There are rich proper noun derivative semantic relationships in geographic entity vector data. The identification of traditional proper noun derivative semantic relationships usually requires toponym researchers to examine the source of derived toponyms by consulting a large number of toponym documents. This method cannot adapt to the mining of proper noun derivative semantic relationships for large-scale geographical entity. In this regard, this paper proposes a method of identifying the proper noun derivative semantic relationships for geographical entity by combining prompt learning and XGBoost model. This method transforms the extraction problem of proper noun derivative semantic relationships into a binary classification problem by analyzing the characteristics of the derivation relationship of toponyms in the form of toponyms and the spatial and temporal distribution of geography. Firstly, prompt learning and gaussian mixture model are used to extract and cluster the derivation words of toponyms, so as to realize the recognition of derived toponyms collections. Then, enumerate the possible proper noun derivations in the toponym set, and then the XGBoost model is used to identify the semantic relations derived from the proper noun of geographical entities. In the experiment, the recognition method of proper noun derivative semantic relationships based on prompt learning and XGBoost proposed in this paper has achieved good relationship recognition effect in the experiment. This method has certain practical value in the fields of toponym management and toponym translation.