Accelerated Low-Rank Tensor Completion via Projected Tensor Block Coordinate Descent

The low-rank tensor completion problem aims to find a low-rank approximation of a tensor by filling in missing entries from partially observed entries to enhance the accuracy of the tensor data analysis. Among various low-rank tensor approximation methods, Tucker decomposition with nuclear norm minimization is widely employed due to its ability to clear represent low-rank structure and its compatibility to existing matrix completion algorithms. However, it demands significant computational resources to perform singular value decomposition along each matricized tensor. In this study, we propose a novel Tucker decomposition based low-rank tensor completion algorithm with nuclear norm minimization. To mitigate the computational burden, we introduce a projected tensor block coordinate descent for tensor completion, which computes the factor matrix from the projected tensor obtained in the previous iteration rather than recalculating it from the full-sized tensor at every iteration. Experimental results from practical applications, such as color image inpainting and traffic data analysis, demonstrate that the proposed algorithm produces an excellent balance between the prediction accuracy and execution speed compared to the other reference algorithms.