A Tree-to-Tree Distance and Its Application to Cluster Analysis

Lu, Shin-Yee

doi:10.1109/tpami.1979.6786615

Cited by 95 publications

(32 citation statements)

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“…The tree edit distance computation for unordered trees is NP-complete [Zhang89]. Polynomial-time algorithms [Zhang89,Demaine07,Touzet03,Bille05,Klein98,Lu79,Wang94] only exist for ordered trees. As for classification or clustering hierarchies, there is no specific order among siblings.…”

Section: Introductionmentioning

confidence: 99%

Split-Order Distance for Clustering and Classification Hierarchies

Zhang

Liu

Sarkar

et al. 2009

Lecture Notes in Computer Science

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Abstract. Clustering and classification hierarchies are organizational structures of a set of objects. Multiple hierarchies may be derived over the same set of objects, which makes distance computation between hierarchies an important task for summarization and similarity search of hierarchical patterns. In this paper, we model the classification and clustering hierarchies as rooted, leaf-labeled, unordered trees. We propose a novel distance metric Split-Order distance to evaluate the organizational structure difference between two hierarchies over the same set of leaf objects. The Split-Order distance reflects the order in which subsets of the tree leaves are differentiated from each other and can be used to explain the relationships between the leaf objects. We also propose an efficient algorithm for computing Split-Order distance between two trees in O(n 2 d 4 ) time, where n is the number of leaves, and d is the maximum number of children of any node. Our experiments on both real and synthetic data demonstrate the efficiency and effectiveness of our algorithm.

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Section: Introductionmentioning

confidence: 99%

Split-Order Distance for Clustering and Classification Hierarchies

Zhang

Liu

Sarkar

et al. 2009

Lecture Notes in Computer Science

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“…In the early seventies, Wagner and Fisher [42] presented an algorithm which computes the distance between two strings of characters as the minimum cost sequence of elementary operations needed to transform one string into the other. In order to define a distance between rooted tree graphs, Tai [37], Selkow [32] and Lu [24] proposed a generalization of the Wagner and Fisher algorithm with application in different fields [27,28,32]. All the tree graphs discussed in these papers are ordered, meaning that the sets of sons of any vertex are ordered sets.…”

Section: Plant Comparison Methodsmentioning

confidence: 99%

A distance measure between plant architectures

Ferraro

Godin

2000

Ann. For. Sci.

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“…The distance between T 1 and T 2 is then defined to be the cost of such a sequence. Many approaches generalizing string edit distance to trees have been proposed (Lu, 1979;Selkow, 1977;Tai, 1979;Tanaka & Tanaka, 1988) and the best known result for ordered trees is by Zhang and Shasha (1989). Given two ordered trees T 1 and T 2 , their algorithm finds an optimal edit script in time O(|T 1 | × |T 2 | × min{depth(T 1 ), leaves(T 1 )} × min{depth(T 2 ), leaves(T 2 )}), where |T| denotes the number of nodes in a tree T, depth(T) denotes the depth of a tree T, and leaves(T) denotes the number of leaves of a tree T. Edit distance for unordered trees has been investigated by Zhang, Statman, and Shasha (1992).…”

Section: Related Workmentioning

confidence: 99%

Measuring the structural similarity among XML documents and DTDs

2007

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Measuring the structural similarity between an XML document and a DTD has many relevant applications that range from document classification and approximate structural queries on XML documents to selective dissemination of XML documents and document protection. The problem is harder than measuring structural similarity among documents, because a DTD can be considered as a generator of documents. Thus, the problem is to evaluate the similarity between a document and a set of documents. An effective structural similarity measure should face different requirements that range from considering the presence and absence of required elements, as well as the structure and level of the missing and extra elements to vocabulary discrepancies due to the use of synonymous or syntactically similar tags. In the paper, starting from these requirements, we provide a definition of the measure and present an algorithm for matching a document against a DTD to obtain their structural similarity. Finally, experimental results to assess the effectiveness of the approach are presented.

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A Tree-to-Tree Distance and Its Application to Cluster Analysis

Cited by 95 publications

References 0 publications

Split-Order Distance for Clustering and Classification Hierarchies

Split-Order Distance for Clustering and Classification Hierarchies

A distance measure between plant architectures

Measuring the structural similarity among XML documents and DTDs

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