HOQRI: Higher-Order QR Iteration for Scalable Tucker Decomposition
HOQRI: Higher-Order QR Iteration for Scalable Tucker Decomposition
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HOQRI：可扩展 Tucker 分解的高阶 QR 迭代
DOI：
10.1109/icassp43922.2022.9746726
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Kejun Huang
中科院分区：
文献类型：
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作者：
Yuchen Sun;Kejun Huang
我们提出了一种新的算法称为高阶QR迭代（HO-QRI）的大型和稀疏张量的Tucker分解计算。与著名的高阶正交迭代（HOOI）相比，HOQRI在每次迭代中依赖于一个简单的正交化步骤，而不是像HOOI中那样更复杂的奇异值分解步骤。更重要的是，在处理极其庞大和稀疏的数据张量时，HOQRI通过定义一个名为TTMcTC的新稀疏张量操作，完全消除了中间内存爆炸。此外，HOQRI示出单调改善的目标函数，从而享受相同的收敛保证的HOOI。对合成和真实的数据的数值试验表明了HOQRI的有效性。
We propose a new algorithm called higher-order QR iteration (HO-QRI) for computing the Tucker decomposition of large and sparse tensors. Compared to the celebrated higher-order orthogonal iterations (HOOI), HOQRI relies on a simple orthogonalization step in each iteration rather than a more sophisticated singular value de-composition step as in HOOI. More importantly, when dealing with extremely large and sparse data tensors, HOQRI completely eliminates the intermediate memory explosion by defining a new sparse tensor operation called TTMcTC. Furthermore, HOQRI is shown to monotonically improve the objective function, thus enjoying the same convergence guarantee as that of HOOI. Numerical experiments on synthetic and real data showcase the effectiveness of HOQRI.