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.
Although learning among heterogeneous data sources has attracted much attention, works on metric learning across heterogeneous domains are relatively rare. @cite_13 focused on metric learning only for the target domain, but not that across the source and the target domains, thus concern different setting from ours. To the best of our knowledge, @cite_22 's work is the only one closest to ours, although what they learned is, strictly speaking, a similarity function rather than a metric across the source and the target domains. They proposed a Frobenuis-norm regularized large margin model to learn the (linear) similarity function, which, from this paper's perspective, can be seen as only aligning the posteriors rather than the priors. Thus, they don't explore the abundant available unlabeled samples in target domain to leverage the learning.
@cite_13 @cite_22
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The problem of transfer learning has recently been of great interest in a variety of machine learning applications. In this paper, we examine a new angle to the transfer learning problem, where we examine the problem of distance function learning. Specifically, we focus on the problem of how our knowledge of distance functions in one domain can be transferred to a new domain. A good semantic understanding of the feature space is critical in providing the domain specific understanding for setting up good distance functions. Unfortunately, not all domains have feature representations which are equally interpretable. For example, in some domains such as text, the semantics of the feature representation are clear, as a result of which it is easy for a domain expert to set up distance functions for specific kinds of semantics. In the case of image data, the features are semantically harder to interpret, and it is harder to set up distance functions, especially for particular semantic criteria. In this paper, we focus on the problem of transfer learning as a way to close the semantic gap between different domains, and show how to use correspondence information between two domains in order to set up distance functions for the semantically more challenging domain. In real-world applications, “what you saw” during training is often not “what you get” during deployment: the distribution and even the type and dimensionality of features can change from one dataset to the next. In this paper, we address the problem of visual domain adaptation for transferring object models from one dataset or visual domain to another. We introduce ARC-t, a flexible model for supervised learning of non-linear transformations between domains. Our method is based on a novel theoretical result demonstrating that such transformations can be learned in kernel space. Unlike existing work, our model is not restricted to symmetric transformations, nor to features of the same type and dimensionality, making it applicable to a significantly wider set of adaptation scenarios than previous methods. Furthermore, the method can be applied to categories that were not available during training. We demonstrate the ability of our method to adapt object recognition models under a variety of situations, such as differing imaging conditions, feature types and codebooks.