## 5 Experiments
### Impact of Random White Noise in the Proposed Algorithm  
This experiment evaluates the impact of random white noise on the proposed algorithm for mining frequent approximate subgraphs with structural and label variations. To perform this experiment, we introduced 5%, 10%, 15%, and 20% of noise to the PTC  
Figure 11: Runtime and memory usage of the proposed algorithm as the graph collection size increases. (**a**) Runtime; (**b**) Memory usage.  
datasets in Table 9. Then, we apply our proposed algorithm to the noisy datasets to mine frequent approximate subgraphs at the different noise levels.  
Noise was added randomly, including the addition of nodes with their corresponding edges, the addition of only edges, and label substitutions in both nodes and edges. For each noisy dataset, we mined frequent approximate subgraphs using AGCM-SLV, employing dissimilarity thresholds of 1 and 2. In all cases, we used a support threshold of 90%. The frequent approximate subgraphs mined from the original, noise-free datasets served as reference.  
Figure 12 shows the impact of different levels of noise on the frequent approximate subgraphs mined. This figure contains four bar graphs, each corresponding to a different PTC dataset (FM, FR, MM, and MR). In each graph, the x-axis represents different noise levels (0% (noise-free), 5%, 10%, 15%, and 20%) grouped by dissimilarity thresholds (1 and 2). The bars are stacked vertically, with each bar's height indicating the number of frequent approximate subgraphs mined. Each bar is split into two segments: a blue segment labeled _Preserved_ that represents the frequent approximate subgraphs preserved from those mined in the original noise-free (0% noise level) dataset, and a green segment labeled _Additional_ that represents the new frequent approximate subgraphs mined at the current noise level.  
The results reveal that as noise increases, the number of frequent approximate subgraphs also increases, suggesting that certain subgraphs become frequent because the noise introduces additional occurrences. These occurrences allow previously infrequent subgraphs to now satisfy the required support threshold and become frequent. Moreover, when noise is included, the majority (99.49% on average) of the frequent approximate subgraphs mined from the noise-free dataset (see 0% in Figure 12) were preserved, indicating  
Figure 12: Number of frequent approximate subgraphs mined by the proposed algorithm when varying the dissimilarity thresholds \(\beta=1\) and \(\beta=2\) with a constant support threshold \(\alpha=90\%\).  
the algorithm's tolerance to white noise. Table 10 shows that every frequent subgraph (100%) is maintained when the dissimilarity threshold is 1, and 98.88% are preserved when the dissimilarity threshold is 2. Thus, only a few of the frequent approximate subgraphs are lost. This happens because occurrences disappear (i.e., an occurrence that previously required only two modifications may now need more, making it no longer match the frequent approximate subgraph). As a result, these subgraphs no longer satisfy the required support threshold.  
Due to the random nature of the introduced noise, datasets with higher noise levels may sometimes maintain more frequent approximate subgraphs than those with lower noise levels. As the noise level increases, additional frequent approximate subgraphs may appear that are not present in the noise-free dataset. However, the majority of frequent subgraphs from the original dataset are consistently maintained across the different noise levels, which shows the algorithm's low sensitivity to white noise.