Convex Hull-Based Topic Similarity Mapping in Multidimensional Data

This research presents a large-scale thematic analysis of 66,002 Slovak university thesis abstracts, aimed at identifying, categorizing, and visualizing research trends across multiple academic disciplines. Using BERTopic for unsupervised topic modeling with K-Means clustering, 3000 distinct thematic clusters were extracted through rigorous coherence optimization, with each topic characterized by representative keywords derived from class-based TF-IDF weighting. Text embeddings were generated using SlovakBERT-STS, a domain-adapted Slovak BERT model fine-tuned for semantic textual similarity, producing 768-dimensional vectors that enable precise computation of cosine similarity between topics, resulting in a 3000 × 3000 topic similarity matrix. The optimal topic count was determined through systematic evaluation of K values ranging from 1000 to 10,000, with K = 3000 identified as the optimal configuration based on coherence elbow analysis, yielding a mean coherence score of 0.433. Thematic relationships were visualized through Multidimensional Scaling (MDS) projection to 3-D space, where convex hull geometries reveal semantic boundaries and topic separability. The methodology incorporates dynamic stopword filtering, Stanza-based lemmatization for Slovak morphology, and UMAP dimensionality reduction, achieving a balanced distribution of approximately 22 abstracts per topic. Results demonstrate that fine-grained topic models with 3000 clusters can extract meaningful semantic structure from multi-domain, morphologically complex Slovak academic corpora, despite inherent coherence constraints. The reproducible pipeline provides a framework for large-scale topic discovery, coherence-driven optimization, and geometric visualization of thematic relationships in academic text collections.