  In this paper we propose an algorithm to classify tensor data. Our
methodology is built on recent studies about matrix classification with the
trace norm constrained weight matrix and the tensor trace norm. Similar to
matrix classification, the tensor classification is formulated as a convex
optimization problem which can be solved by using the off-the-shelf accelerated
proximal gradient (APG) method. However, there are no analytic solutions as the
matrix case for the updating of the weight tensors via the proximal gradient.
To tackle this problem, the Douglas-Rachford splitting technique and the
alternating direction method of multipliers (ADM) used in tensor completion are
adapted to update the weight tensors. Further more, due to the demand of real
applications, we also propose its online learning approaches. Experiments
demonstrate the efficiency of the methods.
