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Tracking Online Low-Rank Approximations of Higher-Order Incomplete Streaming Tensors
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  • Le Trung Thanh ,
  • karim abed-meraim ,
  • Nguyen Linh-Trung ,
  • adel hafiane
Le Trung Thanh
University of Orleans, University of Orleans, University of Orleans, University of Orleans

Corresponding Author:[email protected]

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karim abed-meraim
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Nguyen Linh-Trung
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adel hafiane
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Abstract

Abstract:  In this paper, we propose two new provable algorithms for tracking online low-rank approximations of high-order streaming tensors with missing data. The first algorithm, dubbed adaptive Tucker decomposition (ATD), minimizes a weighted recursive least-squares cost function to obtain the tensor factors and the core tensor in an efficient way, thanks to the alternating minimization framework and the randomized sketching technique. Under the Canonical Polyadic (CP) model, the second algorithm called ACP is developed as a variant of ATD when the core tensor is imposed to be identity. Both algorithms are low-complexity tensor trackers that have fast convergence and low memory storage requirements. A unified convergence analysis is presented for ATD and ACP to justify their performance. Experiments indicate that the two proposed algorithms are capable of streaming tensor decomposition with competitive performance with respect to estimation accuracy and runtime on both synthetic and real data.
Code: https://github.com/thanhtbt/tensor_tracking
Comment: to appear in Elsevier Patterns
Jun 2023Published in Patterns volume 4 issue 6 on pages 100759. 10.1016/j.patter.2023.100759