Block Tensor Train Decomposition for Missing Value Imputation

We propose a new method for imputation of missing values in large scale matrix data based on a low-rank tensor approximation technique called the block tensor train (TT) decomposition. Given sparsely observed data points, the proposed method iteratively computes the soft-thresholded singular value decomposition (SVD) of the underlying data matrix with missing values. The SVD of matrices is performed based on a low-rank block TT decomposition for large scale data matrices with a low-rank tensor structure. Experimental results on simulated data demonstrate that the proposed method can estimate a large amount of missing values accurately compared to a matrix-based standard method.