# A New Cascade-Correlation Growing Deep Learning Neural Network Algorithm
## 4 Experimental Results
### Classification Problems at Real-World Data Sets  
The proposed CCG-DLNN algorithm was tested on a number of different real classification problems such as: the Lung Image Database Consortium image collection (LIDC-IDRI) [32], and some benchmark problems from the UCI Machine Learning Repository [33]: Diabetes 130-US hospitals (DH) [34], Hepatitis C Virus (HCV) for Egyptian patients, Heart Disease (HD), Breast Cancer Wisconsin (Diagnostic) (BCW) [33], Breast Cancer Coimbra (BCC) [35], Liver Disorders Data Set (LD) [33], Acute Inflammations Data Set (AI) [36], and Pima Indians Diabetes Database (PID) [33]. Table 3 explains the description of all data sets as it shows the number of training and testing samples and the overlapping level which is visually represented in Figure 8 using the t-distributed stochastic neighbor embedding (t-SNE) projection. Figure 8 shows the 2-D representation of LIDC-IDRI, DH, HCV, HD, and BCC data sets. The t-SNE 2D representation of BCW, AI, LD, and PID data sets will be founded at [2]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Two-Spiral Architecture** & **Number of Neurons** & **Accuracy (\%)** & **Avg Cost** \\ \hline Initial NN & 0 & 44 & 1.004625 \\ \hline Adding 1 st Hidden Layer & 10 & 53 & 0.932671 \\ \hline Adding 2 nd Hidden Layer & 22 & 99.5 & 0.054119 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Testing two-spiral problem using CCG-DLNN. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **\# Hidden Layers** & **\# Neurons** & **Accuracy (\%)** & **Avg Cost** \\ \hline CCG-DLNN & 2 & 22 & 99.50 & 0.054119 \\ \hline CCNN & 10 & 10 & 87.21 & 0.254895 \\ \hline GP-DLNN (growing step) [2] & 3 & 70 & 92.23 & 0.075852 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation results of CCG-DLNN, CCNN and GP-DLNN on the two-spiral problem. Figure 7: Testing two-spiral problem using CCG-DLNN algorithm. For each event, 100 proceedings are performed and the resulting averages are shown in Table 4 as well as Figures 9 and 10, where the best of each test are in bold face. The three cases have the same condition for stopping. We can observe that the CCG-DLNN algorithm obtains lower errors for all cases than the other two algorithms. The loss rate for the three algorithms on the LIDC-IDR data set is shown at Figure 11. It can be seen from Figure 11 that the loss of CCG-DLNN strictly decreases faster than CCNN and slightly faster or equal to GP-DLNN [2]. Figure 12 gives the curves of loss obtained by CCG-DLNN, GP-DLNN and CCN on the LIDC-IDR data set. Figure 12 shows that the loss of CCG-DLNN decreases as the number of hidden units increases. In addition, the CCG-DLNN loss curve will reach zero at limited steps of the CCG-DLNN, which is the number of training data samples. We observe that the CCG-DLNN algorithm will prevent a local minimum problem. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Data Set** & \multicolumn{3}{c}{**Training Rate**} & \multicolumn{3}{c}{**Testing Rate**} & \multicolumn{3}{c}{**Number of Hidden Units**} \\ \hline  & **CCG-DLNN** & **CCNN** & **GP-DLNN** & **CCG-DLNN** & **CCN** & **GP-DLNN** & **CCG-DLNN** & **CCN** & **GP-DLNN** \\ \hline LIDC-IDRI & **0.98** & 0.93 & 0.95 & **0.96** & 0.95 & 0.94 & 10 & 13 & **  
The criteria used to measure the efficiency of the tests were sensitivity, specificity and accuracy. The first performance, testing the accuracy of the proposed CCG-DLNN algorithm, was compared to the GP-DLNN (growing step) [2] and CNN algorithms. The best outcomes for all data sets resulted from the CCG-DLNN algorithm, as shown in Table 5.  
The classification performance related to the CCG-DLNN, CCNN and GP-DLNN on the LIDC-IDRI data set is presented in Figure 13 and the classification performance for all data sets is represented in Table 6. All methods achieved good performance in the classification. The highest AUC value was obtained for the proposed algorithm CCG-DLNN.