Joint Tensor and Inter-View Low-Rank Recovery for Incomplete Multiview Clustering

TL;DR

This work tackles incomplete multiview clustering by formulating a joint optimization that learns a complete multi-view similarity graph tensor and recovers tensor representations under inter-view and intra-view low-rank constraints. The JTIV-LRR method enforces low-tubal-rank structure across multiple mode permutations via three mode-wise tensor nuclear norms and an accompanying sparse noise term, solved efficiently with an ADMM scheme that includes Sylvester, SVT, and soft-thresholding subproblems. Empirical results on synthetic data and seven real-world datasets show that JTIV-LRR outperforms state-of-the-art IMVC methods, especially at high missing rates, demonstrating robustness and scalability. The approach provides a principled way to exploit high-order cross-view correlations for robust clustering in the presence of missing data, with practical implications for multimodal data analysis.

Abstract

Incomplete multiview clustering (IMVC) has gained significant attention for its effectiveness in handling missing sample challenges across various views in real-world multiview clustering applications. Most IMVC approaches tackle this problem by either learning consensus representations from available views or reconstructing missing samples using the underlying manifold structure. However, the reconstruction of learned similarity graph tensor in prior studies only exploits the low-tubal-rank information, neglecting the exploration of inter-view correlations. This paper propose a novel joint tensor and inter-view low-rank Recovery (JTIV-LRR), framing IMVC as a joint optimization problem that integrates incomplete similarity graph learning and tensor representation recovery. By leveraging both intra-view and inter-view low rank information, the method achieves robust estimation of the complete similarity graph tensor through sparse noise removal and low-tubal-rank constraints along different modes. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of the proposed approach, achieving significant improvements in clustering accuracy and robustness compared to state-of-the-art methods.

Figures (7)

• Figure 1: Construction of similarity graph tensor $\mathcal{G}\in\mathbb{R}^{n\times n\times V}$ (left), and its two permutation format are $\mathcal{G}_{(1,3,2)} \in \mathbb{R}^{n\times V\times n}$ (middle) and $\mathcal{G}_{(3,2,1)}\in\mathbb{R}^{V\times n\times n}$. $\mathbf{G}^{(v)}\in\mathbb{R}^{n\times n}$ denotes the $v$th similarity graph matrix.
• Figure 2: Comparison of Reconstruction Errors: Performance of Low-Rank and Sparse Noise Components under Different Mode Combinations.
• Figure 3: Comparison of Reconstruction Errors under Different Mutual Information.
• Figure 4: ORL data: visualization of the graphs recovered by ETLSRR (top row), JPLTD (middle row), and the proposed JTIV-LRR method (bottom row) under various missing rates $p$.
• Figure 5: Enhanced t-SNE visualization of recovered graphs for ETLSRR, JPLTD, and our method on ORL data across different missing rate $p$.

Theorems & Definitions (6)

• Definition 1: Tensor Nuclear Norm semerci2014tensor
• Definition 2: The block circulant operator kilmer2011factorization
• Definition 3: Folding and unfolding operator kilmer2011factorization
• Definition 4: t-Productkilmer2013third
• Definition 5: Tensor SVD (t-SVD) kilmer2011factorization
• Definition 6: Tensor singular value thresholding (t-SVT) kilmer2011factorizationliu2012tensorzhang2016exact