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An active set approach to the elastic-net and its applications in mass spectrometry

Abstract : This paper uses the framework of a Mass Spectrometry application to introduce a new method of peak picking as well as two active set methods for the minimization of the elastic-net-functional. The application of peak picking is essential in mass spectrometry and is often based on mean spectra. In contrast our procedure uses a set of spectra obtained from a basis learning method. Our procedure utilizes the well known l1-minimization and corresponding active set algorithms but comprises ill conditioned operators such that regularization is required. We show, that the elastic-net gives a natural justification for Tikhonov-Philipsregularization in the used algorithms. Therefore we introduce adaptions of known active set algorithms for l1-minimization to the elastic net. Furthermore, we emphasize the differences of the algorithms for `1 and the elastic-net in numerical examples.
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https://hal.inria.fr/inria-00369397
Contributor : Ist Rennes <>
Submitted on : Thursday, March 19, 2009 - 4:09:41 PM
Last modification on : Tuesday, February 13, 2018 - 4:24:03 PM
Long-term archiving on: : Friday, October 12, 2012 - 1:50:42 PM

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Theodore Alexandrov, Oliver Keszöcze, Dirk A. Lorenz, Stefan Schiffler, Klaus Steinhorst. An active set approach to the elastic-net and its applications in mass spectrometry. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Apr 2009, Saint Malo, France. ⟨inria-00369397⟩

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