## 2 Results and Discussion
### Methods
#### 2.1.5 Validity of clusters and antibiotics classification
Analyzing the cluster tree, one can conclude that the antibiotics have formed clusters, starting from similarity threshold equal to 0.2 and these clusters still exist at 0.9 similarity threshold. Clusters multiply with increasing the similarity threshold (with exception of similarity threshold 0.9). Clusters reduce in size and become more distinct in similarity of structures. Figure 5: Implementation of _Representative_ filter for TESTDB clusters tree view. \begin{table}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline
**Similarity** & \multicolumn{6}{|c|}{**No. of clusters (upper value) and number of compounds in clusters (lower value)**} \\ \cline{2-10}
**threshold** & **0.1** & **0.2** & **0.3** & **0.4** & **0.5** & **0.6** & **0.7** & **0.8** & **0.9** \\ \hline
**Unfiltered** & 103 & 2186 & 18024 & 65560 & 125426 & 167529 & 184916 & 178515 & 137349 \\  & 1001174 & 1001030 & 998525 & 980144 & 924788 & 833572 & 715498 & 567843 & 649206 \\ \hline
**Minimal** & 41 & 133 & 169 & 173 & 179 & 203 & 233 & 265 & 204 \\  & 938335 & 321443 & 25978 & 3636 & 1389 & 1171 & 1047 & 899 & 544 \\ \hline
**Representative** & 34 & 88 & 118 & 143 & 163 & 192 & 228 & 263 & 203 \\  & 918634 & 136643 & 8359 & 1565 & 1238 & 1127 & 1030 & 893 & 541 \\ \hline \end{tabular}
\end{table} 
Table 2: Results of clustering TESTDB with _Nst_=10 and minimal cluster size=2. To illustrate it, a tree, generating cluster, selected in Figure 5 (number of compounds=65) was investigated. A modified algorithm [39] was used to find a common independent substructure set for a cluster. An independent substructure set is a set of substructures of maximal size, which are common for selected dataset and none of them is a subgraph of another. A cluster with 65 structures at similarity threshold=0.3 (Figure 5) has the maximal common fragment A (Figure 6). It forms four clusters B-E at similarity threshold 0.4. Together they contain 64 compounds, plus one compound forming a singleton at 0.4 threshold. A maximal common fragment is identical for clusters C and E. They are distinguished by presence of phenyl at different positions in C and by presence of nitrogen-oxygen bond in E. Cluster B is not specific and contains the same common fragment as cluster A. At threshold 0.5 cluster E remains unchanged. Cluster D forms two clusters - G and H (Figure 6). One of them (G) is distinct and does not change up to 0.8-similarity threshold. Cluster C produces a cluster with 13 structures (three singletons), the common fragments being the same as in C, but hydroxyphenyl is detected as a common fragment instead of phenyl. Finally, cluster D produces two clusters; one of them (F, Figure 6) is distinct. This cluster leaves singleton at similarity threshold 0.6 and forms a cluster with 19 compounds, where atom A is equal to nitrogen (Figure 6). This cluster (A=N) remains unchanged up to threshold 0.8. The second cluster, formed from B at 0.5 threshold (the size was eight compounds), is not distinct and is divided into three small clusters and two singletons at 0.6 threshold. Figure 6: Common fragments, found for clusters at different similarity threshold. Number of compounds in each cluster is displayed. Parents for structures F, G, H are shown with arrows. Thus, both distinct and non-distinct clusters are formed at similarity thresholds 0.5. The more the similarity threshold, the more distinct clusters are. But at high values of similarity threshold a lot of small-size clusters and singletons are generated. The more singletons (or small-sized clusters) in the final data, the greater the probability of incorrect classification of compounds in external databases is. In reality, a singleton can form a new cluster if a number of similar compounds are present in the external database. But, if this singleton would be absent in ABIO database, then compounds similar to the above singleton might be classified in other clusters with common, but non-informative structural fragments (phenyl, furyl, etc). If such clusters are marked as inactive, a wrong conclusion may be reached.