Global vector comparisons, which are computationally costly, symmetric by design, and frequently challenging to interpret, have historically been used to address document similarity, a fundamental task in information retrieval and text classification. A neighborhood-based document similarity framework based on ideas from mathematical topology is proposed in this paper. Instead of using exhaustive pairwise comparisons to determine similarity, local neighborhood structures are used to model documents as elements of a finite topological space induced by a similarity relation. The suggested method allows for the natural ordering of documents according to their relative proximity, supports asymmetric similarity relations, and captures local continuity using β-neighborhoods and near-open sets. A hybrid extension is presented that uses contextual embeddings produced by BERT to induce the underlying neighborhood structure in order to improve semantic representation while maintaining interpretability. Neural embeddings function as a semantic basis on which topological relations and near-set approximations are built, rather than taking the place of the topological model. Neighborhood overlap and topological refinement are then used to calculate document similarity, which enables the identification and explanation of both direct and indirect semantic relationships using explicit neighborhood paths. In comparison to TF-IDF and standalone BERT models experimental evaluation on benchmark datasets shows that the suggested topological and hybrid approaches achieve competitive or superior accuracy while enhancing scalability, asymmetry handling, and explainability. The findings show that neighborhood-based topological modeling offers a transparent and ethical framework for document similarity analysis in large-scale and interpretability-critical applications, especially when paired with neural embeddings.
Barbary et al. (Fri,) studied this question.