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2,297 bytes added ,  12:35, 22 June 2015
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*GATK v3.1-1-g07a4bf8
 
*GATK v3.1-1-g07a4bf8
 
*vt normalize v0.5
 
*vt normalize v0.5
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= Here is an example where this normalization algorithm fails =
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We distinguish the concepts of normalization and decomposition/reconstruction of variants as follows:
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Normalization involves reducing representations of a variant to a canonical representation. Normalization can be applied to biallelic variants or multiallelic variants. The problem of normalization is solvable and there exists a unique representation that is left aligned and parsimonious. Mathematical proof is published. [http://bioinformatics.oxfordjournals.org/content/early/2015/03/22/bioinformatics.btv112]
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Decomposition of variants involves the breaking down of a variant record into multiple records. It may be done vertically - as in multiallelics becoming biallelics or it can be done horizontally - a cluster of indels and SNPs represented as a complex variant being splitted up into several records. Horizontal decompositions in general do not have a unique solution.  Similarly, reconstruction combines several variant records into a single record and can be done vertically and horizontally too. Vertical decomposition of a multiallelic variant to a set of biallelic records is a many to one function.  Construction of a set of biallelic variants into a multiallelic record is not unique as you need to considered all possible permutations of the haplotypes containing your alleles. 
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If your example contains the decomposition or reconstruction of variants, then it is probable that you can find inconsistencies. 
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It is important to distinguish the difference between normalization and decomposition/reconstruction.  The notion of normalization implies that a variant can be reduced to a standardized form.  If you were to include decomposition and reconstruction in your notion of normalization, you are  bound to find inconsistencies simply due to the inherent issues of identifiability. 
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When performing decomposition and construction, I think the following factors should be considered:
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* Are your variants describing just a single individual or a population?
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* Are the genotypes (if any) in your individual(s) phased?
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Depending on the context, you will obtain different answers.
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[https://github.com/atks/vt/issues/16 An example of inconsistent variant representation due to using vt normalize]
    
= Citation =
 
= Citation =
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