Tensor Grid Decomposition with Application to Tensor Completion
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The recently prevalent tensor train (TT) and tensor ring (TR) decompositions can be graphically interpreted as (locally) linear interconnected latent factors and possess exponential decay of correlation. The projected entangled pair state (PEPS, also called two-dimensional TT) extends the spatial dimension of TT and its polycyclic structure can be considered as a square grid. Compared with TT, its algebraic decay of correlation means the enhancement of interaction between tensor modes. In this paper we adopt the PEPS and develop a tensor grid (TG) decomposition with its efficient realization termed splitting singular value decomposition (SSVD). By utilizing the alternating least squares (ALS) a method called TG-ALS is used to interpolate the missing entries of a tensor from its partial observations. Different kinds of data are used in the experiments, including synthetic data, color images and real-world videos. Experimental results demonstrate that the TG has much power of representation than TT and TR.
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