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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Traditional ranking mainly focuses on one type of data source, and effective modeling still relies on a sufficiently large number of labeled or supervised examples. However, in many real-world applications, in particular with the rapid growth of the Web 2.0, ranking over multiple interrelated (heterogeneous) domains becomes a common situation, where in some domains we may have a large amount of training data while in some other domains we can only collect very little. One important question is: "if there is not sufficient supervision in the domain of interest, how could one borrow labeled information from a related but heterogenous domain to build an accurate model?". This paper explores such an approach by bridging two heterogeneous domains via the latent space. We propose a regularized framework to simultaneously minimize two loss functions corresponding to two related but different information sources, by mapping each domain onto a "shared latent space", capturing similar and transferable oncepts. We solve this problem by optimizing the convex upper bound of the non-continuous loss function and derive its generalization bound. Experimental results on three different genres of data sets demonstrate the effectiveness of the proposed approach. We propose a new learning method for heterogeneous domain adaptation (HDA), in which the data from the source domain and the target domain are represented by heterogeneous features with different dimensions. Using two different projection matrices, we first transform the data from two domains into a common subspace in order to measure the similarity between the data from two domains. We then propose two new feature mapping functions to augment the transformed data with their original features and zeros. The existing learning methods (e.g., SVM and SVR) can be readily incorporated with our newly proposed augmented feature representations to effectively utilize the data from both domains for HDA. Using the hinge loss function in SVM as an example, we introduce the detailed objective function in our method called Heterogeneous Feature Augmentation (HFA) for a linear case and also describe its kernelization in order to efficiently cope with the data with very high dimensions. Moreover, we also develop an alternating optimization algorithm to effectively solve the nontrivial optimization problem in our HFA method. Comprehensive experiments on two benchmark datasets clearly demonstrate that HFA outperforms the existing HDA methods. We propose a manifold alignment based approach for heterogeneous domain adaptation. A key aspect of this approach is to construct mappings to link different feature spaces in order to transfer knowledge across domains. The new approach can reuse labeled data from multiple source domains in a target domain even in the case when the input domains do not share any common features or instances. As a pre-processing step, our approach can also be combined with existing domain adaptation approaches to learn a common feature space for all input domains. This paper extends existing manifold alignment approaches by making use of labels rather than correspondences to align the manifolds. This extension significantly broadens the application scope of manifold alignment, since the correspondence relationship required by existing alignment approaches is hard to obtain in many applications. This paper investigates a new machine learning strategy called translated learning. Unlike many previous learning tasks, we focus on how to use labeled data from one feature space to enhance the classification of other entirely different learning spaces. For example, we might wish to use labeled text data to help learn a model for classifying image data, when the labeled images are difficult to obtain. An important aspect of translated learning is to build a "bridge" to link one feature space (known as the "source space") to another space (known as the "target space") through a translator in order to migrate the knowledge from source to target. The translated learning solution uses a language model to link the class labels to the features in the source spaces, which in turn is translated to the features in the target spaces. Finally, this chain of linkages is completed by tracing back to the instances in the target spaces. We show that this path of linkage can be modeled using a Markov chain and risk minimization. Through experiments on the text-aided image classification and cross-language classification tasks, we demonstrate that our translated learning framework can greatly outperform many state-of-the-art baseline methods. 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. Multi-task learning aims at improving the generalization performance of a learning task with the help of some other related tasks. Although many multi-task learning methods have been proposed, they are all based on the assumption that all tasks share the same data representation. This assumption is too restrictive for general applications. In this paper, we propose a multi-task extension of linear discriminant analysis (LDA), called multi-task discriminant analysis (MTDA), which can deal with learning tasks with different data representations. For each task, MTDA learns a separate transformation which consists of two parts, one specific to the task and one common to all tasks. A by-product of MTDA is that it can alleviate the labeled data deficiency problem of LDA. Moreover, unlike many existing multi-task learning methods, MTDA can handle binary and multi-class problems for each task in a generic way. Experimental results on face recognition show that MTDA consistently outperforms related methods. We describe an approach to domain adaptation that is appropriate exactly in the case when one has enough “target” data to do slightly better than just using only “source” data. Our approach is incredibly simple, easy to implement as a preprocessing step (10 lines of Perl!) and outperforms stateof-the-art approaches on a range of datasets. Moreover, it is trivially extended to a multidomain adaptation problem, where one has data from a variety of different domains.