# Multi-View Spectral Clustering with High-Order Optimal Neighborhood Laplacian Matrix

arXiv: https://arxiv.org/abs/2008.13539 · HTML: https://mlsanity.com/paper/2008.13539/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2020.

## Built on by (most cited first, 12 of 12)

- [Fast Multi-view Clustering via Ensembles: Towards Scalability, Superiority, and Simplicity](https://mlsanity.com/paper/2203.11572/) (2022)
- [Auto-weighted Multi-view Clustering for Large-scale Data](https://mlsanity.com/paper/2303.01983/) (2023)
- [Fast Continual Multi-View Clustering with Incomplete Views](https://mlsanity.com/paper/2306.02389/) (2023)
- [One-step Multi-view Clustering with Diverse Representation](https://mlsanity.com/paper/2306.05437/) (2023)
- [A Comprehensive Survey on Spectral Clustering with Graph Structure Learning](https://mlsanity.com/paper/2501.13597/) (2025)
- [Contrastive Continual Multi-view Clustering with Filtered Structural Fusion](https://mlsanity.com/paper/2309.15135/) (2023)
- [Deep Contrastive Multi-view Clustering under Semantic Feature Guidance](https://mlsanity.com/paper/2403.05768/) (2024)
- [Discriminative Anchor Learning for Efficient Multi-view Clustering](https://mlsanity.com/paper/2409.16904/) (2024)
- [Advanced Unsupervised Learning: A Comprehensive Overview of Multi-View Clustering Techniques](https://mlsanity.com/paper/2512.05169/) (2025)
- [Multi-view Clustering with Deep Matrix Factorization and Global Graph Refinement](https://mlsanity.com/paper/2105.00248/) (2021)
- [Late Fusion Multi-view Clustering via Global and Local Alignment Maximization](https://mlsanity.com/paper/2208.01198/) (2022)
- [Uniform tensor clustering by jointly exploring sample affinities of various orders](https://mlsanity.com/paper/2302.01569/) (2023)

## Abstract (arXiv)

Multi-view spectral clustering can effectively reveal the intrinsic cluster structure among data by performing clustering on the learned optimal embedding across views. Though demonstrating promising performance in various applications, most of existing methods usually linearly combine a group of pre-specified first-order Laplacian matrices to construct the optimal Laplacian matrix, which may result in limited representation capability and insufficient information exploitation. Also, storing and implementing complex operations on the n× n Laplacian matrices incurs intensive storage and computation complexity. To address these issues, this paper first proposes a multi-view spectral clustering algorithm that learns a high-order optimal neighborhood Laplacian matrix, and then extends it to the late fusion version for accurate and efficient multi-view clustering. Specifically, our proposed algorithm generates the optimal Laplacian matrix by searching the neighborhood of the linear combination of both the first-order and high-order base Laplacian matrices simultaneously. By this way, the representative capacity of the learned optimal Laplacian matrix is enhanced, which is helpful to better utilize the hidden high-order connection information among data, leading to improved clustering performance. We design an efficient algorithm with proved convergence to solve the resultant optimization problem. Extensive experimental results on nine datasets demonstrate the superiority of our algorithm against state-of-the-art methods, which verifies the effectiveness and advantages of the proposed algorithm.