Robust Seriation and Applications to Cancer Genomics

Abstract : The seriation problem seeks to reorder a set of elements given pairwise similarity information, so that elements with higher similarity are closer in the resulting sequence. When a global ordering consistent with the similarity information exists, an exact spectral solution recovers it in the noiseless case and seriation is equivalent to the combinatorial 2-SUM problem over permutations, for which several relaxations have been derived. However, in applications such as DNA assembly, similarity values are often heavily corrupted, and the solution of 2-SUM may no longer yield an approximate serial structure on the elements. We introduce the robust seriation problem and show that it is equivalent to a modified 2-SUM problem for a class of similarity matrices modeling those observed in DNA assembly. We explore several relaxations of this modified 2-SUM problem and compare them empirically on both synthetic matrices and real DNA data. We then introduce the problem of seriation with duplications, which is a generalization of Seriation motivated by applications to cancer genome reconstruction. We propose an algorithm involving robust seriation to solve it, and present preliminary results on synthetic data sets.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01851960
Contributeur : Antoine Recanati <>
Soumis le : mardi 31 juillet 2018 - 12:47:48
Dernière modification le : mercredi 6 février 2019 - 10:20:48

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  • HAL Id : hal-01851960, version 1
  • ARXIV : 1806.00664

Citation

Antoine Recanati, Nicolas Servant, Jean-Philippe Vert, Alexandre D'Aspremont. Robust Seriation and Applications to Cancer Genomics. 2018. 〈hal-01851960〉

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