The existing multiview clustering models learn a consistent low-dimensional embedding either from multiple feature matrices or multiple similarity matrices, which ignores the interaction between the two procedures and limits the improvement of clustering performance on multiview data. To address this issue, a bidirectional probabilistic subspaces approximation (BPSA) model is developed in this article to learn a consistently orthogonal embedding from multiple feature matrices and multiple similarity matrices simultaneously via the disturbed probabilistic subspace modeling and approximation. A skillful bidirectional fusion strategy is designed to guarantee the parameter-free property of the BPSA model. Two adaptively weighted learning mechanisms are introduced to ensure the inconsistencies among multiple views and the inconsistencies between bidirectional learning processes. To solve the optimization problem involved in the BPSA model, an iterative solver is derived, and a rigorous convergence guarantee is provided. Extensive experimental results on both toy and real-world datasets demonstrate that our BPSA model achieves state-of-the-art performance even if it is parameter-free.

中文翻译：

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多视图聚类的双向概率子空间近似。

现有的多视图聚类模型从多个特征矩阵或多个相似矩阵中学习一致的低维嵌入，忽略了两个过程之间的交互，限制了多视图数据聚类性能的提高。为了解决这个问题，本文开发了双向概率子空间逼近 (BPSA) 模型，通过受干扰的概率子空间建模和逼近，同时从多个特征矩阵和多个相似度矩阵中学习一致的正交嵌入。巧妙的双向融合策略被设计来保证BPSA模型的无参数特性。引入了两种自适应加权学习机制，以确保多个视图之间的不一致和双向学习过程之间的不一致。针对BPSA模型中涉及的优化问题，推导了迭代求解器，并提供了严格的收敛保证。玩具和真实世界数据集上的广泛实验结果表明，我们的 BPSA 模型即使在无参数的情况下也能达到最先进的性能。