  Distance metric learning (DML) plays a crucial role in diverse machine
learning algorithms and applications. When the labeled information in target
domain is limited, transfer metric learning (TML) helps to learn the metric by
leveraging the sufficient information from other related domains. Multi-task
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. But they are often limited in that only two domains can be
handled. To appropriately handle multiple domains, we develop a novel
heterogeneous multi-task metric learning (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.
