## 3 Models of Vector Presentation of Text Documents Using Lexical and Semantic Approaches
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Total Number of Clusters which** & **Mean Clustering** & **Mean Clustering** & **Mean Clustering** & **Mean Clustering** \\
**Algorithm** & **Topic** & **Include a** & **Accuracy for a** & **Computeless for** **a Given Topic** & **Accuracy for the** **E**utrine Corpus** & **Completeness for** **the Entire Corpus** \\ \hline  & Economics & 5 & 0.30 & 0.12 & \\  & IT and innovation & 2 & 0.30 & 0.16 & \\  & Education & 4 & 0.34 & 0.16 & \\  & Politics & 4 & 0.30 & 0.14 & \\ Propagation—I (lex) & Industry & 5 & 0.24 & 0.11 & \\  & Travel and tourism & 3 & 0.31 & 0.25 & \\  & Agriculture & 3 & 0.23 & 0.15 & \\  & Health care and medicine & 3 & 0.35 & 0.19 & \\ \hline  & Economics & 2 & 0.45 & 0.32 & \\  & IT and innovation & 1 & 0.23 & 0.16 & \\ Affinity & Education & 2 & 0.27 & 0.24 & \\ Propagation—II (sem) & Industry & 2 & 0.19 & 0.14 & \\  & Travel and tourism & 2 & 0.72 & 0.48 & \\  & Agriculture & 1 & 0.18 & 0.14 & \\  & Health care and medicine & 2 & 0.26 & 0.19 & \\ \hline  & Economics & 4 & 0.28 & 0.12 & \\  & IT and innovation & 2 & 0.26 & 0.16 & \\ Affinity & Education & 3 & 0.40 & 0.19 & \\ Propagation—III (matrix) & Politics & 2 & 0.36 & 0.24 & \\  & Industry & 4 & 0.30 & 0.13 & 0.35 & 0.18 \\  & Travel and tourism & 2 & 0.51 & 0.24 & \\  & Agriculture & 2 & 0.21 & 0.14 & \\  & Health care and medicine & 2 & 0.32 & 0.16 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Assessing the mean values of clustering accuracy and completeness for each of the corpus topics. The mean accuracy and completeness for all corpus topics can be calculated as the mean arithmetic value of the mean values for each of the corpus topics. Let us analyze the data presented in Table 3.  
We shall start by analyzing how the lexical, semantic, and combined presentation of texts affect the processing of cosine metric value matrices and clustering accuracy when using the affinity propagation algorithm as a research tool (Table 3). When using the lexical, semantic, and combined (with an averaged value matrix representing the lexico-semantic bond) approaches, the number of resulting clusters was equal to 29, 14, and 21 (Table 3), respectively, whereas the respective clustering accuracy values were 29%, 31%, and 35% (Table 3). Therefore, we can assume that the transition from the lexical presentation of documents to the semantic one allows us to increase the clustering accuracy (approximately by absolute 3% or relative 10%) and reduce the cluster number (from 29 to 14). When moving from the semantic approach to the combined one, the clustering accuracy increases (approximately by absolute 3% or relative 10%); however, the number of clusters increases as well (from 14 to 21). This suggests that the relationship between the cluster number and the clustering accuracy is not unambiguous, but that the combined approach increases the clustering accuracy, which correlates with the data obtained using the UMAP algorithm from the visualization of cosine metric value matrices using the lexical (Figure 4b), semantic (Figure 5b), and combined approaches toward document vectorization (Figure 6). The clustering completeness when using the affinity propagation algorithm with lexical, semantic, and combined approaches is 15%, 23%, and 18%, respectively (Table 3). It should be noted that assessing the clustering accuracy and completeness in the event where there are many topics and many clusters in which documents from these topics can be included in different ratios is a very difficult issue; however, this is a problem for a separate study. Our assessments do not claim to be absolutely accurate, but they suggest that using the combined approach based on the lexico-semantic bond of texts allows one to increase the clustering accuracy compared to the approaches based only on lexical or semantic document presentation.