论文标题
GOCPT：广义在线规范的多边形张量分解和完成
GOCPT: Generalized Online Canonical Polyadic Tensor Factorization and Completion
论文作者
论文摘要
低量张量分解或完成已进行了充分研究和应用于各种在线设置，例如在线张量分解（时间模式增长）和在线张量完成（其中不完整的切片逐渐到达）。但是，在许多现实世界中，张量可能具有更复杂的发展模式：（i）一种或多种模式可以增长； （ii）可能会填补丢失的条目； （iii）现有的张量元件可能会改变。现有方法不能支持这种复杂的方案。为了填补空白，本文提出了在这种一般环境中使用广义的在线规范多核（CP）张量分解和完成框架（名为GOCPT），在此过程中，我们在演变过程中维护了这种动态张量的CP结构。我们表明，在GOCPT框架下可以统一现有的在线张量分解和完成设置。此外，我们提出了一个名为Gocpte的变体，以处理不可用的历史张量元素（例如，隐私保护）的情况，该元件的适应性与GoCpt相似，但计算成本却降低了。实验结果表明，我们的GOCPT可以在JHU COVID数据上提高适应性高达2：8％，而专有患者索赔数据集的数据集则可以提高9：2％。与最佳型号相比，我们的变体Gocpte在两个数据集上最多可提高1：2％和5：5％的健身性。
Low-rank tensor factorization or completion is well-studied and applied in various online settings, such as online tensor factorization (where the temporal mode grows) and online tensor completion (where incomplete slices arrive gradually). However, in many real-world settings, tensors may have more complex evolving patterns: (i) one or more modes can grow; (ii) missing entries may be filled; (iii) existing tensor elements can change. Existing methods cannot support such complex scenarios. To fill the gap, this paper proposes a Generalized Online Canonical Polyadic (CP) Tensor factorization and completion framework (named GOCPT) for this general setting, where we maintain the CP structure of such dynamic tensors during the evolution. We show that existing online tensor factorization and completion setups can be unified under the GOCPT framework. Furthermore, we propose a variant, named GOCPTE, to deal with cases where historical tensor elements are unavailable (e.g., privacy protection), which achieves similar fitness as GOCPT but with much less computational cost. Experimental results demonstrate that our GOCPT can improve fitness by up to 2:8% on the JHU Covid data and 9:2% on a proprietary patient claim dataset over baselines. Our variant GOCPTE shows up to 1:2% and 5:5% fitness improvement on two datasets with about 20% speedup compared to the best model.
