No abstract

In this paper, a new definition of tensor p-shrinkage nuclear norm (p-TNN) is proposed based on tensor singular value decomposition (t-SVD). In particular, it can be proved that p-TNN is a better approximation of the tensor average rank than the tensor nuclear norm when −∞ < p < 1. Therefore, by employing the p-shrinkage nuclear norm, a novel low-rank tensor completion (LRTC) model is proposed to estimate a tensor from its partial observations. Statistically, the upper bound of recovery error is provided for the LRTC model. Furthermore, an efficient algorithm, accelerated by the adaptive momentum scheme, is developed to solve the resulting nonconvex optimization problem. It can be further guaranteed that the algorithm enjoys a global convergence rate under the smoothness assumption. Numerical experiments conducted on both synthetic and real-world data sets verify our results and demonstrate the superiority of our p-TNN in LRTC problems over several state-of-the-art methods.

No abstract

SummaryAccurate individual (per‐user) traffic prediction in cellular networks is considered a critical capability for the system performance improvement in terms of dynamic bandwidth allocation and network optimization. However, existing methods have limitations in capturing the characteristics of individual traffic, because the observed traffic data are usually incomplete and traffic consumption patterns significantly differ among users. In this paper, to fully exploit the inherent temporal‐spatial correlations of individual traffic data, this work models the traffic data as a three‐dimensional traffic tensor. Different from the “three‐step” strategies (i.e., “data processing + decomposition + prediction”) in the existing methods, we propose a novel tensor completion (TC)‐based “two‐step” strategy, that is, “data processing & decomposition + prediction” for individual traffic prediction, which can recover and decompose the traffic data simultaneously. Furthermore, an efficient algorithm based on the alternating direction method of multipliers (ADMM) framework is proposed to solve the resulting model. To the best of our knowledge, this is the first work to apply the TC‐based “two‐step” strategy for individual traffic prediction in cellular networks. Experiments conducted on a real cellular traffic dataset empirically validate the superiority of the proposed method.

Many practical problems involve the recovery of a binary matrix from partial information, which makes the binary matrix completion (BMC) technique received increasing attention in machine learning. In particular, we consider a special case of BMC problem, in which only a subset of positive elements can be observed. In recent years, convex regularization based methods are the mainstream approaches for this task. However, the applications of nonconvex surrogates in standard matrix completion have demonstrated better empirical performance. Accordingly, we propose a novel BMC model with nonconvex regularizers and provide the recovery guarantee for the model. Furthermore, for solving the resultant nonconvex optimization problem, we improve the popular proximal algorithm with acceleration strategies. It can be guaranteed that the convergence rate of the algorithm is in the order of 1/T , where T is the number of iterations. Extensive experiments conducted on both synthetic and real-world data sets demonstrate the superiority of the proposed approach over other competing methods.Binary matrix completion, Link prediction, Nonconvex regularizers, Topology inference 1 δ 2 √ mn , where δ denotes the sampling rate of positive entries.• We develop an accelerated version of the proximal algorithm for solving the resultant nonconvex optimization model. It can be guaranteed that the proposed algorithm has a convergence rate of O (1/T ), where T denotes the number of iterations.• We implement and analyze the proposed algorithm on both synthetic and real-world data sets. Experimental results demonstrate the superiority of the resultant algorithm to state-of-the-art methods.