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.
翻译:低调的感应因子化或完成率在各种在线环境,例如在线加压因子化(在时间模式增长的情况下)和在线加压(在不完全的切片逐渐到达时)完成率(在不完全的切片逐渐到达时)等,都得到了很好的研究和应用。然而,在许多现实世界环境中,高压可能具有更复杂的演变模式:(一) 一种或多种模式可以增长;(二) 缺失的条目可以填补;(三) 现有的强力元素可以改变。现有的方法无法支持这种复杂的假设。为了填补空白,本文件提议为这一总体设置建立一个通用的在线加热因子化(CP)和完成框架(名为GOCPT), 用于这个总设置,我们在演变过程中维持这种动态的强力强力压器的CP结构结构。我们显示,现有的在线加压因子化和完成设置可以统一到GOCPT框架下。此外,我们提议了一个名为GCPTE的变异体化器化器化器化器化模型(例如隐私保护),在历史的模型中取得了类似于GOCPTTT,但最佳计算成本则要低得多。实验结果比我们的GCP2比我们的Q%2号数据更精确数据更接近于数据要求。