# Multi-view Spectral Clustering on the Grassmannian Manifold With Hypergraph Representation

arXiv: https://arxiv.org/abs/2503.06066 · HTML: https://mlsanity.com/paper/2503.06066/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 50 references that are in the map.
- First posted on arXiv 8 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [A Survey on Multi-View Clustering](https://mlsanity.com/paper/1712.06246/) (2017)
- [Multi-View Spectral Clustering via Structured Low-Rank Matrix Factorization](https://mlsanity.com/paper/1709.01212/) (2017)
- [Random walks on hypergraphs](https://mlsanity.com/paper/1911.06523/) (2019)
- [Incomplete Contrastive Multi-View Clustering with High-Confidence Guiding](https://mlsanity.com/paper/2312.08697/) (2023)
- [Convex Sparse Spectral Clustering: Single-view to Multi-view](https://mlsanity.com/paper/1511.06860/) (2015)
- [Learning Hypergraph-regularized Attribute Predictors](https://mlsanity.com/paper/1503.05782/) (2015)
- [Elastic Net Hypergraph Learning for Image Clustering and Semi-supervised Classification](https://mlsanity.com/paper/1603.01096/) (2016)
- [High-order Multi-view Clustering for Generic Data](https://mlsanity.com/paper/2209.10838/) (2022)
- [Hypergraph p-Laplacian Regularization for Remote Sensing Image Recognition](https://mlsanity.com/paper/1806.08104/) (2018)
- [Multiway p-spectral graph cuts on Grassmann manifolds](https://mlsanity.com/paper/2008.13210/) (2020)

## Built on by (most cited first, 2 of 2)

- [Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger](https://mlsanity.com/paper/2603.00599/) (2026)
- [Multiscale Grassmann Manifolds for Single-Cell Data Analysis](https://mlsanity.com/paper/2511.11717/) (2025)

## Abstract (arXiv)

Graph-based multi-view spectral clustering methods have achieved notable progress recently, yet they often fall short in either oversimplifying pairwise relationships or struggling with inefficient spectral decompositions in high-dimensional Euclidean spaces. In this paper, we introduce a novel approach that begins to generate hypergraphs by leveraging sparse representation learning from data points. Based on the generated hypergraph, we propose an optimization function with orthogonality constraints for multi-view hypergraph spectral clustering, which incorporates spectral clustering for each view and ensures consistency across different views. In Euclidean space, solving the orthogonality-constrained optimization problem may yield local maxima and approximation errors. Innovately, we transform this problem into an unconstrained form on the Grassmannian manifold. Finally, we devise an alternating iterative Riemannian optimization algorithm to solve the problem. To validate the effectiveness of the proposed algorithm, we test it on four real-world multi-view datasets and compare its performance with seven state-of-the-art multi-view clustering algorithms. The experimental results demonstrate that our method outperforms the baselines in terms of clustering performance due to its superior low-dimensional and resilient feature representation.