[Paper Review] Spectral Perturbation Meets Incomplete Multi-view Data

Hao Wang, Linlin Zong+3 more|arXiv (Cornell University)|May 31, 2019

Remote-Sensing Image Classification19 references16 citations

TL;DR

This paper proposes Perturbation-oriented Incomplete multi-view Clustering (PIC), a novel method that transfers feature missing in multi-view data to similarity matrix missing and uses spectral perturbation theory to minimize inter-view perturbation risk, enabling robust consensus clustering. PIC outperforms state-of-the-art methods on both synthetic and real-world incomplete multi-view datasets by jointly completing similarity matrices and learning a robust consensus Laplacian via perturbation-aware weighting.

ABSTRACT

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.

Motivation & Objective

• Address the realistic challenge of incomplete multi-view clustering, where some data instances are missing in certain views, violating the strong complete sampling assumption.
• Overcome limitations of existing methods that naively impute missing features with averages, which can distort inter- and intra-class variance.
• Establish a theoretical link between spectral perturbation risk and incomplete multi-view clustering to guide robust fusion across views.
• Develop a new clustering framework that operates on completed similarity matrices and uses perturbation theory to weight views for consensus representation learning.

Proposed method

• Transforms missing feature values into missing similarity entries by constructing view-specific similarity matrices from raw data.
• Completes missing similarity entries using average similarity values from other views that contain the corresponding instances.
• Computes the Laplacian matrix for each completed similarity matrix to represent the graph structure of each view.
• Applies spectral perturbation theory to derive a perturbation risk bound and uses it to weight each Laplacian matrix, minimizing inter-view eigenspace divergence.
• Fuses the weighted Laplacian matrices into a consensus Laplacian matrix that balances all views based on perturbation risk.
• Performs spectral clustering on the final consensus Laplacian to obtain the unified clustering result.

Experimental results

Research questions

• RQ1 Can spectral perturbation theory be leveraged to model and minimize the risk of inconsistency in multi-view clustering under incomplete data?
• RQ2 Does transferring the missing data problem from feature space to similarity space lead to more robust clustering performance?
• RQ3 Can a perturbation-aware fusion strategy that weights views based on spectral stability improve clustering accuracy on incomplete multi-view data?
• RQ4 How does the proposed method compare to existing matrix completion and clustering baselines on both synthetic and real-world incomplete multi-view datasets?

Key findings

• PIC significantly outperforms all baselines, including recent methods like DAIMC, across all Partial Example Ratio (PER) settings on synthetic datasets, with consistent improvements in both ACC and NMI.
• On three real-world incomplete multi-view datasets, PIC achieves the best average performance in both ACC and NMI, demonstrating superior robustness and generalization.
• The method maintains strong performance across varying levels of data incompleteness, with optimal results observed when the perturbation parameter $\tilde{\beta}$ is set to 0.1.
• The parameter study confirms that the balance scheme $\beta = \tilde{\beta} \times \|\sum_{v}\mathbf{Q}^{v}\|_F / \|\mathbf{I}\|_F$ allows a single $\tilde{\beta}$ value to be effective across diverse datasets.
• Multi-view clustering methods, including PIC, consistently outperform two-view and single-view baselines, confirming the benefit of leveraging multiple views even when incomplete.