Tensor learning on preconditioned Tucker manifold and application to tensor regression of spatiotemporal forecasting problem

摘要

This report considers the tensor learning problem with the preconditioned Tucker manifold geometry [1]. We first summarize the mathematical problem formulations of some existing tensor learning models [1]～[5]. Then, we elaborate on the proposed application of the Tucker manifold geometry into the higher-order low-rank regression model (HOLRR). Finally, we conduct performance evaluations of the proposed optimization approach with state-of-the-arts learning algorithms in a spatiotemporal forecasting problem.