Time-Aware Tensor Decomposition for Sparse Tensors

Abstract

Given a sparse time-evolving tensor, how can we effectively factorize it to accurately discover latent patterns? Tensor decomposition has been extensively utilized for analyzing various multi-dimensional real-world data. However, existing tensor decomposition models have disregarded the temporal property for tensor decomposition 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), an accurate tensor decomposition method for sparse temporal tensors. TATD is designed to exploit time 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 decomposition with our smoothing regularization. Extensive experiments show that TATD provides the state-of-the-art accuracy for decomposing temporal tensors.