Tensor-valued data benefits greatly from dimension reduction as the reduction in size is exponential in the number of modes. To achieve maximal reduction without loss in information, our objective in this work is to give an automated procedure for the optimal selection of the 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.
翻译:由于模式数量的减缩是指数式的,因此,从尺寸的减少中可以大大获益。为了在不损失信息的情况下实现最大程度的减少,我们这项工作的目标是为最佳选择降低的维度提供一个自动程序。我们的方法是将最近提出的数据增强程序与高阶单值分解(HOSVD)相结合,采用强度自然的方式。我们给出理论指南,说明如何选择调试参数,并在模拟研究中进一步检查其影响。我们的主要结果是,我们显示该程序在人口和抽样层次上都一致估计了在噪音高压模型下的真正潜伏维度。此外,我们提出了一种基于增压估计器的测深器替代方法。我们使用模拟方法来显示不同环境中两种方法的估计准确性。