Order Determination for Tensor-Valued Observations Using Data Augmentation
提出一种结合数据增强与高阶奇异值分解的自动化方法，用于确定张量数据的最优降维阶数，并在理论和模拟中证明其一致性。
Tensor-valued data benefit greatly from dimension reduction as the reduction in size is exponential in the number of modes. To achieve maximal reduction without loss of information, our objective in this work is to provide an automated procedure for the optimal selection of reduced dimensionality. Our approach combines a recently proposed data augmentation procedure with the higher-order singular value decomposition (HOSVD) in a tensorially natural way. We give theoretical guidelines on how to choose the tuning parameters and further inspect their influence in a simulation study. As our primary result, we show that the procedure consistently estimates the true latent dimensions under a noisy tensor model, both at the population and sample levels. Additionally, we propose a bootstrap-based alternative to the augmentation estimator. Simulations are used to demonstrate the estimation accuracy of the two methods under various settings.