Guo Jipeng, Sun Yanfeng, Gao Junbin, Hu Yongli, Yin Baocai
IEEE Trans Neural Netw Learn Syst. 2022 Jul;33(7):3157-3170. doi: 10.1109/TNNLS.2021.3071797. Epub 2022 Jul 6.
Multiview subspace clustering has been demonstrated to achieve excellent performance in practice by exploiting multiview complementary information. One of the strategies used in most existing methods is to learn a shared self-expressiveness coefficient matrix for all the view data. Different from such a strategy, this article proposes a rank consistency induced multiview subspace clustering model to pursue a consistent low-rank structure among view-specific self-expressiveness coefficient matrices. To facilitate a practical model, we parameterize the low-rank structure on all self-expressiveness coefficient matrices through the tri-factorization along with orthogonal constraints. This specification ensures that self-expressiveness coefficient matrices of different views have the same rank to effectively promote structural consistency across multiviews. Such a model can learn a consistent subspace structure and fully exploit the complementary information from the view-specific self-expressiveness coefficient matrices, simultaneously. The proposed model is formulated as a nonconvex optimization problem. An efficient optimization algorithm with guaranteed convergence under mild conditions is proposed. Extensive experiments on several benchmark databases demonstrate the advantage of the proposed model over the state-of-the-art multiview clustering approaches.
多视图子空间聚类已被证明通过利用多视图互补信息在实践中能取得优异的性能。大多数现有方法所采用的策略之一是为所有视图数据学习一个共享的自表达系数矩阵。与这种策略不同，本文提出了一种基于秩一致性的多视图子空间聚类模型，以在特定视图的自表达系数矩阵之间追求一致的低秩结构。为了构建一个实用的模型，我们通过带有正交约束的三因子分解对所有自表达系数矩阵上的低秩结构进行参数化。这种设定确保不同视图的自表达系数矩阵具有相同的秩，从而有效地促进多视图之间的结构一致性。这样一个模型能够同时学习一致的子空间结构，并充分利用来自特定视图自表达系数矩阵的互补信息。所提出的模型被表述为一个非凸优化问题。我们提出了一种在温和条件下保证收敛的高效优化算法。在几个基准数据库上进行的大量实验证明了所提出模型相对于现有最先进的多视图聚类方法的优势。
