Wireless edge caching is a popular strategy to avoid backhaul congestion in the next generation networks, where the content is cached in advance at the base stations to fulfil the redundant requests during peak periods. In the edge caching data, the missing observations are inevitable due to dynamic selective popularity. Among the completion methods, the tensor-based models have been shown to be the most advantageous for missing data imputation. Also, since the observations are correlated across time, files, and base stations, in this paper, we formulate the caching, prediction and recommendation problem as a fourth-order tensor completion problem. Since the content library can be large leading to a large dimension tensor, we modify the latent norm-based Frank-Wolfe (FW) algorithm with tensor-ring decomposition towards a lower time complexity using random mode selection. Analyzing the time and space complexity of the algorithm shows $N$-times reduction in computational time where $N$ is the order of tensor. Simulations with MovieLens dataset shows the approximately similar reconstruction errors for the presented FW algorithm as compared to that of the recent FW algorithm, albeit with lower computation overhead. It is also demonstrated that the completed tensor improves normalized cache hit rates for linear prediction schemes.

中文翻译：

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无线边缘缓存中用于张量完成的随机模式Frank-Wolfe算法

无线边缘缓存是一种流行的策略，可避免下一代网络中的回程拥塞，在下一代网络中，内容将预先缓存在基站中，以在高峰时段满足冗余请求。在边缘缓存数据中，由于动态的选择性流行，缺少的观察结果是不可避免的。在完成方法中，基于张量的模型已显示出对缺失数据插补最有利。另外，由于观测值在时间，文件和基站之间是相关的，因此在本文中，我们将缓存，预测和推荐问题表述为四阶张量完成问题。由于内容库可能很大，导致张量很大，我们使用张量环分解修改了基于潜在范数的Frank-Wolfe（FW）算法，使用随机模式选择，以降低时间复杂度。分析该算法的时间和空间复杂度，可以看到$ N $的计算时间减少了，其中$ N $是张量的阶数。使用MovieLens数据集进行的仿真显示，与最新的FW算法相比，所提出的FW算法的重构误差近似相似，尽管计算开销较低。还证明了完整的张量可提高线性预测方案的归一化缓存命中率。使用MovieLens数据集进行的仿真显示，与最新的FW算法相比，所提出的FW算法的重构误差近似相似，尽管计算开销较低。还证明了完整的张量可提高线性预测方案的归一化缓存命中率。使用MovieLens数据集进行的仿真显示，与最新的FW算法相比，所提出的FW算法的重构误差近似相似，尽管计算开销较低。还证明了完整的张量可提高线性预测方案的归一化缓存命中率。