## 5 Results
The processing time of TF-IDF was the most efficient at 12.81 s.  
The dataset was divided into training, validation, and test subsets. A small validation subset (20% of the training data) was separated from the training corpus and used to tune threshold values. The main part of the training set was used solely for training LSA, LDA, and constructing MinHash representations, while the test set was used for final evaluation. During the experiments, special attention was paid to ensuring that fragments from the same source document did not appear in both training and test sets simultaneously. To guarantee no overlap, a group-based split was used (GroupKFold by source document ID). In the hybrid method using LSA, LDA, and MinHash, there is no classical \"training\" phase involving gradient descent. However, there is a parameter-fitting stage (e.g., fitting SVD for LSA, training LDA models, and generating hashes), which was carried out only on the training data. The hybrid approach involved multiple threshold values (\(\lambda\)) that affected the final decision: thresholds for Jaccard similarity (MinHash), for cosine similarity in the LSA space, for cosine similarity in the LDA space, and a final aggregated threshold \(\lambda_{\text{fused}}\). Each of these thresholds was treated as a hyperparameter, as their values directly influenced the model's precision, recall, and ultimately the F1-score. A grid search over combinations of these thresholds was conducted on the validation subset. As a result, the optimal final threshold was determined to be \(\lambda_{\text{fused}}=0.7\), which provided the best trade-off: precision \(\approx\) 1.00 (no false positives), recall \(\approx\) 0.73 (still a high detection rate), F1-score \(\approx\) 0.84. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**N-gram (n)** & **Precision** & **Recall** & **F1-Score** & **Processing Time (s)** \\ \hline
1 (Unigram) & 1.00 & 1.00 & 1.00 & 19.55 \\
2 (Bigram) & 1.00 & 0.51 & 0.67 & 14.81 \\
3 (Trigram) & 1.00 & 0.51 & 0.67 & 16.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of N-gram for different values of n.  
Figure 2: N-gram comparison of metrics. Setting a lower \(\lambda_{\text{fused}}\) value (e.g., 0.5) resulted in a drop in precision to \(\sim\)0.50, which is unacceptable for industrial systems, where each false positive requires manual review. On the other hand, setting \(\lambda_{\text{fused}}\geq 0.8\) led to a recall below 0.65, indicating an unacceptably low level of detection. Below are Table 5 and Figure 3 summarizing the comparison of metrics for the N-gram, TF-IDF, and hybrid models. Figure 3 presents a comparison of the models in terms of execution time on the validation set. As shown in Table 3, although all models yield a comparable F1-score of around 0.67, they differ in terms of precision, recall, and processing time. The N-gram model offers high precision but lower recall, whereas TF-IDF demonstrates high recall with lower precision. The hybrid model maintains high recall that is similar to that of TF-IDF but at the expense of significantly increased computational cost. We conducted a series of experiments with the threshold value and confirmed that increasing \(\lambda_{\text{fused}}\) to 0.7 completely eliminates false positives on the test set while maintaining an acceptable detection level (Table 3). Thus, by accepting a minimal reduction in recall, we achieved perfect precision, making the system highly reliable for automated text verification tasks where false positives are critical. To justify the relevance and competitiveness of the hybrid approach, we conducted a direct comparison with the baseline BERT-like model bert-base-multilingual-cased [35]. The proposed hybrid method demonstrates comparable accuracy while requiring significantly fewer computational resources and avoiding the need for large pre-trained transformer models.