## 4 Simulation Experiments
### Classification Tasks
#### 4.3.2 Results  
Table 5 shows the results of the classification performance. The best value in each metric is indicated in bold for each dataset. The standard deviation is indicated in parentheses. N/A indicates that the corresponding algorithm could not build a predictive model. Training time is in [second]. The brighter the cell color, the better the performance. In ASC, \(k\)-means is applied to adjust the position of the generated nodes in order to achieve a good approximation of the distribution of data points. In addition, some generated nodes and edges are deleted during the learning process. Therefore, the number of clusters is not shown for ASC in Table 5.  
As an overall trend, ASC, CAEAC, CAEAC-I, and CAEAC-C show better classification performance than SOINN + C, and GSOINN+. FTCAC shows the best classification performance on several datasets, whereas FTCAC cannot build a predictive model for TOX171. Regarding training time, ASC, FTCAC, and CAEAC are shorter than SOINN + C, GSOINN+, CAEAC-I, and CAEAC-C. With respect to generated nodes and clusters, CAEAC and its variants tend to generate a larger number of nodes and clusters than those of compared algorithms. Here, the null hypothesis was rejected on the Friedman test over all the evaluation metrics and datasets. Thus, we applied the Nemenyi post hoc analysis. Figure 6 shows a critical difference diagram based on the classification performance including all the evaluation metrics and datasets. Better performance is shown by lower average ranks, i.e., on the right side of a critical distance diagram. In theory, different algorithms within a critical distance (i.e., a red line) do not have a statistically significant difference [54]. In Figure 6, CAEAC-C shows the lowest rank value, but there is no statistically significant difference from CAEAC, CAEAC-I, ASC, and FTCAC. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Type** & **Dataset** & **Metric** & **ASC** & **FTAC** & **SOINN + C** & **CGONNN+** & **CAEAC** & **CAEAC-I** & **CAEAC-C** \\ \hline Synthetic & Aggregation & Accuracy & 0.999 (0.003)  
capability when learning additional data points after the deletion process. This can be regarded as the functional limitation of ASC. The effect of the different attribute processing of CAEAC and its variants shown in Figure 5 on the classification performance may be considered based on the difference in the number of clusters. In CAEAC, the difference in the range of attribute values may greatly affect the similarity measurement between a node and a given data point by CIM. Since CAEAC-I calculates similarity on each attribute, the difference in the range of each attribute value has no effect. Therefore, CAEAC-I can compute the similarity between a node and a given data point more accurately than CAEAC. On the other hand, the similarity tends to be smaller, i.e., CAEAC-I tends to generate many clusters. In CAEAC-C, the similarity measurement can be viewed as an intermediate approach between CAEAC and CAEAC-I, allowing for the suppression of excessive cluster generation while maintaining accurate similarity measures. This can be considered the reason why CAEAC-C shows superior classification performance on average to CAEAC and CAEAC-I (see Table 5). The above observations suggest that CAEAC, CAEAC-I, and CAEAC-C have several advantages over teh compared algorithms not only in classification performance but also from a functional perspective. The characteristics of CAEAC and its variants are summarized as follows:  
* CAEAC This algorithm shows stable and good classification performance and maintains fast computation. * CAEAC-I The classification performance and computation time of this algorithm are both inferior to CAEAC and CAEAC-C. However, in Table 5, it has the highest number of the best evaluation metric values among CAEAC and its variants. Therefore, this algorithm is worth trying when high classification performance is desired.