# Fast Hypergraph Regularized Nonnegative Tensor Ring Factorization Based on Low-Rank Approximation

arXiv: https://arxiv.org/abs/2109.02314 · HTML: https://mlsanity.com/paper/2109.02314/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 6 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Compressing Recurrent Neural Networks with Tensor Ring for Action Recognition](https://mlsanity.com/paper/1811.07503/) (2018)
- [Efficient Nonnegative Tucker Decompositions: Algorithms and Uniqueness](https://mlsanity.com/paper/1404.4412/) (2014)
- [Randomized Tensor Ring Decomposition and Its Application to Large-scale Data Reconstruction](https://mlsanity.com/paper/1901.01652/) (2019)
- [Matrix Product State for Higher-Order Tensor Compression and Classification](https://mlsanity.com/paper/1609.04541/) (2016)

## Abstract (arXiv)

For the high dimensional data representation, nonnegative tensor ring (NTR) decomposition equipped with manifold learning has become a promising model to exploit the multi-dimensional structure and extract the feature from tensor data. However, the existing methods such as graph regularized tensor ring decomposition (GNTR) only models the pair-wise similarities of objects. For tensor data with complex manifold structure, the graph can not exactly construct similarity relationships. In this paper, in order to effectively utilize the higher-dimensional and complicated similarities among objects, we introduce hypergraph to the framework of NTR to further enhance the feature extraction, upon which a hypergraph regularized nonnegative tensor ring decomposition (HGNTR) method is developed. To reduce the computational complexity and suppress the noise, we apply the low-rank approximation trick to accelerate HGNTR (called LraHGNTR). Our experimental results show that compared with other state-of-the-art algorithms, the proposed HGNTR and LraHGNTR can achieve higher performance in clustering tasks, in addition, LraHGNTR can greatly reduce running time without decreasing accuracy.