# HyperNTF: A Hypergraph Regularized Nonnegative Tensor Factorization for Dimensionality Reduction

arXiv: https://arxiv.org/abs/2101.06827 · HTML: https://mlsanity.com/paper/2101.06827/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 53 references that are in the map.
- First posted on arXiv 18 Jan 2021.

## Builds on (most cited first, 3 of 3)

- [Computationally Tractable Riemannian Manifolds for Graph Embeddings](https://mlsanity.com/paper/2002.08665/) (2020)
- [Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization](https://mlsanity.com/paper/1504.01777/) (2015)
- [Columnwise Element Selection for Computationally Efficient Nonnegative Coupled Matrix Tensor Factorization](https://mlsanity.com/paper/2003.03506/) (2020)

## Built on by (most cited first, 5 of 5)

- [Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey](https://mlsanity.com/paper/2405.03615/) (2024)
- [Uncovering cognitive taskonomy through transfer learning in masked autoencoder-based fMRI reconstruction](https://mlsanity.com/paper/2407.00033/) (2024)
- [Identifiability of Nonnegative Tucker Decompositions -- Part I: Theory](https://mlsanity.com/paper/2505.12713/) (2025)
- [Robust Manifold Nonnegative Tucker Factorization for Tensor Data Representation](https://mlsanity.com/paper/2211.03934/) (2022)
- [Adaptive regularization parameter selection for high-dimensional inverse problems: A Bayesian approach with Tucker low-rank constraints](https://mlsanity.com/paper/2603.16066/) (2026)

## Abstract (arXiv)

Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by tensors. However, most of tensor decomposition methods are the linear feature extraction techniques, which are unable to reveal the nonlinear structure within high-dimensional data. To address such problem, a lot of algorithms have been proposed for simultaneously performs linear and non-linear feature extraction. A representative algorithm is the Graph Regularized Non-negative Matrix Factorization (GNMF) for image clustering. However, the normal 2-order graph can only models the pairwise similarity of objects, which cannot sufficiently exploit the complex structures of samples. Thus, we propose a novel method, named Hypergraph Regularized Non-negative Tensor Factorization (HyperNTF), which utilizes hypergraph to encode the complex connections among samples and employs the factor matrix corresponding with last mode of Canonical Polyadic (CP) decomposition as low-dimensional representation. Extensive experiments on synthetic manifolds, real-world image datasets, and EEG signals, demonstrating that HyperNTF outperforms the state-of-the-art methods in terms of dimensionality reduction, clustering, and classification.