A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> 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. <s> BIB001 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> Most machine learning algorithms, including many online learners, assume that the data distribution to be learned is fixed. There are many real-world problems where the distribution of the data changes as a function of time. Changes in nonstationary data distributions can significantly reduce the generalization ability of the learning algorithm on new or field data, if the algorithm is not equipped to track such changes. When the stationary data distribution assumption does not hold, the learner must take appropriate actions to ensure that the new/relevant information is learned. On the other hand, data distributions do not necessarily change continuously, necessitating the ability to monitor the distribution and detect when a significant change in distribution has occurred. In this work, we propose and analyze a feature based drift detection method using the Hellinger distance to detect gradual or abrupt changes in the distribution. <s> BIB002 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> Domain adaptation algorithms that handle shifts in the distribution between training and testing data are receiving much attention in computer vision. Recently, a Grassmann manifold-based domain adaptation algorithm that models the domain shift using intermediate subspaces along the geodesic connecting the source and target domains was presented in [6]. We build upon this work and propose replacing the step of concatenating feature projections on a very few sampled intermediate subspaces by directly integrating the distance between feature projections along the geodesic. The proposed approach considers all the intermediate subspaces along the geodesic. Thus, it is a more principled way of quantifying the cross-domain distance. We present the results of experiments on two standard datasets and show that the proposed algorithm yields favorable performance over previous approaches. <s> BIB003 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> In real-world applications of visual recognition, many factors — such as pose, illumination, or image quality — can cause a significant mismatch between the source domain on which classifiers are trained and the target domain to which those classifiers are applied. As such, the classifiers often perform poorly on the target domain. Domain adaptation techniques aim to correct the mismatch. Existing approaches have concentrated on learning feature representations that are invariant across domains, and they often do not directly exploit low-dimensional structures that are intrinsic to many vision datasets. In this paper, we propose a new kernel-based method that takes advantage of such structures. Our geodesic flow kernel models domain shift by integrating an infinite number of subspaces that characterize changes in geometric and statistical properties from the source to the target domain. Our approach is computationally advantageous, automatically inferring important algorithmic parameters without requiring extensive cross-validation or labeled data from either domain. We also introduce a metric that reliably measures the adaptability between a pair of source and target domains. For a given target domain and several source domains, the metric can be used to automatically select the optimal source domain to adapt and avoid less desirable ones. Empirical studies on standard datasets demonstrate the advantages of our approach over competing methods. <s> BIB004 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> 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. <s> BIB005 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> In visual recognition problems, the common data distribution mismatches between training and testing make domain adaptation essential. However, image data is difficult to manually divide into the discrete domains required by adaptation algorithms, and the standard practice of equating datasets with domains is a weak proxy for all the real conditions that alter the statistics in complex ways (lighting, pose, background, resolution, etc.) We propose an approach to automatically discover latent domains in image or video datasets. Our formulation imposes two key properties on domains: maximum distinctiveness and maximum learnability. By maximum distinctiveness, we require the underlying distributions of the identified domains to be different from each other to the maximum extent; by maximum learnability, we ensure that a strong discriminative model can be learned from the domain. We devise a nonparametric formulation and efficient optimization procedure that can successfully discover domains among both training and test data. We extensively evaluate our approach on object recognition and human activity recognition tasks. <s> BIB006 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> Domain-invariant representations are key to addressing the domain shift problem where the training and test examples follow different distributions. Existing techniques that have attempted to match the distributions of the source and target domains typically compare these distributions in the original feature space. This space, however, may not be directly suitable for such a comparison, since some of the features may have been distorted by the domain shift, or may be domain specific. In this paper, we introduce a Domain Invariant Projection approach: An unsupervised domain adaptation method that overcomes this issue by extracting the information that is invariant across the source and target domains. More specifically, we learn a projection of the data to a low-dimensional latent space where the distance between the empirical distributions of the source and target examples is minimized. We demonstrate the effectiveness of our approach on the task of visual object recognition and show that it outperforms state-of-the-art methods on a standard domain adaptation benchmark dataset. <s> BIB007 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> 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. <s> BIB008 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> We pose the following question: what happens when test data not only differs from training data, but differs from it in a continually evolving way? The classic domain adaptation paradigm considers the world to be separated into stationary domains with clear boundaries between them. However, in many real-world applications, examples cannot be naturally separated into discrete domains, but arise from a continuously evolving underlying process. Examples include video with gradually changing lighting and spam email with evolving spammer tactics. We formulate a novel problem of adapting to such continuous domains, and present a solution based on smoothly varying embeddings. Recent work has shown the utility of considering discrete visual domains as fixed