## 2 Results and Discussion
### Methods
#### 2.1.5 Validity of clusters and antibiotics classification  
Applicability of clustering results for chemical compounds classification is the best confirmation of clusters' validity and the correct choice of a clustering algorithm [6, 8]. Antibiotics were classified to evaluate the efficiency of clustering. A database of 3,249 compounds with anti-bacterial activity (ABIO) [36] was used for model calculations. After removing duplicate structures and stereoisomers, the ABIO database was reduced to 1,183 topologically unique structures. It contained 868 \(\beta\)-lactams, 325 quinolones (Figure 4), several compounds with both elements, and 37 other antibiotics (macrolides, etc.). The content of the ABIO database was clustered to produce six clusters at 0.1 similarity threshold and 78 clusters at 0.5 threshold. Clusters at 0.1 threshold are mixed: each contains both quinolones and \(\beta\)-lactams. One should expect such results: antibiotics contain several substitutents which are bigger than a \(\beta\)-lactam ring and affect more bits in the screen vector. On the other hand, the non-informative rings (pyridine) produce structural screens, which are part of quinolones. To estimate possibilities of classification of antibiotics in large databases, the ABIO database was combined at random with 999,994 unique structures from the AUORA database. Thus, the input database (TESTDB) with 1,001,177 records was formed. The field _Activity_ was created for TESTDB. Its value was set to 1 for all records from ABIO and to 0 otherwise. The number of steps was defined as 10 (Nst = 10) to create similarity thresholds of 0.1, 0.2, etc. The minimal cluster size was set to 2. The obtained cluster tree displayed information of 879,609 clusters and 8,672,957 chemical structures at different similarity thresholds! TESTDB database contained only 0.12 of target compounds. The large size of the database and the low probability of discovering target compounds made manual analysis of the cluster tree absolutely inapplicable. Data preprocessing, filtering, and visualization tools were required for better assessment. Filtering could be performed by assigning a variable value for some parameters. For TESTDB database the field _Activity_ value was used for visualization. Conditional colors were applied to display the values as described in [37]. The average value of the selected parameter was calculated for each cluster and displayed as an icon of appropriate color at tree view control. Two types of cluster filtering: _minimal_ and _representative,_ were created for cluster tree reduction. Both filters used external properties (_Activity_ value for the described calculations). The range of target properties was defined by the user. Two types of filtering differ by applicability of a predefined range of target properties. _Minimal_. The cluster is displayed if one chemical structure has a property value in the specified range. Figure 4: Main classes of antibiotics under study. _Representative._ The cluster is displayed if more, than 50% of structures has property values in the specified range. Such criterion divides clusters into two groups: active and inactive. We do not use more complex statistical criteria [38], which divide clusters into several groups and are used for experiment optimization only. Both types of filtering visualized selected clusters as well as parent clusters, even if parent clusters did not satisfy filter conditions. The data obtained as a result of TESTDB clustering were summarized in Table 2. It also displays the results of filtration using _Activity_ field in the range 0.9-1.0. Calculation time was 3 hr 59 min. The structures not assigned to clusters in the _Unfiltered_ field form singletons. Figure 5 shows the clusters tree after _Representative_ filtering. The chart is more compact compared to non-filtered clustering. Due to smaller number of tree nodes, run-time operations (expanding, collapsing) required less time, than for unfiltered data.