Convex Relaxations for Permutation Problems - Inria - Institut national de recherche en sciences et technologies du numérique
Conference Papers Year : 2013

Convex Relaxations for Permutation Problems

Abstract

Seriation seeks to reconstruct a linear order between variables using unsorted similarity information. It has direct applications in archeology and shotgun gene sequencing for example. We prove the equivalence between the seriation and the combinatorial 2-sum problem (a quadratic minimization problem over permutations) over a class of similarity matrices. The seriation problem can be solved exactly by a spectral algorithm in the noiseless case and we produce a convex relaxation for the 2-sum problem to improve the robustness of solutions in a noisy setting. This relaxation also allows us to impose additional structural constraints on the solution, to solve semi-supervised seriation problems. We present numerical experiments on archeological data, Markov chains and gene sequences.

Dates and versions

hal-00907528 , version 1 (21-11-2013)

Identifiers

Cite

Fajwel Fogel, Rodolphe Jenatton, Francis Bach, Alexandre d'Aspremont. Convex Relaxations for Permutation Problems. Neural Information Processing Systems (NIPS) 2013, Dec 2013, United States. http://nips.cc/Conferences/2013/Program/speaker-info.php?ID=12863. ⟨hal-00907528⟩
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