DOCUMENT SIMILARITY AND ENTITY NETWORKS

Persistent homology tracks how topological features—connected components (H₀) and cycles/loops (H₁)—appear and disappear as the similarity threshold changes. Features that persist across a wide range of thresholds represent robust structure in the data, while short-lived features are likely noise. The optimal threshold is found where stable clusters (H₀) and meaningful loops (H₁) are most prominent.