## 2 Results and Discussion
### Methods
#### 2.1.5 Validity of clusters and antibiotics classification
Approximately 87% antibiotics were successfully classified at similarity thresholds 0.5 and 0.6. The number of compounds in \(Error2\) group at similarity threshold 0.5 (seven compounds) and 0.6 (five compounds) was considerably less than at similarity threshold 0.4. This should be treated as stopping criteria [41]. Also, if one considers \(Error\) 1 as penalty function [40], clustering should be stopped at similarity threshold 0.4. On the other hand, the fuzzy clustering approach gives better values for 0.6 similarity threshold. 87.6% of the antibiotics were classified at 0.5 threshold, while a slightly lesser value (85.7%) was observed for 0.6. The 0.5 similarity threshold produces a lesser number of singletons and small-sized clusters, which, in turn, diminishes the prediction possibilities. On the other hand, a fuzzy clustering approach (rows 8 and 9, Table 3) gives a better value for 0.6 threshold (0.03% overlapping), than for 0.5(0.74%). At 0.7 threshold clusters become almost distinct, but the small average cluster size (3) makes the data unsuitable for external database classification. Thus, a similarity threshold of 0.6 can be considered optimal for classification of antibiotics. There is \begin{table}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline
1 & Similarity threshold & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 & 0.8 & 0.9 \\
2 & No. representative clusters & 8 & 70 & 117 & 151 & 185 & 225 & 263 & 203 \\
3 & No. non-clustered ABIO structures & 734 & 222 & 144 & 147 & 169 & 199 & 304 & 645 \\  & (\(Error1\)) & & & & & & & & \\
4 & No. clustered AURORA structures & 238 & 154 & 109 & 73 & 32 & 25 & 14 & 3 \\  & (\(Error2\)) & & & & & & & & \\
5 & AURORA structures, having \(\beta\)-lactam & 27 & 94 & 85 & 66 & 27 & 22 & 13 & 3 \\  & or quinolinone fragments & & & & & & & \\
6 & 4 and 5 difference (“pure” \(Error2\)) & 211 & 60 & 24 & 7 & 5 & 3 & 1 & 0 \\
7 & \% successfully classified ABIO compounds & 38.0 & 81.2 & 87.8 & 87.6 & 85.7 & 81.0 & 79.1 & 45.5 \\
8 & No. of AURORA structures (top) and No. of AURORA structures without antibiotic fragment (bottom), overlapped with representative clusters & 24296 & 15219 & 475 & 748 & 609 & 153 & 45 & 8 \\
9 & No. of ABIO structures, overlapped with non-representative clusters & 7 & 2 & 71 & 3 & 321 & 1 & 0 & 0 \\ \hline \end{tabular}
\end{table} 
Table 3: Classification errors at different similarity thresholds. The smaller are the values in Rows 3 and 6, the better classification is. The term _“Representative clusters”_ stands for the number of clusters containing over 50% compounds from ABIO database. some ambiguity in selecting best the threshold among the two values 0.5 and 0.6. The data for 0.5 and 0.6 thresholds are very similar, and it is impossible to determine an optimal threshold with precision better than 0.1 in the problem under consideration, so, it is no good to increase number of steps (_Nst_) for antibiotic classifications because of different criteria give different optimal similarity thresholds, the difference being greater 0.1. The program allows saving probe molecules for the selected similarity threshold in SD files for further clustering of external databases. SD files with probe molecules and singletons for similarity threshold 0.6 are available in this work. Singletons may form clusters in databases with other content. Saved data can be used for classification of antibiotics in large databases with random content, like PubChem [42]. The validity of the obtained set of clusters was confirmed. 85.7% of the studied compounds were successfully classified with 0.4% of error. Such result is remarkable as classification was performed at a very high noise level: TESTDB database contained 0.12% antibiotics only.