Missing values in the Internet traffic data pose a serious challenge for use in several traffic engineering applications. Compressive sensing is a generic methodology for the reconstruction of missing values in the tensor representation of the data. Existing decomposition techniques for compressive sensing suffer from two limitations; need to know the tensor rank apriori and the usage of alternating least squares (ALS) procedure. To avoid these limitations, we propose tensor-CUR decomposition technique for compressive sensing based on statistical leverage score for selection of frontal slices and tubes of traffic tensor, that in turn give a relative-error bound on reconstruction. We establish that the proposed relative-error bound tensor-CUR (TCUR-REB) decomposition technique is better than the known additive-error bound tensor-CUR (TCUR-AEB) decomposition. Application of the TCUR-REB to the reconstruction of missing values in Internet traffic tensor using two public datasets shows that it has the smallest computational time. The proposed decomposition method also shows the smallest error in the reconstruction of missing values compared to the other tensor decomposition methods.

中文翻译：

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使用相对误差界限张量-CUR 分解对互联网流量数据进行压缩感知

互联网流量数据中的缺失值对多种流量工程应用的使用提出了严峻的挑战。压缩感知是一种用于重建数据张量表示中缺失值的通用方法。现有的压缩感知分解技术有两个局限性：需要了解张量先验秩和交替最小二乘（ALS）过程的用法。为了避免这些限制，我们提出了基于统计杠杆分数的压缩感知张量-CUR 分解技术，用于选择交通张量的额叶和管，从而给出重建的相对误差范围。我们确定所提出的相对误差界限张量-CUR (TCUR-REB) 分解技术优于已知的加性误差界限张量-CUR (TCUR-AEB) 分解。将 TCUR-REB 应用到使用两个公共数据集重建互联网流量张量中的缺失值表明它具有最小的计算时间。与其他张量分解方法相比，所提出的分解方法还显示了缺失值重建中的最小误差。