## 5 Conclusions  
The proposed RBFCCN network combines the concepts of RBFN and CCN. During the training of RBF hidden units, a RBFCCN applies both the initialization technique similar to that of the SCRBFN and the optimization technique of CCNs. The cascade correlation algorithm furnishes the incremental learning ability of the RBFCCN. The incremental learning ability ensures the RBFCCN automatically builds its network topology during training. Before training RBFCCNs, no prior information about network topology is required. As a result, training RBFCCNs are more convenient than training BNNs. Another advantage of cascade-correlated structure is that it avoids the moving target problem and converges more rapidly than the BNNs.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cl number** & **Total** & **BNN** & **SCRBFN** & **RBFN** & **RBFCCN** \\ \hline
2 & 13 & 13 & 11 & \(12.1\pm 0.1\) & 12 \\
3 & 20 & \(17.5\pm 0.4\) & 17 & \(16.6\pm 0.2\) & 16 \\
4 & 28 & \(26.8\pm 0.4\) & 19 & \(24.9\pm 0.2\) & 27 \\
5 & 21 & \(17.2\pm 0.4\) & 20 & \(15.5\pm 0.4\) & 16 \\
6 & 13 & \(11.3\pm 0.3\) & 10 & \(11.0\pm 0.5\) & 7 \\
7 & 7 & \(6.7\pm 0.2\) & 5 & \(5.0\pm 0.1\) & 6 \\
8 & 7 & 6 & 3 & \(4.8\pm 0.4\) & 5 \\
0,1,9,10 & 45 & \(0.3\pm 0.4\) & 45 & \(23.5\pm 8.3\) & 43 \\ \hline Prediction accuracy without unknown (\%) & \(90.4\pm 0.6\) & 78.0 & \(82.4\pm 0.5\) & 81.7 \\ Total prediction accuracy (\%) & \(64.0\pm 0.5\) & 84.4 & \(73.6\pm 6\) & 85.7 \\ \hline \hline
**Cl number** & **Total** & **PLS-DA** & **SVM** & **RF** \\ \hline
2 & 13 & 10 & 13 & 13 \\
3 & 20 & 14 & 19 & \(18.6\pm 0.2\) \\
4 & 28 & 28 & 28 & \(26.3\pm 0.2\) \\
5 & 21 & 11 & 17 & \(15.0\pm 0.1\) \\
6 & 13 & 8 & 11 & \(11.1\pm 0.2\) \\
7 & 7 & 7 & 7 & 5 \\
8 & 7 & 6 & 6 & 6 \\
0,1,9,10 & 45 & 0 & - & - \\ \hline Prediction accuracy without unknown (\%) & \(77.1\) & \(92.7\) & \(87.2\pm 0.4\) \\ Total prediction accuracy (\%) & \(54.5\) & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 9: Average numbers of correctly predicted spectra with 95% confidence intervals of PCB external validation data set. All modeling methods were reconstructed 30 times. The prediction accuracy without unknown is the prediction accuracy calculated by the external validation set excluding the congeners that contain 0, 1, 9 and 10 chlorine atoms. The total prediction accuracy is the prediction accuracy calculated by the complete external validation set.  
RBFCCNs, BNNs, RBFNs, SCRBFNs, PLS-DAs, SVMs and RFs were tested with four data sets. The test results were obtained with statistical measurements of confidence intervals. The SVM and RF methods proved their excellence over the neural network approaches on these classification problems. All three neural networks were generally yielded better performance than PLS-DA in prediction. Compared with the RBFN and SCRBFN models in four test data sets, the RBFCCN models generally yielded better prediction accuracies. The RBF transfer function applied in RBFCCNs makes RBFCCNs a reliable approach for novel class evaluation. RBFCCNs generally yielded better novel class evaluation ability compared with RBFNs, BNNs and PLS-DA by setting an output threshold 0.5. The RBFCCN is also capable of modeling imbalanced data set. The RBFCCN was statistically shown to be a robust and effective classification algorithm for chemometrics, especially in novel class evaluation and outlier detection.  
Future work will involve in developing novel training methods to train the networks more rapidly. Investigations of different optimization algorithms such as the genetic algorithms and particle swarm optimizations to train RBFCCNs are necessary. In addition, it is important to compare RBFCCNs with other methods for outlier or novel class evaluation, such as one-class SVM in chemical data sets.