Geometric Structures and Patterns of Meaning: A PHATE Manifold Analysis of Chinese Character Embeddings

We systematically investigate geometric patterns in Chinese character embeddings using PHATE manifold analysis. Through cross-validation across seven embedding models and eight dimensionality reduction methods, we observe clustering patterns for content words ( 实词) and branching patterns for function words ( 虚词). Analysis of 1000+ characters across 12 semantic domains reveals that geometric complexity correlates with semantic content: meaningful characters exhibit rich geometric diversity while structural radicals collapse into tight clusters. The comprehensive 子-network analysis (123 phrases) demonstrates systematic semantic expansion from fundamental element character. These findings provide computational evidence supporting traditional linguistic theory and establish a novel framework for geometric analysis of semantic organization.