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Distance metric learning plays a crucial role in diverse machine learning algorithms and applications. When the labeled information in a target domain is limited, transfer metric learning (TML) helps to learn the metric by leveraging the sufficient information from other related domains. Multitask metric learning (MTML), which can be regarded as a special case of TML, performs transfer across all related domains. Current TML tools usually assume that the same feature representation is exploited for different domains. However, in real-world applications, data may be drawn from heterogeneous domains. Heterogeneous transfer learning approaches can be adopted to remedy this drawback by deriving a metric from the learned transformation across different domains. However, they are often limited in that only two domains can be handled. To appropriately handle multiple domains, we develop a novel heterogeneous MTML (HMTML) framework. In HMTML, the metrics of all different domains are learned together. The transformations derived from the metrics are utilized to induce a common subspace, and the high-order covariance among the predictive structures of these domains is maximized in this subspace. There do exist a few heterogeneous transfer learning approaches that deal with multiple domains, but the high-order statistics (correlation information), which can only be exploited by simultaneously examining all domains, is ignored in these approaches. Compared with them, the proposed HMTML can effectively explore such high-order information, thus obtaining more reliable feature transformations and metrics. Effectiveness of our method is validated by the extensive and intensive experiments on text categorization, scene classification, and social image annotation.

Heterogeneous Multitask Metric Learning Across Multiple Domains