Neural Comput - Alternating proximal regularized dictionary learning.

Tópicos

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Resumo

We present an algorithm for dictionary learning that is based on the alternating proximal algorithm studied by Attouch, Bolte, Redont, and Soubeyran (2010), coupled with a reliable and efficient dual algorithm for computation of the related proximity operators. This algorithm is suitable for a general dictionary learning model composed of a Bregman-type data fit term that accounts for the goodness of the representation and several convex penalization terms on the coefficients and atoms, explaining the prior knowledge at hand. As Attouch et al. recently proved, an alternating proximal scheme ensures better convergence properties than the simpler alternating minimization. We take care of the issue of inexactness in the computation of the involved proximity operators, giving a sound stopping criterion for the dual inner algorithm, which keeps under control the related errors, unavoidable for such a complex penalty terms, providing ultimately an overall effective procedure. Thanks to the generality of the proposed framework, we give an application in the context of genome-wide data understanding, revising the model proposed by Nowak, Hastie, Pollack, and Tibshirani (2011). The aim is to extract latent features (atoms) and perform segmentation on array-based comparative genomic hybridization (aCGH) data. We improve several important aspects that increase the quality and interpretability of the results. We show the effectiveness of the proposed model with two experiments on synthetic data, which highlight the enhancements over the original model.

Resumo Limpo

present algorithm dictionari learn base altern proxim algorithm studi attouch bolt redont soubeyran coupl reliabl effici dual algorithm comput relat proxim oper algorithm suitabl general dictionari learn model compos bregmantyp data fit term account good represent sever convex penal term coeffici atom explain prior knowledg hand attouch et al recent prove altern proxim scheme ensur better converg properti simpler altern minim take care issu inexact comput involv proxim oper give sound stop criterion dual inner algorithm keep control relat error unavoid complex penalti term provid ultim overal effect procedur thank general propos framework give applic context genomewid data understand revis model propos nowak hasti pollack tibshirani aim extract latent featur atom perform segment arraybas compar genom hybrid acgh data improv sever import aspect increas qualiti interpret result show effect propos model two experi synthet data highlight enhanc origin model

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