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Given a time-evolving tensor with missing entries, how can we effectivelyfactorize it for precisely predicting the missing entries? Tensor factorizationhas been extensively utilized for analyzing various multi-dimensionalreal-world data. However, existing models for tensor factorization havedisregarded the temporal property for tensor factorization while mostreal-world data are closely related to time. Moreover, they do not addressaccuracy degradation due to the sparsity of time slices. The essential problemsof how to exploit the temporal property for tensor decomposition and considerthe sparsity of time slices remain unresolved. In this paper, we propose TATD(Time-Aware Tensor Decomposition), a novel tensor decomposition method forreal-world temporal tensors. TATD is designed to exploit temporal dependencyand time-varying sparsity of real-world temporal tensors. We propose a newsmoothing regularization with Gaussian kernel for modeling time dependency.Moreover, we improve the performance of TATD by considering time-varyingsparsity. We design an alternating optimization scheme suitable for temporaltensor factorization with our smoothing regularization. Extensive experimentsshow that TATD provides the state-of-the-art accuracy for decomposing temporaltensors.

Time-Aware Tensor Decomposition for Missing Entry Prediction