缺失数据下的鲁棒张量跟踪

Thanh Trung LE, K. Abed-Meraim, N. Trung, A. Hafiane
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引用次数: 3

摘要

鲁棒张量跟踪或流张量的鲁棒自适应张量分解是至关重要的,当观测被稀疏的异常值和丢失的数据破坏。本文介绍了一种新的张量跟踪算法,用于在张量序列(TT)格式下分解具有稀疏离群值的不完全流张量。该算法包括两个主要阶段:在线异常值抑制和tt核心跟踪。在前一阶段,通过ADMM求解器有效地检测影响数据流的异常值。在后一阶段,我们提出了一个有效的递归最小二乘求解器,以每次$t$增量更新tt核心。在模拟和实际数据上进行了数值实验,验证了该算法的有效性。
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Robust Tensor Tracking With Missing Data Under Tensor-Train Format
Robust tensor tracking or robust adaptive tensor decomposition of streaming tensors is crucial when observations are corrupted by sparse outliers and missing data. In this paper, we introduce a novel tensor tracking algorithm for factorizing incomplete streaming tensors with sparse outliers under tensor-train (TT) format. The proposed algorithm consists of two main stages: online outlier rejection and tracking of TT-cores. In the former stage, outliers affecting the data streams are efficiently detected by an ADMM solver. In the latter stage, we propose an effective recursive least-squares solver to incrementally update TT-cores at each time $t$. Several numerical experiments on both simulated and real data are presented to verify the effectiveness of the proposed algorithm.
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