Traditional terrestrial wireless communication networks cannot support the requirements for high-quality services for artificial intelligence applications such as smart cities. The space-air-ground integrated network (SAGIN) provides a solution to address this challenge. However, SAGIN is heterogeneous, time-varying, and multi-dimensional information sources, making it difficult for traditional network architectures to support resource allocation in large-scale complex network environments. This paper proposes a service provision method based on Service Function Chaining (SFC) to solve this problem. Network Function Virtualization (NFV) is essential for efficient resource allocation in SAGIN to meet the resource requirements of user service requests. We propose a federation learning (FL) based algorithm to solve the embedding problem of SFCs in SAGIN. The algorithm considers different characteristics of nodes and resource load to balance resource consumption. Then an SFC scheduling mechanism is proposed that allows SFC reconfiguration to reduce the service blocking rate. Simulation results show that our proposed FL-VNFE algorithm is more advantageous compared to other algorithms, with 12.9%, 2.52%, and 10.5% improvement in long-term average revenue, acceptance rate, and long-term average revenue-cost ratio, respectively.