Efficient Structure-preserving Support Tensor Train Machine

An increasing amount of collected data are high-dimensional and it is crucial for efficient learning algorithms to exploit the tensorial structure as much as possible. The ever present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor methods. In the presence of small amounts of training data kernel methods offer an attractive choice as they provide the possibility for a nonlinear decision boundary. We introduce the Tensor Train Multi-way Multi-level Kernel (TT-MMK) as a method that combines the simplicity of Canonical Polyadic (CP) with the robustness of the tensor train (TT) decomposition. We embed this approach into a Dual Structure-preserving Support Vector Machine and show that the TT-MMK method is more reliable computationally, less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification when benchmarked against other state-of-the-art techniques.