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Tree edit distance for leaf-labelled trees on free leafset and its comparison with frequent subsplit dissimilarity and popular distance measures.

Koperwas J, Walczak K - BMC Bioinformatics (2011)

Bottom Line: Two of the presented methods carry the most interesting properties.E(3,1) is very discriminative (having a wide range of values) and has a very regular distance distribution which is similar to a normal distribution in its shape and is good both for similar and non-similar trees.NFC(2,1) on the other hand is proportional or nearly proportional to the number of mutation operations used, irrespective of their type.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Computer Science, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland. j.koperwas@elka.pw.edu.pl

ABSTRACT

Background: This paper is devoted to distance measures for leaf-labelled trees on free leafset. A leaf-labelled tree is a data structure which is a special type of a tree where only leaves (terminal) nodes are labelled. This data structure is used in bioinformatics for modelling of evolution history of genes and species and also in linguistics for modelling of languages evolution history. Many domain specific problems occur and need to be solved with help of tree postprocessing techniques such as distance measures.

Results: Here we introduce the tree edit distance designed for leaf labelled trees on free leafset, which occurs to be a metric. It is presented together with tree edit consensus tree notion. We provide statistical evaluation of provided measure with respect to R-F, MAST and frequent subsplit based dissimilarity measures as the reference measures.

Conclusions: The tree edit distance was proven to be a metric and has the advantage of using different costs for contraction and pruning, therefore their properties can be tuned depending on the needs of the user. Two of the presented methods carry the most interesting properties. E(3,1) is very discriminative (having a wide range of values) and has a very regular distance distribution which is similar to a normal distribution in its shape and is good both for similar and non-similar trees. NFC(2,1) on the other hand is proportional or nearly proportional to the number of mutation operations used, irrespective of their type.

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Edit-consensus tree. Trees T1 and T2 together with their edit-consensus tree TCe.
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Figure 12: Edit-consensus tree. Trees T1 and T2 together with their edit-consensus tree TCe.

Mentions: 2) The second drawback of the R-F distance is that even if the trees are on the same leafset, one noisy leaf may cause the trees to be considered totally different (all splits must be removed). Removal of one leaf may significantly reduce the distance between trees. Such a situation is illustrated in Figure 12. Trees T1 and T2 look totally different, in terms of the R-F distance, because of leaf d, thus all non-trivial splits must be removed (all the information!) in order to make them identical. R-F Distance = 10, however, removing only leaf d would result in trees differing by only 2 splits! Therefore, the MAST distance equals 2 and the Edit Distance equals 6.


Tree edit distance for leaf-labelled trees on free leafset and its comparison with frequent subsplit dissimilarity and popular distance measures.

Koperwas J, Walczak K - BMC Bioinformatics (2011)

Edit-consensus tree. Trees T1 and T2 together with their edit-consensus tree TCe.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3117735&req=5

Figure 12: Edit-consensus tree. Trees T1 and T2 together with their edit-consensus tree TCe.
Mentions: 2) The second drawback of the R-F distance is that even if the trees are on the same leafset, one noisy leaf may cause the trees to be considered totally different (all splits must be removed). Removal of one leaf may significantly reduce the distance between trees. Such a situation is illustrated in Figure 12. Trees T1 and T2 look totally different, in terms of the R-F distance, because of leaf d, thus all non-trivial splits must be removed (all the information!) in order to make them identical. R-F Distance = 10, however, removing only leaf d would result in trees differing by only 2 splits! Therefore, the MAST distance equals 2 and the Edit Distance equals 6.

Bottom Line: Two of the presented methods carry the most interesting properties.E(3,1) is very discriminative (having a wide range of values) and has a very regular distance distribution which is similar to a normal distribution in its shape and is good both for similar and non-similar trees.NFC(2,1) on the other hand is proportional or nearly proportional to the number of mutation operations used, irrespective of their type.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of Computer Science, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland. j.koperwas@elka.pw.edu.pl

ABSTRACT

Background: This paper is devoted to distance measures for leaf-labelled trees on free leafset. A leaf-labelled tree is a data structure which is a special type of a tree where only leaves (terminal) nodes are labelled. This data structure is used in bioinformatics for modelling of evolution history of genes and species and also in linguistics for modelling of languages evolution history. Many domain specific problems occur and need to be solved with help of tree postprocessing techniques such as distance measures.

Results: Here we introduce the tree edit distance designed for leaf labelled trees on free leafset, which occurs to be a metric. It is presented together with tree edit consensus tree notion. We provide statistical evaluation of provided measure with respect to R-F, MAST and frequent subsplit based dissimilarity measures as the reference measures.

Conclusions: The tree edit distance was proven to be a metric and has the advantage of using different costs for contraction and pruning, therefore their properties can be tuned depending on the needs of the user. Two of the presented methods carry the most interesting properties. E(3,1) is very discriminative (having a wide range of values) and has a very regular distance distribution which is similar to a normal distribution in its shape and is good both for similar and non-similar trees. NFC(2,1) on the other hand is proportional or nearly proportional to the number of mutation operations used, irrespective of their type.

Show MeSH
Related in: MedlinePlus