Tree edit distance for leaf-labelled trees on free leafset and its comparison with frequent subsplit dissimilarity and popular distance measures.
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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.
Affiliation: Institute of Computer Science, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland. j.koperwas@elka.pw.edu.pl
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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. Related in: MedlinePlus |
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Mentions: In this experiment trees with at most 8 leaves were generated. Both binary and unconstrained versions will be discussed together as the differences are only with the R-F distance. Characteristics of R-F distribution in this experiment does not recall typical R-F distribution. The main reason is that it is unsuitable for comparing trees with different leafsets as it will always return the maximum value, which will also be dependent on the number of leaves of the trees. Therefore the distribution reflects the conditional probability of selecting two trees with the same leafset(left part of graph) and trees with different leafsets (right part of graph) of Figure 24 (binary) and Figure 25 (unconstrained). As for the other distances, both E(3,1) and FS behave similarly, having a wide range of values, while E(3,1) is more regular (see Figure 26). Both E(3,1) (Figure 22) and FS (Figure 23) look better than MAST and F-S as they take more values E(3,1) - 24, FS - 27 versus R-F - 8 and MAST - 4, which make them more discriminative. |
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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
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.