Self-representation based subspace learning has shown its effectiveness in many applications. In this paper, we promote the traditional subspace representation learning by simultaneously taking advantages of multiple views and prior constraint. Accordingly, we establish a novel algorithm termed as Tensorized Multi-view Subspace Representation Learning. To exploit different views, the subspace representation matrices of different views are regarded as a low-rank tensor, which effectively models the high-order correlations of multi-view data. To incorporate prior information, a constraint matrix is devised to guide the subspace representation learning within a unified framework. The subspace representation tensor equipped with a low-rank constraint models elegantly the complementary information among different views, reduces redundancy of subspace representations, and then improves the accuracy of subsequent tasks. We formulate the model with a tensor nuclear norm minimization problem constrained with $$\ell _{2,1}$$ ℓ 2 , 1 -norm and linear equalities. The minimization problem is efficiently solved by using an Augmented Lagrangian Alternating Direction Minimization method. Extensive experimental results on diverse multi-view datasets demonstrate the effectiveness of our algorithm.

中文翻译：

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张量多视图子空间表示学习

基于自我表示的子空间学习已在许多应用中显示出其有效性。在本文中，我们通过同时利用多视图和先验约束的优势来促进传统的子空间表示学习。因此，我们建立了一种称为张量多视图子空间表示学习的新算法。为了利用不同的视图，不同视图的子空间表示矩阵被视为一个低秩张量，它有效地模拟了多视图数据的高阶相关性。为了结合先验信息，设计了一个约束矩阵来指导统一框架内的子空间表示学习。配备低秩约束的子空间表示张量优雅地模拟了不同视图之间的互补信息，减少子空间表示的冗余，进而提高后续任务的准确性。我们使用受 $$\ell _{2,1}$$ ℓ 2 , 1 -norm 和线性等式约束的张量核范数最小化问题来制定模型。通过使用增强拉格朗日交替方向最小化方法可以有效地解决最小化问题。在不同的多视图数据集上的大量实验结果证明了我们算法的有效性。