# Graph Regularized Nonnegative Tensor Ring Decomposition for Multiway Representation Learning

arXiv: https://arxiv.org/abs/2010.05657 · HTML: https://mlsanity.com/paper/2010.05657/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [Many-body Approximation for Non-negative Tensors](https://mlsanity.com/paper/2209.15338/) (2022)
- [Semi-supervised multi-view concept decomposition](https://mlsanity.com/paper/2307.00924/) (2023)
- [Tucker-O-Minus Decomposition for Multi-view Tensor Subspace Clustering](https://mlsanity.com/paper/2210.12638/) (2022)

## Abstract (arXiv)

Tensor ring (TR) decomposition is a powerful tool for exploiting the low-rank nature of multiway data and has demonstrated great potential in a variety of important applications. In this paper, nonnegative tensor ring (NTR) decomposition and graph regularized NTR (GNTR) decomposition are proposed, where the former equips TR decomposition with local feature extraction by imposing nonnegativity on the core tensors and the latter is additionally able to capture manifold geometry information of tensor data, both significantly extend the applications of TR decomposition for nonnegative multiway representation learning. Accelerated proximal gradient based methods are derived for NTR and GNTR. The experimental result demonstrate that the proposed algorithms can extract parts-based basis with rich colors and rich lines from tensor objects that provide more interpretable and meaningful representation, and hence yield better performance than the state-of-the-art tensor based methods in clustering and classification tasks.