Non-negative tensor factorization (NTF) is an important tool in data analysis and signal processing, and non-negative triple decomposition is a new kind of NTF. In this paper, we study the non-negative triple decomposition of third order non-negative tensors. For this purpose, an alternating proximal gradient method is introduced and the global convergence of the algorithm is also established. As an application of the proposed results, we consider the non-negative tensor completion problem. Numerical experiments show that the proposed algorithm offers competitive performance even though the given tensor is highly sparse.
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