# Tensor-based Graph Learning with Consistency and Specificity for Multi-view Clustering

arXiv: https://arxiv.org/abs/2403.18393 · HTML: https://mlsanity.com/paper/2403.18393/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 81 references that are in the map.
- First posted on arXiv 27 Mar 2024.

## Builds on (most cited first, 15 of 15)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [A Survey of Multi-View Representation Learning](https://mlsanity.com/paper/1610.01206/) (2016)
- [Essential Tensor Learning for Multi-view Spectral Clustering](https://mlsanity.com/paper/1807.03602/) (2018)
- [Multi-view Low-rank Sparse Subspace Clustering](https://mlsanity.com/paper/1708.08732/) (2017)
- [Effective and Efficient Graph Learning for Multi-view Clustering](https://mlsanity.com/paper/2108.06734/) (2021)
- [Multi-graph Fusion for Multi-view Spectral Clustering](https://mlsanity.com/paper/1909.06940/) (2019)
- [On Unifying Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization](https://mlsanity.com/paper/1610.07126/) (2016)
- [Structured Graph Learning for Clustering and Semi-supervised Classification](https://mlsanity.com/paper/2008.13429/) (2020)
- [Multi-View Multi-Graph Embedding for Brain Network Clustering Analysis](https://mlsanity.com/paper/1806.07703/) (2018)
- [Efficient Multi-view Clustering via Unified and Discrete Bipartite Graph Learning](https://mlsanity.com/paper/2209.04187/) (2022)
- [Multi-view MERA Subspace Clustering](https://mlsanity.com/paper/2305.09095/) (2023)
- [Enhanced Latent Multi-view Subspace Clustering](https://mlsanity.com/paper/2312.14763/) (2023)
- [Nonlinear subspace clustering by functional link neural networks](https://mlsanity.com/paper/2402.02051/) (2024)
- [Variational Distillation for Multi-View Learning](https://mlsanity.com/paper/2206.09548/) (2022)

## Abstract (arXiv)

In the context of multi-view clustering, graph learning is recognized as a crucial technique, which generally involves constructing an adaptive neighbor graph based on probabilistic neighbors, and then learning a consensus graph for clustering. However, it is worth noting that these graph learning methods encounter two significant limitations. Firstly, they often rely on Euclidean distance to measure similarity when constructing the adaptive neighbor graph, which proves inadequate in capturing the intrinsic structure among data points in practice, particularly for high-dimensional data. Secondly, most of these methods focus solely on consensus graph, ignoring unique information from each view. Although a few graph-based studies have considered using specific information as well, the modelling approach employed does not exclude the noise impact from the common or specific components. To this end, we propose a novel tensor-based multi-view graph learning framework that simultaneously considers consistency and specificity, while effectively eliminating the influence of noise. Specifically, we calculate similarity using pseudo-Stiefel manifold distance to preserve the intrinsic properties of data. By making an assumption that the learned neighbor graph of each view comprises a consistent part, a specific part, and a noise part, we formulate a new tensor-based target graph learning paradigm for noise-free graph fusion. Owing to the benefits of tensor singular value decomposition (t-SVD) in uncovering high-order correlations, this model is capable of achieving a comprehensive understanding of the target graph. Furthermore, we derive an algorithm to address the optimization problem. Experiments on six datasets have demonstrated the superiority of our method. We have released the source code on https://github.com/lshi91/CSTGL-Code.