A-Loc: Efficient Alternating Iterative Methods for Locating the $k$ Largest/Smallest Elements in a Factorized Tensor

Xiao Chuanfu, Cuiyu Liu, Qianchao Zhu, Min Li, Chao Yang

Primary Area: optimization

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Keywords: factorized tensor, top-k elements, alternating iterative method, maximum block increasing, block-search

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Abstract: Tensors, especially higher-order tensors, are typically represented in low-rank formats to preserve the main information of the high-dimensional data while saving memory space. Locating the largest/smallest elements in a tensor with the low-rank format is a fundamental task in a large variety of applications. However, existing algorithms often suffer from low computational efficiency or poor accuracy. In this work, we propose a general continuous optimization model for this task, on top of which an alternating iterative method combined with the maximum block increasing (MBI) approach is presented. Then we develop a novel block-search strategy to further improve the accuracy. The theoretical analysis of the convergence behavior of the alternating iterative algorithm is also provided. Numerical experiments with tensors from synthetic and real-world applications demonstrate that our proposed algorithms achieve significant improvements in both accuracy and efficiency over the existing works.

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Submission Number: 4425