33 research outputs found

    Iterative Singular Tube Hard Thresholding Algorithms for Tensor Completion

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    Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be further used to define the best low-rank approximation of a tensor to significantly reduce the dimensionality for signal compression and recovery. In this paper, we consider the low-rank tensor completion problem. We propose a novel class of iterative singular tube hard thresholding algorithms for tensor completion based on the low-tubal-rank tensor approximation, including basic, accelerated deterministic and stochastic versions. Convergence guarantees are provided along with the special case when the measurements are linear. Numerical experiments on tensor compressive sensing and color image inpainting are conducted to demonstrate convergence and computational efficiency in practice

    Tensor Completion via Leverage Sampling and Tensor QR Decomposition for Network Latency Estimation

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    In this paper, we consider the network latency estimation, which has been an important metric for network performance. However, a large scale of network latency estimation requires a lot of computing time. Therefore, we propose a new method that is much faster and maintains high accuracy. The data structure of network nodes can form a matrix, and the tensor model can be formed by introducing the time dimension. Thus, the entire problem can be be summarized as a tensor completion problem. The main idea of our method is improving the tensor leverage sampling strategy and introduce tensor QR decomposition into tensor completion. To achieve faster tensor leverage sampling, we replace tensor singular decomposition (t-SVD) with tensor CSVD-QR to appoximate t-SVD. To achieve faster completion for incomplete tensor, we use the tensor L2,1L_{2,1}-norm rather than traditional tensor nuclear norm. Furthermore, we introduce tensor QR decomposition into alternating direction method of multipliers (ADMM) framework. Numerical experiments witness that our method is faster than state-of-art algorithms with satisfactory accuracy.Comment: 20 pages, 7 figure
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