具有pq-图的有序标记树的度量学习
Metric Learning for Ordered Labeled Trees with pq-grams
摘要：
计算两个数据点之间的相似性在许多机器学习算法中起着至关重要的作用。度量学习的目的是从数据中自动学习一个好的度量。现有的树结构数据度量学习研究大多采用树编辑距离的学习方法。然而，编辑距离不适合大数据分析，因为它会导致高计算成本。在本文中，我们提出了一个新的度量学习方法的树结构数据与pq-gram。pq-gram距离是有序标记树的距离，并且具有比树编辑距离低得多的计算成本。为了进行基于pq-gram的度量学习，我们提出了一种新的可微参数化距离，加权pq-gram距离。我们还提出了一种基于大间隔最近邻（LMNN）学习建议距离的方法，这是一种经过充分研究和实用的度量学习方案。我们制定的度量学习问题作为一个优化问题，并使用梯度下降技术来执行度量学习。我们的经验表明，所提出的方法不仅取得了竞争力的结果与国家的最先进的编辑距离为基础的方法在各种分类问题，但也解决了分类问题更迅速地比编辑距离为基础的方法。
英文摘要：
Computing the similarity between two data points plays a vital role in many machine learning algorithms. Metric learning has the aim of learning a good metric automatically from data. Most existing studies on metric learning for tree-structured data have adopted the approach of learning the tree edit distance. However, the edit distance is not amenable for big data analysis because it incurs high computation cost. In this paper, we propose a new metric learning approach for tree-structured data with pq-grams. The pq-gram distance is a distance for ordered labeled trees, and has much lower computation cost than the tree edit distance. In order to perform metric learning based on pq-grams, we propose a new differentiable parameterized distance, weighted pq-gram distance. We also propose a way to learn the proposed distance based on Large Margin Nearest Neighbors (LMNN), which is a well-studied and practical metric learning scheme. We formulate the metric learning problem as an optimization problem and use the gradient descent technique to perform metric learning. We empirically show that the proposed approach not only achieves competitive results with the state-of-the-art edit distance-based methods in various classification problems, but also solves the classification problems much more rapidly than the edit distance-based methods.
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