In this paper, we attempts to learn a single metric across two heterogeneous do-mains where source domain is fully labeled and has many samples while targetdomain has only a few labeled samples but abundant unlabeled samples. Tothe best of our knowledge, this task is seldom touched. The proposed learningmodel has a simple underlying motivation: all the samples in both the sourceand the target domains are mapped into a common space, where both theirpriors P(sample)s and their posteriors P(label|sample)s are forced to be re-spectively aligned as much as possible. We show that the two mappings, fromboth the source domain and the target domain to the common space, can bereparameterized into a single positive semi-deﬁnite(PSD) matrix. Then we de-velop an eﬃcient Bregman Projection algorithm to optimize the PDS matrixover which a LogDet function is used to regularize. Furthermore, we also showthat this model can be easily kernelized and verify its eﬀectiveness in cross-language retrieval task and cross-domain object recognition task.
Heterogeneous learning may date back to @cite_0 . They used some co-occurrence data to estimate the feature-level conditional distribution from source feature to target feature. Later, many other methods were proposed @cite_2 @cite_7 @cite_3 @cite_19 @cite_21 . A common character of these methods is that they all map the samples in the source and the target domains into a common space for the learning tasks. For example, @cite_3 embedded all the samples in different domains into a common space according to a large manifold structure covering both the within-domain geometrical structure and the between-domain label structure. @cite_2 mapped all the samples into a common space and applied the classic linear discriminant analysis(LDA). @cite_19 used a collective matrix factorization model to find out the common space. However, the algorithm requires the same number of samples of source and target domains, which is usually could not be satisfied. Thus before conducting the algorithm, they had to bring in a sampling procedure. @cite_21 constructed a parameterized augmented space as the common space motivated by a domain adaptation method proposed by did @cite_17 . And the parameters are learned through optimizing a large margin classification model.
@cite_7 @cite_21 @cite_3 @cite_0 @cite_19 @cite_2 @cite_17
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Most previous heterogeneous transfer learning methods learn a cross-domain feature mapping between heterogeneous feature spaces based on a few cross-domain instance-correspondences, and these corresponding instances are assumed to be representative in the source and target domains respectively. However, in many real-world scenarios, this assumption may not hold. As a result, the constructed feature mapping may not be precise due to the bias issue of the correspondences in the target or (and) source domain(s). In this case, a classifier trained on the labeled transformed-source-domain data may not be useful for the target domain. In this paper, we present a new transfer learning framework called Hybrid Heterogeneous Transfer Learning (HHTL), which allows the corresponding instances across domains to be biased in either the source or target domain. Specifically, we propose a deep learning approach to learn a feature mapping between cross-domain heterogeneous features as well as a better feature representation for mapped data to reduce the bias issue caused by the cross-domain correspondences. Extensive experiments on several multilingual sentiment classification tasks verify the effectiveness of our proposed approach compared with some baseline methods. In this paper, we study the heterogeneous domain adaptation (HDA) problem, in which the data from the source domain and the target domain are represented by heterogeneous features with different dimensions. By introducing two different projection matrices, we first transform the data from two domains into a common subspace such that the similarity between samples across different domains can be measured. We then propose a new feature mapping function for each domain, which augments the transformed samples with their original features and zeros. Existing supervised learning methods ( e.g., SVM and SVR) can be readily employed by incorporating our newly proposed augmented feature representations for supervised HDA. As a showcase, we propose a novel method called Heterogeneous Feature Augmentation (HFA) based on SVM. We show that the proposed formulation can be equivalently derived as a standard Multiple Kernel Learning (MKL) problem, which is convex and thus the global solution can be guaranteed. To additionally utilize the unlabeled data in the target domain, we further propose the semi-supervised HFA (SHFA) which can simultaneously learn the target classifier as well as infer the labels of unlabeled target samples. Comprehensive experiments on three different applications clearly demonstrate that our SHFA and HFA outperform the existing HDA methods. Heterogeneous domain adaptation aims to exploit labeled training data from a source domain for learning prediction models in a target domain under the condition that the two domains have different input feature representation spaces. In this paper, we propose a novel semi-supervised subspace co-projection method to address multi-class heterogeneous domain adaptation. The proposed method projects the instances of the two domains into a co-located latent subspace to bridge the feature divergence gap across domains, while simultaneously training prediction models in the co-projected representation space with labeled training instances from both domains. It also exploits the unlabeled data to promote the consistency of co-projected subspaces from the two domains based on a maximum mean discrepancy criterion. Moreover, to increase the stability and discriminative informativeness of the subspace co-projection, we further exploit the error-correcting output code schemes to incorporate more binary prediction tasks shared across domains into the learning process. We formulate this semi-supervised learning process as a non-convex joint minimization problem and develop an alternating optimization algorithm to solve it. To investigate the empirical performance of the proposed approach, we conduct experiments on cross-lingual text classification and cross-domain digit image classification tasks with heterogeneous feature spaces. The experimental results demonstrate the efficacy of the proposed method on these heterogeneous domain adaptation problems. Labeled examples are often expensive and time-consuming to obtain. One practically important problem is: can the labeled data from other related sources help predict the target task, even if they have (a) different feature spaces (e.g., image vs. text data), (b) different data distributions, and (c) different output spaces? This paper proposes a solution and discusses the conditions where this is possible and highly likely to produce better results. It works by first using spectral embedding to unify the different feature spaces of the target and source data sets, even when they have completely different feature spaces. The principle is to cast into an optimization objective that preserves the original structure of the data, while at the same time, maximizes the similarity between the two. Second, a judicious sample selection strategy is applied to select only those related source examples. At last, a Bayesian-based approach is applied to model the relationship between different output spaces. The three steps can bridge related heterogeneous sources in order to learn the target task. Among the 12 experiment data sets, for example, the images with wavelet-transformed-based features are used to predict another set of images whose features are constructed from color-histogram space. By using these extracted examples from heterogeneous sources, the models can reduce the error rate by as much as 50 , compared with the methods using only the examples from the target task.