Structured Tensor-Train Decomposition for Speeding-Up Kernel-Based Learning

In this chapter, we present an algebraic relation between the Tucker model and the Tensor-Train decomposition with structured cores. Exploiting this link, we present a new fast algorithm to compute the dominant singular subspaces of a Q-order tensor. As opposedt o the state of the art methods (usually called HOSVD for high-order SVD), our approach mitigates the well-known “curse of dimentionality”. This approach is applied to speed up kernel-based supervised tensor classification.