# Probabilistic Block Term Decomposition for the Modelling of Higher-Order Arrays

arXiv: https://arxiv.org/abs/2310.02694 · HTML: https://mlsanity.com/paper/2310.02694/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 15 references that are in the map.
- First posted on arXiv 4 Oct 2023.

## Builds on (most cited first, 1 of 1)

- [Block-Term Tensor Decomposition Model Selection and Computation: The Bayesian Way](https://mlsanity.com/paper/2101.02931/) (2021)

## Abstract (arXiv)

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.