  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.
