Nonconvex Tensor Model Refines Multi-View Subspace Clustering Across Real Datasets

Researchers have developed a Sliced Sparse regularized Nonconvex low-rank Multi-view Subspace Clustering model, designated by the authors as SSN-MSC, to address fundamental mathematical limitations in existing unsupervised machine learning systems. The research was conducted by Xiao Li, Xianli Pan, and Yitian Xu.

Within computational data analysis, multi-view subspace clustering functions as an unsupervised machine learning technique that leverages complementary information acquired across multiple views to organize and classify unlabelled datasets. Currently, existing advanced multi-view subspace clustering approaches are based on tensors. However, these tensor-based approaches encounter two primary issues.

The first primary issue identified in existing multi-view subspace clustering methodologies is the widespread practice of substituting the tensor nuclear norm in place of the actual tensor rank. This replacement results in the loss of important information. The second major limitation highlighted by the investigators is that standard tensor models focus predominantly on capturing similarity metrics between data points while largely ignoring between-class differences, thereby failing to separate distinct categories effectively.

To tackle both structural drawbacks within a unified framework, the authors designed the Sliced Sparse regularized Nonconvex low-rank Multi-view Subspace Clustering model incorporating two key mathematical components. In SSN-MSC, a nonconvex approximation term is used to better estimate the low-rank structure of the data. Second, the framework introduces a sliced sparse regularization term specifically tailored to maintain high similarity among samples belonging to the same class while explicitly preserving the differences between different classes.

Alongside the design of the model, the investigators established rigorous theoretical proofs to validate each mathematical component. Specifically, the authors provided a theoretical proof demonstrating that their nonconvex approximation term achieves a closer approximation to the actual tensor rank under defined operating conditions. Furthermore, the authors analyzed the validity of the sliced sparse regularization term.

To solve the resulting optimization problem posed by the SSN-MSC objective function, the research team formulated an algorithmic framework based on the Alternating Direction Method of Multipliers, commonly known as ADMM. The authors also proved its convergence theoretically.

Finally, the research team carried out extensive computational experiments on several real-world datasets to verify the practical validity and performance of the SSN-MSC model. The complete research study and algorithmic proofs appear in volume 56 of the journal Applied Intelligence.

Subject of Research: Multi-view subspace clustering using nonconvex tensor approximation and sliced sparse regularization

Article Title: Sliced sparse regularized Nonconvex low-rank tensorial multi-view subspace clustering

Article References: Li, X., Pan, X., & Xu, Y. (2026). Sliced sparse regularized Nonconvex low-rank tensorial multi-view subspace clustering. Applied Intelligence, 56(16), Article 533. https://doi.org/10.1007/s10489-026-07493-7

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07493-7

Keywords: multi-view subspace clustering, unsupervised machine learning, tensor rank, nonconvex approximation, sliced sparse regularization, alternating direction method of multipliers, ADMM optimization, low-rank tensor structure, within-class similarity, between-class differences, tensor nuclear norm, theoretical convergence, real dataset evaluation, data classification, tensorial clustering, Applied Intelligence