In this paper, we introduce a new domain adaptation (DA) algorithm where the source and target domains are represented by subspaces spanned by eigenvectors. Our method seeks a domain invariant feature space by learning a mapping function which aligns the source subspace with the target one. We show that the solution of the corresponding optimization problem can be obtained in a simple closed form, leading to an extremely fast algorithm. We present two approaches to determine the only hyper-parameter in our method corresponding to the size of the subspaces. In the first approach we tune the size of subspaces using a theoretical bound on the stability of the obtained result. In the second approach, we use maximum likelihood estimation to determine the subspace size, which is particularly useful for high dimensional data. Apart from PCA, we propose a subspace creation method that outperform partial least squares (PLS) and linear discriminant analysis (LDA) in domain adaptation. We test our method on various datasets and show that, despite its intrinsic simplicity, it outperforms state of the art DA methods.

本研究介绍了一种新的领域自适应算法，其中源域和目标域由特征向量所构成的子空间表示。通过学习将源子空间与目标子空间对齐的映射函数，我们的方法寻求一个不变的特征空间。我们提出了两种方法来确定超参数的大小，一种方法使用所得结果稳定性的理论边界来调整子空间的大小，另一种方法使用最大似然估计来确定子空间的大小。除了PCA，我们还提出一种子空间创建方法，它在领域自适应中优于PLS和LDA，并在各种数据集上对我们的方法进行了测试，结果表明它的性能优于现有的领域自适应方法。

子空间对齐的域自适应