# Convex Sparse Spectral Clustering: Single-view to Multi-view

arXiv: https://arxiv.org/abs/1511.06860 · HTML: https://mlsanity.com/paper/1511.06860/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2015.

## Built on by (most cited first, 14 of 14)

- [Semantic Invariant Multi-view Clustering with Fully Incomplete Information](https://mlsanity.com/paper/2305.12743/) (2023)
- [Contrastive Multi-view Subspace Clustering of Hyperspectral Images based on Graph Convolutional Networks](https://mlsanity.com/paper/2312.06068/) (2023)
- [MMES: Mixture Model based Evolution Strategy for Large-Scale Optimization](https://mlsanity.com/paper/2203.12675/) (2022)
- [Sparse Quadratic Optimisation over the Stiefel Manifold with Application to Permutation Synchronisation](https://mlsanity.com/paper/2110.00053/) (2021)
- [Contrastive Continual Multi-view Clustering with Filtered Structural Fusion](https://mlsanity.com/paper/2309.15135/) (2023)
- [Self-supervised Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2103.01689/) (2021)
- [Nested subspace learning with flags](https://mlsanity.com/paper/2502.06022/) (2025)
- [Multi-view Spectral Clustering on the Grassmannian Manifold With Hypergraph Representation](https://mlsanity.com/paper/2503.06066/) (2025)
- [Improving Spectral Clustering Using Spectrum-Preserving Node Aggregation](https://mlsanity.com/paper/2110.12328/) (2021)
- [Multiview Subspace Clustering of Hyperspectral Images based on Graph Convolutional Networks](https://mlsanity.com/paper/2403.01465/) (2024)
- [Advanced Unsupervised Learning: A Comprehensive Overview of Multi-View Clustering Techniques](https://mlsanity.com/paper/2512.05169/) (2025)
- [One for all: A novel Dual-space Co-training baseline for Large-scale Multi-View Clustering](https://mlsanity.com/paper/2401.15691/) (2024)
- [Intra-view and Inter-view Correlation Guided Multi-view Novel Class Discovery](https://mlsanity.com/paper/2507.12029/) (2025)
- [Advanced spectral clustering for heterogeneous data in credit risk monitoring systems](https://mlsanity.com/paper/2509.00546/) (2025)

## Abstract (arXiv)

Spectral Clustering (SC) is one of the most widely used methods for data clustering. It first finds a low-dimensonal embedding U of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on U^top to get the final clustering result. In this work, we observe that, in the ideal case, UU^top should be block diagonal and thus sparse. Therefore we propose the Sparse Spectral Clustering (SSC) method which extends SC with sparse regularization on UU^top. To address the computational issue of the nonconvex SSC model, we propose a novel convex relaxation of SSC based on the convex hull of the fixed rank projection matrices. Then the convex SSC model can be efficiently solved by the Alternating Direction Method of canyiMultipliers (ADMM). Furthermore, we propose the Pairwise Sparse Spectral Clustering (PSSC) which extends SSC to boost the clustering performance by using the multi-view information of data. Experimental comparisons with several baselines on real-world datasets testify to the efficacy of our proposed methods.