Sequential recommendation (SR) learns users' preferences by capturing the sequential patterns from users' behaviors evolution. As discussed in many works, user-item interactions of SR generally present the intrinsic power-law distribution, which can be ascended to hierarchy-like structures. Previous methods usually handle such hierarchical information by making user-item sectionalization empirically under Euclidean space, which may cause distortion of user-item representation in real online scenarios. In this paper, we propose a Poincar\'{e}-based heterogeneous graph neural network named PHGR to model the sequential pattern information as well as hierarchical information contained in the data of SR scenarios simultaneously. Specifically, for the purpose of explicitly capturing the hierarchical information, we first construct a weighted user-item heterogeneous graph by aliening all the user-item interactions to improve the perception domain of each user from a global view. Then the output of the global representation would be used to complement the local directed item-item homogeneous graph convolution. By defining a novel hyperbolic inner product operator, the global and local graph representation learning are directly conducted in Poincar\'{e} ball instead of commonly used projection operation between Poincar\'{e} ball and Euclidean space, which could alleviate the cumulative error issue of general bidirectional translation process. Moreover, for the purpose of explicitly capturing the sequential dependency information, we design two types of temporal attention operations under Poincar\'{e} ball space. Empirical evaluations on datasets from the public and financial industry show that PHGR outperforms several comparison methods.
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