基于最大间隔聚类森林的半监督非线性距离度量学习
Semi-Supervised Nonlinear Distance Metric Learning via Forests of Max-Margin Cluster Hierarchies
摘要：
度量学习是许多数据挖掘和机器学习应用的关键问题，长期以来一直由马氏方法主导。非线性度量学习的最新进展已经证明了非马氏距离函数的潜在能力，特别是基于树的函数。我们提出了一种新的非线性度量学习方法，它使用半监督最大边缘聚类的迭代，分层变体来构建聚类层次的森林，其中每个层次都可以被解释为数据上的弱度量。通过在层次训练过程中引入随机性，并结合许多半随机弱层次度量的输出，我们可以得到一个强大而鲁棒的非线性度量模型。这种方法有两个主要贡献：第一，它是半监督的，结合了来自约束和无约束点的信息。其次，我们采取了一种宽松的方法来满足约束，允许该方法满足不同层次的约束的不同子集，而不是试图同时满足所有这些。这导致了更强大的学习算法。我们比较我们的方法，一些国家的最先进的基准$k$ -最近邻分类，大规模图像检索和半监督聚类问题，并发现我们的算法产生的结果相当或优于国家的最先进的，是显着更强大的噪声。
英文摘要：
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.
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