We propose a tensor-based domain alignment (DA) algorithm designed to align source and target tensors within an invariant subspace through the use of alignment matrices. These matrices along with the subspace undergo iterative optimization of which constraint is on oblique manifold, which offers greater flexibility and adaptability compared to the traditional Stiefel manifold. Moreover, regularization terms defined to preserve the variance of both source and target tensors, ensures robust performance. Our framework is versatile, effectively generalizing existing tensor-based DA methods as special cases. Through extensive experiments, we demonstrate that our approach not only enhances DA conversion speed but also significantly boosts classification accuracy. This positions our method as superior to current state-of-the-art techniques, making it a preferable choice for complex domain adaptation tasks.

翻译：我们提出了一种基于张量的域对齐算法，旨在通过使用对齐矩阵，将源张量和目标张量在一个不变子空间中对齐。这些矩阵与子空间在斜流形约束下进行迭代优化，相比传统的Stiefel流形，提供了更大的灵活性和适应性。此外，定义了正则化项以保持源张量和目标张量的方差，确保鲁棒性能。我们的框架具有通用性，能够有效地将现有的基于张量的域对齐方法推广为特例。通过大量实验，我们证明我们的方法不仅提高了域对齐转换速度，还显著提升了分类精度。这使得我们的方法优于当前最先进的技术，成为复杂域适应任务的首选方案。