.82 & 0.71 \\ \(eff\) & 0.7 & 0.63 & 0.84 & 0.76 \\ F1 & 0.72 & 0.61 & 0.83 & 0.75 \\ \(\phi\) & 0.46 & 0.27 & 0.63 & 0.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Binary classification results for artificial neural networks with different fully connected layer architecture. Figure 21: The infrared (\(T_{IR}\), (**a**)) and brightness (\(T_{B}\), (**b**)) temperature distributions from the simulations show a characteristic bell-shaped appearance. The value of the mean harmonic measure F1 is close to the value of \(eff\) within approximately 3 percent (see Table 3), which indicates correct classification. The \(\phi\) coefficient (also called the Matthews correlation coefficient (MCC)) turns out to be noticeably smaller than the \(eff\) and F1-score values, but it also indicates the advantage of Topology 3 and the disadvantages of Topology 2. The best value of \(\phi=63\) percent for Topology 3 in our case is significantly less than for complex diagnostic methods, such as ultrasound elastography ([PERSON] et al., 2016) or mammography ([PERSON] et al., 2016), for which F-score and MCC \(\geq 90\) percent is a typical result. This difference is due to the use of fundamentally more accurate physical methods that make it possible to directly visualize the internal three-dimensional tissue structure with a resolution of \(\leq\)0.5 cm for ultrasound ([PERSON] et al., 2016) and \(<\)1 cm for mammography ([PERSON] et al., 2016). Microwave radiometry detects the presence of disease indirectly through temperature with a spatial resolution of approximately 2 cm in the plane and 4 cm along the normal coordinate. An additional negative factor for MWR diagnosis is the more complex relationship between the observed temperature distributions and the presence of the disease and its stage. Therefore, lower values of \(eff\), F1, and \(\phi\) for MWR are a natural result. The significance of MWR diagnostics lies in the possibility of organizing mass, non-invasive, and cheap cancer screening for preliminary diagnosis. It is necessary to control the number of epochs in the process of training the neural network so that overfitting problems do not arise. Figure 22 shows the moment (epoch = 113) at which the retraining of the neural network for Topology 3 occurs. The overfitting problem is solved based on the dropout method. This method allows regularization of artificial neural networks by eliminating random neurons in different epochs of neural network training. Additionally, we control the number of epochs in the training process.