  Tensor (multidimensional array) classification problem has become very
popular in modern applications such as image recognition and high dimensional
spatio-temporal data analysis. Support Tensor Machine (STM) classifier, which
is extended from the support vector machine, takes CANDECOMP / Parafac (CP)
form of tensor data as input and predicts the data labels. The
distribution-free and statistically consistent properties of STM highlight its
potential in successfully handling wide varieties of data applications.
Training a STM can be computationally expensive with high-dimensional tensors.
However, reducing the size of tensor with a random projection technique can
reduce the computational time and cost, making it feasible to handle large size
tensors on regular machines. We name an STM estimated with randomly projected
tensor as Random Projection-based Support Tensor Machine (RPSTM). In this work,
we propose a Tensor Ensemble Classifier (TEC), which aggregates multiple RPSTMs
for big tensor classification. TEC utilizes the ensemble idea to minimize the
excessive classification risk brought by random projection, providing
statistically consistent predictions while taking the computational advantage
of RPSTM. Since each RPSTM can be estimated independently, TEC can further take
advantage of parallel computing techniques and be more computationally
efficient. The theoretical and numerical results demonstrate the decent
performance of TEC model in high-dimensional tensor classification problems.
The model prediction is statistically consistent as its risk is shown to
converge to the optimal Bayes risk. Besides, we highlight the trade-off between
the computational cost and the prediction risk for TEC model. The method is
validated by extensive simulation and a real data example. We prepare a python
package for applying TEC, which is available at our GitHub.
