## 2 Results and Discussion
### Methods
#### 2.1.5 Validity of clusters and antibiotics classification
Thus, the more the number of singletons, the more prediction possibilities are sensitive to initial ABIO content. Additionally, some compound may not be assigned to any cluster at high similarities thresholds, therefore no conclusion about their activity can be made. The number of singletons increases with increasing similarity threshold and the number of clusters are reduced at high similarity threshold (0.9). It is clear, that there is an optimal similarity threshold for classifying antibiotic from random structures. To select such a threshold, it is necessary to study two types of classification errors. 1) _Error1_. Compound from ABIO database was not present in a _Representative_ antibiotic cluster. Such compound might be a singleton. Alternatively, it was present in the cluster formed by compounds from AURORA database mainly. 2) _Error2_. Compound from AURORA database with _Activity\(=\)_0 was included into the _Representative_ cluster of antibiotics (Activity=1). After filtering two lists of compounds corresponding to both kinds of classification errors were formed automatically for the selected similarity threshold. _Error 2_ requires special consideration. All compounds from AURORA database were assumed to have 0 _Activity_ value. However, it was not true. AURORA database combined all classes of compounds, antibiotics among them. Therefore, occurrence of such structures in the antibiotics clusters is not accidental. Since the bioactivity data for AURORA database were not available, the structures with \(\beta\)-lactam or quinolone fragments of antibiotics (Figure 4) cannot be treated as _Error2_. The number of representative clusters (Row 2 in Table 3) should not be compared with the results of representative filtering (Table 2). At low similarity thresholds Table 2 displays non-representative clusters. They are parent clusters for representative ones at high values of similarity threshold. Non-representative clusters are included to maintain the cluster tree integrity. Cluster overlapping data are displayed in rows 8 and 9 in Table 3. A quarter of AURORA structures are overlapped by ABIO clusters and all ABIO structures are overlapped by AURORA clusters at similarity threshold 0.2. Almost non-overlapped clusters occur when the similarity threshold is 0.7 and higher. One may conclude that the reason of such huge overlapping results from the nature of antibiotics. The \(\beta\)-lactam fragment is too small and gives a small number of non-zero components in bit vector, as well as another substituents of approximately equal size. A lot of non-informative substituents (pyridine, furyl, etc) satisfy these conditions. So, if a \(\beta\)-lactam antibiotic would have two or more substituents (this is true in the majority of cases), it might be assigned to a cluster which contains other chemical structures with the same substituents. Contrary to this, if a structure without a \(\beta\)-lactam ring has two or more substituents, identical with some antibiotics, it may have high similarity being in single or overlapped clusters. The quinolone fragment is larger, but it gives a lot of non-zerobit vector components, which are identical with non-informative phenyl and pyridyl substituents. This also results in overlapped clusters. To reduce overlapping, one can restrict fragments and leave informative ones only. But such approach reduces application of the clustering algorithm: non-informative fragments may have great significance in other tasks. There are different ways to select optimal similarity threshold, like penalty functions [40] or stopping rules [41]. In these approaches a substantial change in properties take place at optimal threshold. One may observe that the majority of antibiotics were assigned to representative clusters at similarity threshold 0.4. Only 144 antibiotics (12.2%) remain unassigned, but 24 compounds from AURORA database without antibiotic fragments (Table 3) were erroneously classified as active (\(Error2\)).