Nonconvex Low-Rank Tensor Representation with Deep Priors for Multiview Subspace Clustering

Multiview subspace clustering (MvSC) has shown remarkable potential in exploring underlying structures of high-dimensional data. However, existing MvSC methods still suffer from two shortcomings: (1) the commonly use of convex low-rank approximations inadequately capture high-order correlations across views, while sensitivity to noise and outliers degrades clustering performance, and (2) they lack the ability to preserve global correlations and local geometric patterns simultaneously. To address these issues, we propose a novel nonconvex regularized MvSC model with deep prior, which not only accurately characterizes the intrinsic low-rank structure and suppresses the effect of outliers, but also preserves local structural properties through deep networks. By mathematically analyzing the optimal solution of the optimization problem in our proposed model, we develop an efficient ADMM-based algorithm with provable convergence guarantees to solve it. Extensive experiments on various datasets demonstrate the superiority of the proposed model.

In the real world, data often comes from multiple sources or perspectives. For example, understanding a multimedia clip may require combining audio, video, and text information. Multiview clustering aims to automatically group such complex data and uncover hidden patterns. However, existing methods often struggle to capture complicated relationships across different data sources, especially when the data is noisy or incomplete. They also find it difficult to preserve both overall patterns and important local details at the same time. To address these challenges, we propose a new AI-based clustering method that combines advanced mathematical modeling with deep learning techniques. Our approach is designed to reduce the impact of noise while learning meaningful patterns shared across multiple data sources. At the same time, it preserves important local structures within the data, leading to more reliable clustering results. We also develop an efficient optimization procedure to ensure the method works reliably in practice. Experiments on a wide range of datasets show that our approach consistently achieves more accurate and robust performance than existing methods.