  This work introduces a tensor-based method to perform supervised
classification on spatiotemporal data processed in an echo state network.
Typically when performing supervised classification tasks on data processed in
an echo state network, the entire collection of hidden layer node states from
the training dataset is shaped into a matrix, allowing one to use standard
linear algebra techniques to train the output layer. However, the collection of
hidden layer states is multidimensional in nature, and representing it as a
matrix may lead to undesirable numerical conditions or loss of spatial and
temporal correlations in the data.
  This work proposes a tensor-based supervised classification method on echo
state network data that preserves and exploits the multidimensional nature of
the hidden layer states. The method, which is based on orthogonal Tucker
decompositions of tensors, is compared with the standard linear output weight
approach in several numerical experiments on both synthetic and natural data.
The results show that the tensor-based approach tends to outperform the
standard approach in terms of classification accuracy.
