Tensors are ubiquitous in science and engineering and tensor factorization approaches have become important tools for the characterization of higher order structure. Factorizations includes the outer-product rank Canonical Polyadic Decomposition (CPD) as well as the multi-linear rank Tucker decomposition in which the Block-Term Decomposition (BTD) is a structured intermediate interpolating between these two representations. Whereas CPD, Tucker, and BTD have traditionally relied on maximum-likelihood estimation, Bayesian inference has been use to form probabilistic CPD and Tucker. We propose, an efficient variational Bayesian probabilistic BTD, which uses the von-Mises Fisher matrix distribution to impose orthogonality in the multi-linear Tucker parts forming the BTD. On synthetic and two real datasets, we highlight the Bayesian inference procedure and demonstrate using the proposed pBTD on noisy data and for model order quantification. We find that the probabilistic BTD can quantify suitable multi-linear structures providing a means for robust inference of patterns in multi-linear data.

在这篇文章中，我们提出了一种高效的变分贝叶斯概率BTD方法，利用von-Mises Fisher矩阵分布对多线性Tucker部分在BTD中施加正交性，通过合成和两个真实数据集的实验，我们突出了贝叶斯推断过程，并演示了在噪声数据和模型顺序量化中使用所提出的pBTD的能力，我们发现概率BTD能够量化适用的多线性结构，为多线性数据中模式的鲁棒推断提供了一种方法。

高阶数组建模的概率块术语分解