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.

中文翻译：

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通过低秩矩阵分解的秩一致性诱导多视图子空间聚类


多视图子空间聚类已被证明可以通过利用多视图互补信息在实践中实现出色的性能。大多数现有方法中使用的策略之一是学习所有视图数据的共享自我表达系数矩阵。与这种策略不同，本文提出了一种秩一致性诱导的多视图子空间聚类模型，以追求视图特定的自我表达系数矩阵之间一致的低秩结构。为了促进实用模型，我们通过三因子分解和正交约束对所有自我表达系数矩阵上的低秩结构进行参数化。该规范确保不同视图的自我表达系数矩阵具有相同的秩，以有效促进多视图之间的结构一致性。这样的模型可以学习一致的子空间结构，并同时充分利用来自特定于视图的自我表达系数矩阵的补充信息。所提出的模型被表述为非凸优化问题。提出了一种在温和条件下保证收敛的高效优化算法。对几个基准数据库的广泛实验证明了所提出的模型相对于最先进的多视图聚类方法的优势。