Mitigating Heterogeneity among Factor Tensors via Lie Group Manifolds
  for Tensor Decomposition Based Temporal Knowledge Graph Embedding
Jiang Li Xiangdong Su Yeyun Gong Guanglai Gao
Recent studies have highlighted the effectiveness of tensor decomposition
methods in the Temporal Knowledge Graphs Embedding (TKGE) task. However, we
found that inherent heterogeneity among factor tensors in tensor decomposition
significantly hinders the tensor fusion process and further limits the
performance of link prediction. To overcome this limitation, we introduce a
novel method that maps factor tensors onto a unified smooth Lie group manifold
to make the distribution of factor tensors approximating homogeneous in tensor
decomposition. We provide the theoretical proof of our motivation that
homogeneous tensors are more effective than heterogeneous tensors in tensor
fusion and approximating the target for tensor decomposition based TKGE
methods. The proposed method can be directly integrated into existing tensor
decomposition based TKGE methods without introducing extra parameters.
Extensive experiments demonstrate the effectiveness of our method in mitigating
the heterogeneity and in enhancing the tensor decomposition based TKGE models.