Fine-Grained Cultural Perception and Evaluation of Beijing’s Capital Culture Integrating Large Language Models with Higher-Order Tensor Decomposition

Fine-grained urban cultural perception is critical for GIScience, yet traditional social media studies struggle with complex cultural semantics and heterogeneous factor integration. Addressing Beijing’s “Capital Culture,” this study couples LLM agents with higher-order tensor decomposition. Using 2019 full-sample geotagged Sina Weibo data, we developed a four-agent collaborative architecture with Chain-of-Thought prompting and human-in-the-loop mechanisms via a locally deployed Qwen3-32B model. A four-way tensor (“Cultural Type–Evaluation Aspect–Sentiment Polarity–Spatial Carrier”) was constructed and integrated with kernel density estimation to characterize spatial differentiation. We address three questions: whether LLMs can reliably classify fine-grained cultural perceptions, how cultural types associate with evaluation dimensions, sentiments, and spatial carriers, and whether tensor decomposition reveals latent patterns beyond marginal frequencies. The agentic workflow achieves over 90% accuracy in cultural and sentiment classification, and the tensor decomposition attains a 94.87% goodness-of-fit, successfully identifying latent patterns. Spatially, Beijing’s capital culture exhibits an unbalanced hierarchical structure—“high coupling in the core area with differentiated expansion at the periphery.” This study validates the transition from “data-driven” to “AI + data dual-driven” spatial analysis, providing a quantifiable pathway for LLM-supported urban cultural governance.