# Multidimensional Data Analysis Based on Block Convolutional Tensor Decomposition

arXiv: https://arxiv.org/abs/2308.01768 · HTML: https://mlsanity.com/paper/2308.01768/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 38 references that are in the map.
- First posted on arXiv 3 Aug 2023.

## Builds on (most cited first, 4 of 4)

- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Robust Kronecker Component Analysis](https://mlsanity.com/paper/1801.06432/) (2018)
- [SABER: A Systems Approach to Blur Estimation and Reduction in X-ray Imaging](https://mlsanity.com/paper/1905.03935/) (2019)

## Built on by (most cited first, 1 of 1)

- [Robust Tensor Completion via Reflective Convolution Nuclear Norm Minimization](https://mlsanity.com/paper/2610.04979/) (2026)

## Abstract (arXiv)

Tensor decompositions are powerful tools for analyzing multi-dimensional data in their original format. Besides tensor decompositions like Tucker and CP, Tensor SVD (t-SVD) which is based on the t-product of tensors is another extension of SVD to tensors that recently developed and has found numerous applications in analyzing high dimensional data. This paper offers a new insight into the t-Product and shows that this product is a block convolution of two tensors with periodic boundary conditions. Based on this viewpoint, we propose a new tensor-tensor product called the starc-Product based on Block convolution with reflective boundary conditions. Using a tensor framework, this product can be easily extended to tensors of arbitrary order. Additionally, we introduce a tensor decomposition based on our starc-Product for arbitrary order tensors. Compared to t-SVD, our new decomposition has lower complexity, and experiments show that it yields higher-quality results in applications such as classification and compression.