  Given a time-evolving tensor with missing entries, how can we effectively
factorize it for precisely predicting the missing entries? Tensor factorization
has been extensively utilized for analyzing various multi-dimensional
real-world data. However, existing models for tensor factorization have
disregarded the temporal property for tensor factorization while most
real-world data are closely related to time. Moreover, they do not address
accuracy degradation due to the sparsity of time slices. The essential problems
of how to exploit the temporal property for tensor decomposition and consider
the sparsity of time slices remain unresolved. In this paper, we propose TATD
(Time-Aware Tensor Decomposition), a novel tensor decomposition method for
real-world temporal tensors. TATD is designed to exploit temporal dependency
and time-varying sparsity of real-world temporal tensors. We propose a new
smoothing regularization with Gaussian kernel for modeling time dependency.
Moreover, we improve the performance of TATD by considering time-varying
sparsity. We design an alternating optimization scheme suitable for temporal
tensor factorization with our smoothing regularization. Extensive experiments
show that TATD provides the state-of-the-art accuracy for decomposing temporal
tensors.
