Heterogeneous information network is a representation of heterogeneous data. How to integrate complex semantic information of heterogeneous data is one of the challenges faced by recommendation systems. A high-order embedded learning framework for heterogeneous information networks based on weak ties featured by semantic information and information transmission abilities is constructed. The framework includes three modules of initial information embedding, high-order information embedding aggregation, and recommendation prediction. The initial information embedding module first adopts the best trust path selection algorithm to avoid information loss caused by sampling a fixed number of neighbors in a full-relational heterogeneous information network. Then the newly defined importance measure factors of multi-task shared characteristics based on multi-head attention are adopted to filter out the semantic information of each node. Additionally, combined with the interactive structure, the network nodes are effectively characterized. The high-order information embedding aggregation module realizes high-order information expression by integrating weak ties and good knowledge representation ability of network embedding. The hierarchical propagation mechanism of heterogeneous information networks is utilized to aggregate the characteristics of sampled nodes into the nodes to be predicted. The recommendation prediction module employs the influence recommendation method of high-order information to complete the recommendation. The framework is characterized by rich embedded nodes, fusion of shared attributes, and implicit interactive information. Finally, the experiments have verified that UI-HEHo can effectively improve the accuracy of rating prediction, as well as the pertinence, novelty and diversity of recommendation generation. Especially in application scenarios with sparse data, UI-HEHo yields good recommendation effects.