•Accurate and interpretable method for city-wide missing traffic speed data recovery.•It automatically discovers traffic speed patterns from partially observed data.•Different initialization strategies for tensor decomposition are tested.•Element-like and fiber-like missing scenarios are investigated. Missing data is an inevitable and ubiquitous problem in data-driven intelligent transportation systems. While there are several studies on the missing traffic data recovery in the last decade, it is still an open issue of making full use of spatial-temporal traffic patterns to improve recovery performance. In this paper, due to the multi-dimensional nature of traffic speed data, we treat missing data recovery as the problem of tensor completion, a three-procedure framework based on Tucker decomposition is proposed to accomplish the recovery task by discovering spatial-temporal patterns and underlying structure from incomplete data. Specifically, in the missing data initialization, intrinsic multi-mode biases based traffic pattern is extracted to perform a robust recovery. Thereby, the truncated singular value decomposition (SVD) is introduced to capture main latent features along each dimension. Finally, applying these latent features, the missing data is eventually estimated by the SVD-combined tensor decomposition (STD). Empirically, relying on the large-scale traffic speed data collected from 214 road segments within two months at 10-min interval, our experiment covers two missing scenarios – element-like random missing and fiber-like random missing. The impacts of different initialization strategies for tensor decomposition are evaluated. From numerical analysis, a sensitivity-driven rank selection can not only choose an appropriate core tensor size but also determine how much features we actually need. By comparison with two baseline tensor decomposition models, our method is shown to successfully recover missing data with the highest accuracy as the missing rate ranges from 20% to 80% under two missing scenarios. Moreover, the results have also indicated that an optimal initialization for tensor decomposition could suggest a better performance.