## 2 Results and Discussion  
### Methods  
#### 2.1.1 Algorithm  
Algorithm basics are described in [14]. At the first stage the set of highly diverse \"probe\" molecules is defined. This set is formed by selecting the most diverse compounds, their number being determined by pre-defined similarity. These structures are used as cluster space. The number of clusters in cluster  
Figure 1: A typical dendrogram, generated by hierarchical clustering algorithms. space is dynamically calculated and depends on initial dataset diversity. Thus, the main disadvantage of k-mean algorithms - predetermined number of clusters, is avoided. The remaining structures are added to the clusters with maximal similarity to the probe molecule. 2D topological descriptors are used for similarity calculations. The algorithm suggested in this work uses divisive (top-down) hierarchical clustering. It has an advantage of an accurate data representation. Moreover, divisive hierarchical clustering requires less time and resources compared to traditional hierarchical clustering (bottom-up). Additionally, divisive hierarchical clustering may be regarded as a step in multi-step algorithms suggested for clustering of very large databases [15, 16]. The initial dataset of diverse probe-molecules described in literature [14] is formed using an original algorithm based on random selection of diverse compounds. This is a fast processing algorithm. However, random selection of molecules results in non-deterministic clustering. The same dataset generates different clusters. The number of clusters may also differ with every procedure. We used a modified Maximum Dissimilarity Selection algorithm [17] instead of that published in [14]. It was successfully implemented to clustering of chemical databases [18]. This algorithm allows selecting the \(L\) most diverse structures from an \(N\) dataset. The Maximum Dissimilarity Selection cannot be regarded as a deterministic algorithm. Various \(L\) datasets may be generated, depending on the order of structures in the \(N\) database. Non-deterministic clustering is explained by the discrete number of structural fragments in a molecule. It also results in inaccuracies in the process of diversity sorting, which is demonstrated by Figure 2. The first compound \(L\) is selected as a probe molecule. There exists another pair of compounds (A and B) with identical diversity to probe molecule. They contain the same number of fragments - both new and the existing ones. Thus, any of the two compounds with the same diversity can be selected as the second probe by diversity sorting. The remaining molecule is placed in the end of diversity sorted set and cannot be selected as a probe molecule. Such ambiguity may be extended by the third, fourth compound, and so on. If dataset \(L\) contains few aromatic fragments and no halogens, it makes no difference, which compound A or B, is selected (Figure2). This problem was described as ties in proximity [19]. However, this is is important for subsequent calculations. If structure A is selected as a probe molecule, the cluster will mainly be formed by chloroaromatic compounds, while fluoroaromatic compounds may be assigned to a different cluster. Thus, there exist several methods of screening  
Figure 2: Ambiguities in Maximum Dissimilarity Selection algorithm. datasets to select \(L\) structures. However, if datasets with identical order of compounds are used, the algorithm returns the same structures \(L\). This results in deterministic clustering. To make initial datasets identical, 12-byte hash codes [20] are generated for chemical structures. The fixed-length chemical structure encoding has advantage compared with variable-length (InChI[21], SMILES[22]), because of calculations with fixed-length variables are simplest and consuming less time. Then hash values are sorted in a decreasing order. Such sorting of datasets leads to deterministic results in most cases.