  Higher-order tensors are becoming prevalent in many scientific areas such as
computer vision, social network analysis, data mining and neuroscience.
Traditional tensor decomposition approaches face three major challenges: model
selecting, gross corruptions and computational efficiency. To address these
problems, we first propose a parallel trace norm regularized tensor
decomposition method, and formulate it as a convex optimization problem. This
method does not require the rank of each mode to be specified beforehand, and
can automatically determine the number of factors in each mode through our
optimization scheme. By considering the low-rank structure of the observed
tensor, we analyze the equivalent relationship of the trace norm between a
low-rank tensor and its core tensor. Then, we cast a non-convex tensor
decomposition model into a weighted combination of multiple much smaller-scale
matrix trace norm minimization. Finally, we develop two parallel alternating
direction methods of multipliers (ADMM) to solve our problems. Experimental
results verify that our regularized formulation is effective, and our methods
are robust to noise or outliers.
