用大模型找最佳聚类数，让结果既准确又易懂。

The challenge of clustering short text data lies in balancing informativeness with interpretability. Traditional evaluation metrics often overlook this trade-off. Inspired by linguistic principles of communicative efficiency, this paper investigates the optimal number of clusters by quantifying the trade-off between informativeness and cognitive simplicity. We use large language models (LLMs) to generate cluster names and evaluate their effectiveness through semantic density, information theory, and clustering accuracy. Our results show that Gaussian Mixture Model (GMM) clustering on embeddings generated by a LLM, increases semantic density compared to random assignment, effectively grouping similar bios. However, as clusters increase, interpretability declines, as measured by a generative LLM's ability to correctly assign bios based on cluster names. A logistic regression analysis confirms that classification accuracy depends on the semantic similarity between bios and their assigned cluster names, as well as their distinction from alternatives. These findings reveal a "Goldilocks zone" where clusters remain distinct yet interpretable. We identify an optimal range of 16-22 clusters, paralleling linguistic efficiency in lexical categorization. These insights inform both theoretical models and practical applications, guiding future research toward optimising cluster interpretability and usefulness.