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.

提出一种新的异构多任务度量学习框架（HMTML），利用多个不同子领域数据学习跨域度量，并在共同子空间中最大化预测结构的高阶协方差，进而有效地探索高阶信息，验证实验表明其方法具有更可靠的特征转换和度量。

跨多个领域进行异构多任务度量学习

Heterogeneous Multi-task Metric Learning across Multiple Domains

Distance metric learning (DML) aims to find an appropriate way to reveal the
underlying data relationship. It is critical in many machine learning, pattern
recognition and data mining algorithms, and usually require large amount of
label information (such as class labels or pair/triplet constraints) to achieve
satisfactory performance. However, the label information may be insufficient in
real-world applications due to the high-labeling cost, and DML may fail in this
case. Transfer metric learning (TML) is able to mitigate this issue for DML in
the domain of interest (target domain) by leveraging knowledge/information from
other related domains (source domains). Although achieved a certain level of
development, TML has limited success in various aspects such as selective
transfer, theoretical understanding, handling complex data, big data and
extreme cases. In this survey, we present a systematic review of the TML
literature. In particular, we group TML into different categories according to
different settings and metric transfer strategies, such as direct metric
approximation, subspace approximation, distance approximation, and distribution
approximation. A summarization and insightful discussion of the various TML
approaches and their applications will be presented. Finally, we indicate some
challenges and provide possible future directions.

本文介绍了关于迁移测度学习的分类和度量传递策略，包括直接度量逼近、子空间逼近、距离逼近和分布逼近。同时，总结和探讨了迁移测度学习的不同方法及其应用，并指出了未来可能的研究方向和挑战。