Canonical Polyadic (CP) decomposition is a powerful multilinear algebra tool for analyzing multiway (a.k.a. tensor) data and has been used for various signal processing and machine learning applications. When the underlying tensor is derived from data streams, adaptive CP decomposition is required. In this paper, we propose a novel method called robust adaptive CP decomposition (RACP) for dealing with high-order incomplete streaming tensors that are corrupted by outliers. At each time instant, RACP first performs online outlier rejection to accurately detect and remove sparse outliers, and then performs tensor factor tracking to efficiently update the tensor basis. A unified convergence analysis of RACP is also established in that the sequence of generated solutions converges asymptotically to a stationary point of the objective function. Extensive experiments were conducted on both synthetic and real data to demonstrate the effectiveness of RACP in comparison with state-of-the-art adaptive CP algorithms.

中文翻译：

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具有缺失数据和异常值的鲁棒张量跟踪：新颖的自适应 CP 分解和收敛分析


规范多元 (CP) 分解是一种强大的多线性代数工具，用于分析多路（又称张量）数据，并已用于各种信号处理和机器学习应用。当底层张量源自数据流时，需要自适应 CP 分解。在本文中，我们提出了一种称为鲁棒自适应 CP 分解（RACP）的新方法，用于处理被异常值损坏的高阶不完整流张量。在每个时刻，RACP首先执行在线异常值拒绝，以准确检测和去除稀疏异常值，然后执行张量因子跟踪以有效更新张量基。还建立了 RACP 的统一收敛分析，生成的解序列渐近收敛于目标函数的驻点。对合成数据和真实数据进行了大量实验，以证明 RACP 与最先进的自适应 CP 算法相比的有效性。