points embedded in a manifold of lower-dimensional subspaces. Adaptation can be achieved via transforms or kernels learned between such stationary source and target subspaces. We propose a method to consider non-stationary domains, which we refer to as Continuous Manifold Adaptation (CMA). We treat each target sample as potentially being drawn from a different subspace on the domain manifold, and present a novel technique for continuous transform-based adaptation. Our approach can learn to distinguish categories using training data collected at some point in the past, and continue to update its model of the categories for some time into the future, without receiving any additional labels. Experiments on two visual datasets demonstrate the value of our approach for several popular feature representations. <s> BIB009 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> With unconstrained data acquisition scenarios widely prevalent, the ability to handle changes in data distribution across training and testing data sets becomes important. One way to approach this problem is through domain adaptation, and in this paper we primarily focus on the unsupervised scenario where the labeled source domain training data is accompanied by unlabeled target domain test data. We present a two-stage data-driven approach by generating intermediate data representations that could provide relevant information on the domain shift. Starting with a linear representation of domains in the form of generative subspaces of same dimensions for the source and target domains, we first utilize the underlying geometry of the space of these subspaces, the Grassmann manifold, to obtain a `shortest' geodesic path between the two domains. We then sample points along the geodesic to obtain intermediate cross-domain data representations, using which a discriminative classifier is learnt to estimate the labels of the target data. We subsequently incorporate non-linear representation of domains by considering a Reproducing Kernel Hilbert Space representation, and a low-dimensional manifold representation using Laplacian Eigenmaps, and also examine other domain adaptation settings such as (i) semi-supervised adaptation where the target domain is partially labeled, and (ii) multi-domain adaptation where there could be more than one domain in source and/or target data sets. Finally, we supplement our adaptation technique with (i) fine-grained reference domains that are created by blending samples from source and target data sets to provide some evidence on the actual domain shift, and (ii) a multi-class boosting analysis to obtain robustness to the choice of algorithm parameters. We evaluate our approach for object recognition problems and report competitive results on two widely used Office and Bing adaptation data sets. <s> BIB010 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> Domain adaptation (DA) has gained a lot of success in the recent years in computer vision to deal with situations where the learning process has to transfer knowledge from a source to a target domain. In this paper, we introduce a novel unsupervised DA approach based on both subspace alignment and selection of landmarks similarly distributed between the two domains. Those landmarks are selected so as to reduce the discrepancy between the domains and then are used to non linearly project the data in the same space where an efficient subspace alignment (in closed-form) is performed. We carry out a large experimental comparison in visual domain adaptation showing that our new method outperforms the most recent unsupervised DA approaches. <s> BIB011 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> 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. <s> BIB012 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> Recently, a particular paradigm [18] in the domain adaptation field has received considerable attention by introducing novel and important insights to the problem. In this case, the source and target domains are represented in the form of subspaces, which are treated as points on the Grassmann manifold. The geodesic curve between them is sampled to obtain intermediate points. Then a classifier is learnt using the projections of the data onto these subspaces. Despite its relevance and popularity, this paradigm [18] contains some limitations. Firstly, in real-world applications, that simple curve (i.e. shortest path) does not provide the necessary flexibility to model the domain shift between the training and testing data sets. Secondly, by using the geodesic curve, we are restricted to only one source domain, which does not allow to take fully advantage of the multiple datasets that are available nowadays. It is then, natural to ask whether this popular concept could be extended to deal with more complex curves and to integrate multi-sources domains. This is a hard problem considering the Riemannian structure of the space, but we propose a mathematically well-founded idea that enables us to solve it. We exploit the geometric insight of rolling maps [30] to compute a spline curve on the Grassmann manifold. The benefits of the proposed idea are demonstrated through several empirical studies on standard datasets. This novel concept allows to explicitly integrate multi-source domains while the previous one [18] uses the mean of all sources. This enables to model better the domain shift and take fully advantage of the training datasets. <s> BIB013 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> Domain-invariant representations are key to addressing the domain shift problem where the training and test examples follow different distributions. Existing techniques that have attempted to match the distributions of the source and target domains typically compare these distributions in the original feature space. This space, however, may not be directly suitable for such a comparison, since some of the features may have been distorted by the domain shift, or may be domain specific. In this paper, we introduce a Distribution-Matching Embedding approach: An unsupervised domain adaptation method that overcomes this issue by mapping the data to a latent space where the distance between the empirical distributions of the source and target examples is minimized. In other words, we seek to extract the information that is invariant across the source and target data. In particular, we study two different distances to compare the source and target distributions: the Maximum Mean Discrepancy and the Hellinger distance. Furthermore, we show that our approach allows us to learn either a linear embedding, or a nonlinear one. We demonstrate the benefits of our approach on the tasks of visual object recognition, text categorization, and WiFi localization. <s> BIB014 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> Domain adaptation (DA) addresses the real-world image classification problem of discrepancy between training (source) and testing (target) data distributions. We propose