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Customizable HMM-based measures to accurately compare tree sets

机译：可定制的基于HMM的措施，准确比较树集

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摘要

Trees have been topics of much interest since many decades due to various emerging applications using data represented as trees. Several techniques have been developed to compare two trees. But there is a serious lack of metrics to compare weighted trees. Existing approaches do not also allow to explicitly specify the targeted nodes properties on which the comparison should be performed. Furthermore, the problem of comparing two tree sets is not specifically addressed by existing techniques. This paper attempts to solve these problems by first proposing a distance and a similarity for the comparison of two finite sets of rooted ordered trees which can be labeled or not, as well as weighted or unweighted. To achieve this goal, a hidden Markov model is associated with each tree set for each targeted nodes property. The model associated with a tree set T for the targeted nodes property p learns how much the nodes of the trees in T verify property p. The resulting models are finally compared to derive a distance and similarity between the two sets of trees. The previous measures are then generalized for the comparison of unrooted and unordered trees. Flat classification experiments were carried out on two synthetic databases named FirstLast-L and FirstLast-LW available online. They both contain four classes of 100 rooted ordered trees whose specific and non-trivial nodes properties are clearly defined. When the distance proposed in this paper is selected as metric for the Nearest Neighbor classifier, a perfect accuracy of 100% is obtained for these two databases. This performance is 41% higher than the accuracy exhibited when the widespread tree Edit distance is selected for FirstLast-L.
机译：由于使用表示为树的数据，因此由于各种新兴应用程序，树木已经有多兴趣了很多兴趣的主题。已经开发了几种技术来比较两棵树。但是，严重缺乏指标来比较加权树。现有方法也不允许明确指定应执行比较的目标节点属性。此外，现有技术没有具体解决比较两种树集的问题。本文试图通过首先提出可以标记或不标记的两个有限的根有序树的比较和相似性来解决这些问题，这是可以标记的，以及加权或未加权。为了实现这一目标，隐藏的马尔可夫模型与每个针对每个目标节点属性的每个树集关联。与目标节点属性的树集T相关联的模型属性P会学习T验证属性p中树的节点。最终将产生的模型与两组树之间的距离和相似性进行了比较。然后将先前的措施推广用于对未加速和无序树木的比较。在名为FirstLast-L和FirstLast-LW的两个合成数据库上进行平面分类实验。它们都包含四个类100个rooted有序树，其特定和非普通节点属性明确定义。当本文提出的距离选择为最近邻分类的度量时，为这两个数据库获得了100％的完美精度。对于FirstLast-L选择广泛的树编辑距离时，这种性能高于所展示的精度的41％。

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