Visual domain adaptation aims to learn robust classifiers for the target domain by leveraging knowledge from a source domain. Existing methods either attempt to align the cross-domain distributions, or perform manifold subspace learning. However, there are two significant challenges: (1) degenerated feature transformation, which means that distribution alignment is often performed in the original feature space, where feature distortions are hard to overcome. On the other hand, subspace learning is not sufficient to reduce the distribution divergence. (2) unevaluated distribution alignment, which means that existing distribution alignment methods only align the marginal and conditional distributions with equal importance, while they fail to evaluate the different importance of these two distributions in real applications. In this paper, we propose a Manifold Embedded Distribution Alignment (MEDA) approach to address these challenges. MEDA learns a domain-invariant classifier in Grassmann manifold with structural risk minimization, while performing dynamic distribution alignment to quantitatively account for the relative importance of marginal and conditional distributions. To the best of our knowledge, MEDA is the first attempt to perform dynamic distribution alignment for manifold domain adaptation. Extensive experiments demonstrate that MEDA shows significant improvements in classification accuracy compared to state-of-the-art traditional and deep methods.
Subspace Alignment (SA) @cite_35 aligned the base vectors of both domains, but failed to adapt feature distributions. Subspace distribution alignment (SDA) @cite_27 extended SA by adding the subspace variance adaptation. However, SDA did not consider the local property of subspaces and ignored conditional distribution alignment. CORAL @cite_7 aligned subspaces in second-order statistics, but it did not consider the distribution alignment. Scatter component analysis (SCA) @cite_14 converted the samples into a set of subspaces (i.e. scatters) and then minimized the divergence between them. GFK @cite_31 extended the idea of sampled points in manifold @cite_17 and proposed to learn the geodesic flow kernel between domains. The work of @cite_34 used a Hellinger distance to approximate the geodesic distance in Riemann space. @cite_20 proposed to use Grassmann for domain adaptation, but they ignored the conditional distribution alignment. Different from these approaches, MEDA can learn a domain-invariant classifier in the manifold and align both marginal and conditional distributions.
@cite_35 @cite_14 @cite_7 @cite_27 @cite_31 @cite_34 @cite_20 @cite_17
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In this paper, we introduce a new domain adaptation (DA) algorithm where the source and target domains are represented by subspaces described by eigenvectors. In this context, our method seeks a domain adaptation solution 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 use a theoretical result to tune the unique hyper parameter corresponding to the size of the subspaces. We run our method on various datasets and show that, despite its intrinsic simplicity, it outperforms state of the art DA methods. Unlike human learning, machine learning often fails to handle changes between training (source) and test (target) input distributions. Such domain shifts, common in practical scenarios, severely damage the performance of conventional machine learning methods. Supervised domain adaptation methods have been proposed for the case when the target data have labels, including some that perform very well despite being "frustratingly easy" to implement. However, in practice, the target domain is often unlabeled, requiring unsupervised adaptation. We propose a simple, effective, and efficient method for unsupervised domain adaptation called CORrelation ALignment (CORAL). CORAL minimizes domain shift by aligning the second-order statistics of source and target distributions, without requiring any target labels. Even though it is extraordinarily simple--it can be implemented in four lines of Matlab code--CORAL performs remarkably well in extensive evaluations on standard benchmark datasets. We propose a novel method for unsupervised domain adaptation. Traditional machine learning algorithms often fail to generalize to new input distributions, causing reduced accuracy. Domain adaptation attempts to compensate for the performance degradation by transferring and adapting source knowledge to target domain. Existing unsupervised methods project domains into a lower-dimensional space and attempt to align the subspace bases, effectively learning a mapping from source to target points or vice versa. However, they fail to take into account the difference of the two distributions in the subspaces, resulting in misalignment even after adaptation. We present a unified view of existing subspace mapping based methods and develop a generalized approach that also aligns the distributions as well as the subspace bases. We provide a detailed evaluation of our approach on benchmark datasets and show improved results over published approaches. In this paper, we tackle the problem of unsupervised domain adaptation for classification. In the unsupervised scenario where no labeled samples from the target domain are provided, a popular approach consists in transforming the data such that the source and target distributions become similar. To compare the two distributions, existing approaches make use of the Maximum Mean Discrepancy (MMD). However, this does not exploit the fact that probability distributions lie on a Riemannian manifold. Here, we propose to make better use of the structure of this manifold and rely on the distance on the manifold to compare the source and target distributions. In this framework, we introduce a sample selection method and a subspace-based method for unsupervised domain adaptation, and show that both these manifold-based techniques outperform the corresponding approaches based on the MMD. Furthermore, we show that our subspace-based approach yields state-of-the-art results on a standard object recognition benchmark. Adapting the classifier trained on a source domain to recognize instances from a new target domain is an important problem that is receiving recent attention. In this paper, we present one of the first studies on unsupervised domain adaptation in the context of object recognition, where we have labeled data only from the source domain (and therefore do not have correspondences between object categories across domains). Motivated by incremental learning, we create intermediate representations of data between the two domains by viewing the generative subspaces (of same dimension) created from these domains as points on the Grassmann manifold, and sampling points along the geodesic between them to obtain subspaces that provide a meaningful description of the underlying domain shift. We then obtain the projections of labeled source domain data onto these subspaces, from which a discriminative classifier is learnt to classify projected data from the target domain. We discuss extensions of our approach for semi-supervised adaptation, and for cases with multiple source and target domains, and report competitive results on standard datasets.