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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.

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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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Comparison of distances with respect to number of contraction mutations.
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Figure 28: Comparison of distances with respect to number of contraction mutations.

Mentions: To analyse the results, let us see the distances counted with respect to the contraction operation (Figure 28). All distances have similar linear dynamics and might have been simply scaled to behave identically on these data. It can be seen that all distances that have a cost of contraction equal to 1, are identical. NFC(2,1) was not identical but very similar, so it is illustrated with the same line. Those distances with a cost of c = 1 and NFC(2,1) scale the most naturally as the distance is simply equal to the number of mutations, the distance is directly proportional to the number of mutations with k = 1. Increasing the cost of contraction makes the edit distances increase quickly.


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)

Comparison of distances with respect to number of contraction mutations.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 28: Comparison of distances with respect to number of contraction mutations.
Mentions: To analyse the results, let us see the distances counted with respect to the contraction operation (Figure 28). All distances have similar linear dynamics and might have been simply scaled to behave identically on these data. It can be seen that all distances that have a cost of contraction equal to 1, are identical. NFC(2,1) was not identical but very similar, so it is illustrated with the same line. Those distances with a cost of c = 1 and NFC(2,1) scale the most naturally as the distance is simply equal to the number of mutations, the distance is directly proportional to the number of mutations with k = 1. Increasing the cost of contraction makes the edit distances increase quickly.

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