The Dynamic Communication Network (DCN) describes the interactions over time among various communication nodes, and it is widely used in Big-data applications as a data source. As the number of communication nodes increases and temporal slots accumulate, each node interacts in with only a few nodes in a given temporal slot, the DCN can be represented by an High-Dimensional Sparse (HDS) tensor. In order to extract rich behavioral patterns from an HDS tensor in DCN, this paper proposes an Adaptive Temporal-dependent Tensor low-rank representation (ATT) model. It adopts a three-fold approach: a) designing a temporal-dependent method to reconstruct temporal feature matrix, thereby precisely represent the data by capturing the temporal patterns; b) achieving hyper-parameters adaptation of the model via the Differential Evolutionary Algorithms (DEA) to avoid tedious hyper-parameters tuning; c) employing nonnegative learning schemes for the model parameters to effectively handle an the nonnegativity inherent in HDS data. The experimental results on four real-world DCNs demonstrate that the proposed ATT model significantly outperforms several state-of-the-art models in both prediction errors and convergence rounds.