an unsupervised DA method that considers the presence of only unlabelled data in the target domain. Our approach centers on finding matches between samples of the source and target domains. The matches are obtained by treating the source and target domains as hyper-graphs and carrying out a class-regularized hyper-graph matching using first-, second-and third-order similarities between the graphs. We have also developed a computationally efficient algorithm by initially selecting a subset of the samples to construct a graph and then developing a customized optimization routine for graph-matching based on Conditional Gradient and Alternating Direction Multiplier Method. This allows the proposed method to be used widely. We also performed a set of experiments on standard object recognition datasets to validate the effectiveness of our framework over previous approaches. <s> BIB015 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> The goal of domain adaptation is to train a high-performance predictive model on the target domain data by using knowledge from the source domain data, which has different but related data distribution. In this paper, we consider unsupervised domain adaptation where we have labelled source domain data but unlabelled target domain data. Our solution to unsupervised domain adaptation is to learn a domain-invariant representation that is also category discriminative. Domain-invariant representations are realized by minimizing the domain discrepancy. To minimize the domain discrepancy, we propose a novel graph-matching metric between the source and target domain representations. Minimizing this metric allows the source and target representations to be in support of each other. We further exploit confident unlabelled target domain samples and their pseudo-labels to refine our proposed model. We expect the refining step to improve the performance further. This is validated by performing experiments on standard image classification adaptation datasets. Results showed our proposed approach out-perform previous domain-invariant representation learning approaches. <s> BIB016 </s> A review of single-source unsupervised domain adaptation <s> Subspace mappings <s> The assumption that training and testing samples are generated from the same distribution does not always hold for real-world machine-learning applications. The procedure of tackling this discrepancy between the training (source) and testing (target) domains is known as domain adaptation. We propose an unsupervised version of domain adaptation that considers the presence of only unlabelled data in the target domain. Our approach centers on finding correspondences between samples of each domain. The correspondences are obtained by treating the source and target samples as graphs and using a convex criterion to match them. The criteria used are first-order and second-order similarities between the graphs as well as a class-based regularization. We have also developed a computationally efficient routine for the convex optimization, thus allowing the proposed method to be used widely. To verify the effectiveness of the proposed method, computer simulations were conducted on synthetic, image classification and sentiment classification datasets. Results validated that the proposed local sample-to-sample matching method out-performs traditional moment-matching methods and is competitive with respect to current local domain-adaptation methods. <s> BIB017
In certain problems, the domains contain domain-specific noise but common subspaces. Adaptation would consist of finding these subspaces and matching the source data to the target data along them. One of the most straightforward of such techniques, called Subspace Alignment, computes the first d principal components in each domain, C S and C T , where d < D BIB005 . A linear transformation matrix is then computed that aligns source components to target components: M = C ⊤ S C T . The adaptive classifier projects data in each domain to their components, maps the projected source data using M and trains on the transformed source data. Extensions of this approach include Landmark-based Alignment BIB011 and Subspace Distribution Alignment BIB012 . A slightly more complicated technique is to model the structure of the data with graph-based methods, instead of aligning directions of variance BIB015 , BIB016 . Data is first summarized using a subset called the exemplars, obtained through clustering. From the set of exemplars, two hyper-graphs are constructed. These two hyper-graphs are matched along their first, second and third orders using tensor-based algorithms BIB015 , BIB016 . Higher-order moments consider other forms of geometric and structural information, beyond pairwise distances between exemplars BIB015 , BIB017 . A further step can be taken by assuming that there exists a manifold of transformations between the source and target domain BIB008 , BIB006 , BIB009 . This manifold consists of a space of parameters, where each point would generate a possible domain. For example, the manifold might consist of a set of camera optics parameters, where each setting would produce data in a different part of feature space BIB008 , BIB001 . The manifold assumption is interesting, because it implies that there exists a path along the manifold's surface from the source to the target domain BIB007 , BIB013 . Every point along that path could generate an intermediate domain  , BIB010 . For example, the space of all linear subspace transformations is termed the Grassmann manifold BIB003 . A path along the Grassmannian generates many linear transformations, which could, in turn, generate intermediate domains BIB010 . These intermediate domains can be used during training to inform a classifier on how to adapt its decision boundary. But it is also possible to incorporate the entire path. Geodesic Flow Kernel (GFK) forms a kernel consisting of the inner product between two feature vectors x i and x j projected onto the t-th subspace, for t ∈ [0, 1] BIB004 . It then integrates over t to account for all intermediate subspaces: where Φ(t) is the projection matrix. At t = 0, the projection consists of purely the source components, Φ(0) = C S , and at t = 1, it consists purely of the target components, Φ(1) = C T . The resulting kernel can be used in combination with a support vector machine or a kernel nearest-neighbour  , BIB004 . An alternative is statistical manifolds, where each point generates a probability distribution BIB008 . A path on the statistical manifold may describe a sequence of parameters that turns one distribution into another, for instance a sequence of means between two Gaussian distributions. The length of the geodesic path along the statistical manifold is called the Hellinger distance, and can be used as a measure of domain discrepancy BIB002 . Adaptation consists of finding a sequence of parameters based on minimum Hellinger distance, and use these in a similar fashion as GFK BIB008 , BIB014 .