Metric learning is a key problem for many data mining and machine learning
applications, and has long been dominated by Mahalanobis methods. Recent
advances in nonlinear metric learning have demonstrated the potential power of
non-Mahalanobis distance functions, particularly tree-based functions. We
propose a novel nonlinear metric learning method that uses an iterative,
hierarchical variant of semi-supervised max-margin clustering to construct a
forest of cluster hierarchies, where each individual hierarchy can be
interpreted as a weak metric over the data. By introducing randomness during
hierarchy training and combining the output of many of the resulting
semi-random weak hierarchy metrics, we can obtain a powerful and robust
nonlinear metric model. This method has two primary contributions: first, it is
semi-supervised, incorporating information from both constrained and
unconstrained points. Second, we take a relaxed approach to constraint
satisfaction, allowing the method to satisfy different subsets of the
constraints at different levels of the hierarchy rather than attempting to
simultaneously satisfy all of them. This leads to a more robust learning
algorithm. We compare our method to a number of state-of-the-art benchmarks on
$k$-nearest neighbor classification, large-scale image retrieval and
semi-supervised clustering problems, and find that our algorithm yields results
comparable or superior to the state-of-the-art, and is significantly more
robust to noise.

提出了一种新的非线性度量学习方法，其使用基于迭代、分层的半监督最大间隔聚类的树型算法来构建聚类层级森林，并将众多半随机弱度量层级的输出结合起来，以获得强大而稳健的非线性度量模型。与一些最先进的基准测试结果相比，这种方法的结果相当或优于现有最先进算法，并且对噪声更具稳健性。同时，这种方法具有两个主要贡献：第一，它是半监督的，同时融合了约束点和非约束点的信息；第二，它采用了一种松散的约束满足方法，在不同层次的层级中满足不同子集的约束，从而得到更加稳健的学习算法。