# Spectral Perturbation Meets Incomplete Multi-view Data

arXiv: https://arxiv.org/abs/1906.00098 · HTML: https://mlsanity.com/paper/1906.00098/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2019.

## Built on by (most cited first, 24 of 24)

- [Multimodal Fusion on Low-quality Data: A Comprehensive Survey](https://mlsanity.com/paper/2404.18947/) (2024)
- [A Survey on Incomplete Multi-view Clustering](https://mlsanity.com/paper/2208.08040/) (2022)
- [Incomplete Multi-view Clustering via Prototype-based Imputation](https://mlsanity.com/paper/2301.11045/) (2023)
- [Unpaired Multi-View Graph Clustering with Cross-View Structure Matching](https://mlsanity.com/paper/2307.03476/) (2023)
- [Localized Sparse Incomplete Multi-view Clustering](https://mlsanity.com/paper/2208.02998/) (2022)
- [DICNet: Deep Instance-Level Contrastive Network for Double Incomplete Multi-View Multi-Label Classification](https://mlsanity.com/paper/2303.08358/) (2023)
- [Latent Heterogeneous Graph Network for Incomplete Multi-View Learning](https://mlsanity.com/paper/2208.13669/) (2022)
- [Self-supervised Image Clustering from Multiple Incomplete Views via Constrastive Complementary Generation](https://mlsanity.com/paper/2209.11927/) (2022)
- [CDIMC-net: Cognitive Deep Incomplete Multi-view Clustering Network](https://mlsanity.com/paper/2403.19514/) (2024)
- [Scalable Incomplete Multi-View Clustering with Structure Alignment](https://mlsanity.com/paper/2308.16541/) (2023)
- [Manifold-based Incomplete Multi-view Clustering via Bi-Consistency Guidance](https://mlsanity.com/paper/2405.10987/) (2024)
- [Incomplete Graph Learning: A Comprehensive Survey](https://mlsanity.com/paper/2502.12412/) (2025)
- [ACTIVE:Augmentation-Free Graph Contrastive Learning for Partial Multi-View Clustering](https://mlsanity.com/paper/2203.00186/) (2022)
- [Explicit View-labels Matter: A Multifacet Complementarity Study of Multi-view Clustering](https://mlsanity.com/paper/2205.02507/) (2022)
- [Cross-view Graph Contrastive Representation Learning on Partially Aligned Multi-view Data](https://mlsanity.com/paper/2211.04906/) (2022)
- [Self-Learning Symmetric Multi-view Probabilistic Clustering](https://mlsanity.com/paper/2305.07307/) (2023)
- [Balancing Complementarity and Consistency via Delayed Activation in Incomplete Multi-view Clustering](https://mlsanity.com/paper/2407.17744/) (2024)
- [Hierarchical Consensus Network for Multiview Feature Learning](https://mlsanity.com/paper/2502.01961/) (2025)
- [Advanced Unsupervised Learning: A Comprehensive Overview of Multi-View Clustering Techniques](https://mlsanity.com/paper/2512.05169/) (2025)
- [Clustering-Induced Generative Incomplete Image-Text Clustering (CIGIT-C)](https://mlsanity.com/paper/2209.13763/) (2022)
- [Preventing Dimensional Collapse of Incomplete Multi-View Clustering via Direct Contrastive Learning](https://mlsanity.com/paper/2303.12241/) (2023)
- [Hierarchical Mutual Information Analysis: Towards Multi-view Clustering in The Wild](https://mlsanity.com/paper/2310.18614/) (2023)
- [Clustering Result Re-guided Incomplete Multi-view Spectral Clustering](https://mlsanity.com/paper/2510.09959/) (2025)
- [Beyond Missing Rates: Rethinking Incomplete Multi-View Clustering with Protocol Divergence](https://mlsanity.com/paper/2606.04857/) (2026)

## Abstract (arXiv)

Beyond existing multi-view clustering, this paper studies a more realistic clustering scenario, referred to as incomplete multi-view clustering, where a number of data instances are missing in certain views. To tackle this problem, we explore spectral perturbation theory. In this work, we show a strong link between perturbation risk bounds and incomplete multi-view clustering. That is, as the similarity matrix fed into spectral clustering is a quantity bounded in magnitude O(1), we transfer the missing problem from data to similarity and tailor a matrix completion method for incomplete similarity matrix. Moreover, we show that the minimization of perturbation risk bounds among different views maximizes the final fusion result across all views. This provides a solid fusion criteria for multi-view data. We motivate and propose a Perturbation-oriented Incomplete multi-view Clustering (PIC) method. Experimental results demonstrate the effectiveness of the proposed method.