Tensor decomposition operation is the basis for many data analysis tasks from clustering, trend detection, anomaly detection, to correlation analysis. One key problem with tensor decomposition, however, is its computational complexity - especially for dense data sets, the decomposition process takes exponential time in the number of tensor modes; the process is relatively faster for sparse tensors, but decomposition is still a major bottleneck in many applications. While it is possible to reduce the decomposition time by trading performance with decomposition accuracy, a drop in accuracy may not always be acceptable. In this paper, we first recognize that in many applications, the user may have a focus of interest - i.e., part of the data for which the user needs high accuracy- and beyond this area focus, accuracy may not be as critical. Relying on this observation, we propose a novel Personalized Tensor Decomposition (PTD) mechanism for accounting for the user's focus: PTD takes as input one or more areas of focus and performs the decomposition in such a way that, when reconstructed, the accuracy of the tensor is boosted for these of focus. We discuss alternative ways PTD can be implemented. Experiments show that PTD helps boost accuracy at the foci of interest, while reducing the overall tensor decomposition time.