Seoul National University, Seoul, Republic of Korea.
PLoS One. 2022 Apr 14;17(4):e0267091. doi: 10.1371/journal.pone.0267091. eCollection 2022.
How can we accurately and efficiently decompose a tensor stream? Tensor decomposition is a crucial task in a wide range of applications and plays a significant role in latent feature extraction and estimation of unobserved entries of data. The problem of efficiently decomposing tensor streams has been of great interest because many real-world data dynamically change over time. However, existing methods for dynamic tensor decomposition sacrifice the accuracy too much, which limits their usages in practice. Moreover, the accuracy loss becomes even more serious when the tensor stream has an inconsistent temporal pattern since the current methods cannot adapt quickly to a sudden change in data. In this paper, we propose DAO-CP, an accurate and efficient online CP decomposition method which adapts to data changes. DAO-CP tracks local error norms of the tensor streams, detecting a change point of the error norms. It then chooses the best strategy depending on the degree of changes to balance the trade-off between speed and accuracy. Specifically, DAO-CP decides whether to (1) reuse the previous factor matrices for the fast running time or (2) discard them and restart the decomposition to increase the accuracy. Experimental results show that DAO-CP achieves the state-of-the-art accuracy without noticeable loss of speed compared to existing methods.
我们如何才能准确高效地对张量流进行分解？张量分解在广泛的应用中是一项关键任务，在潜在特征提取和数据中未观察到的项的估计中发挥着重要作用。由于许多现实世界的数据随时间动态变化，因此高效地分解张量流一直是人们关注的焦点。然而，现有的动态张量分解方法牺牲了太多的准确性，这限制了它们在实际中的应用。此外，当张量流具有不一致的时间模式时，准确性损失会更加严重，因为当前的方法无法快速适应数据的突然变化。在本文中，我们提出了 DAO-CP，这是一种准确高效的在线 CP 分解方法，能够适应数据变化。DAO-CP 跟踪张量流的局部误差范数，检测误差范数的变化点。然后，根据变化的程度选择最佳策略，在速度和准确性之间进行权衡。具体来说，DAO-CP 决定是（1）重用以前的因子矩阵以实现快速运行时间，还是（2）丢弃它们并重新开始分解以提高准确性。实验结果表明，与现有方法相比，DAO-CP 在不明显损失速度的情况下实现了最先进的准确性。
