Multidimensional Shrinkage-Thresholding Operator and Group LASSO Penalties
| Autor: | Arnau Tibau Puig, Ami Wiesel, Gilles Fleury, Alfred O. Hero |
|---|---|
| Přispěvatelé: | Department of Electrical Engineering and Computer Science (EECS), University of Michigan [Ann Arbor], University of Michigan System-University of Michigan System, School of Computer Science and Engineering (The Hebreu University of Jerusalem), The Hebreu University of Jerusalem, Supélec Sciences des Systèmes (E3S), Ecole Supérieure d'Electricité - SUPELEC (FRANCE) |
| Rok vydání: | 2011 |
| Předmět: |
Mathematical optimization
Line search Applied Mathematics Scalar (mathematics) 020206 networking & telecommunications Feature selection 02 engineering and technology 01 natural sciences Thresholding Euclidean distance 010104 statistics & probability ComputingMethodologies_PATTERNRECOGNITION [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing Signal Processing Convex optimization 0202 electrical engineering electronic engineering information engineering Applied mathematics Quadratic programming 0101 mathematics Electrical and Electronic Engineering Convex function [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | IEEE Signal Processing Letters IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2011, 18 (6), pp.363-366. ⟨10.1109/LSP.2011.2139204⟩ |
| ISSN: | 1558-2361 1070-9908 |
| DOI: | 10.1109/lsp.2011.2139204 |
| Popis: | The scalar shrinkage-thresholding operator is a key ingredient in variable selection algorithms arising in wavelet denoising, JPEG2000 image compression and predictive analysis of gene microarray data. In these applications, the decision to select a scalar variable is given as the solution to a scalar sparsity penalized quadratic optimization. In some other applications, one seeks to select multidimensional variables. In this work, we present a natural multidimensional extension of the scalar shrinkage thresholding operator. Similarly to the scalar case, the threshold is determined by the minimization of a convex quadratic form plus an Euclidean norm penalty, however, here the optimization is performed over a domain of dimension N ≥ 1. The solution to this convex optimization problem is called the multidimensional shrinkage threshold operator (MSTO). The MSTO reduces to the scalar case in the special case of N=1. In the general case of N >; 1 the optimal MSTO shrinkage can be found through a simple convex line search. We give an efficient algorithm for solving this line search and show that our method to evaluate the MSTO outperforms other state-of-the art optimization approaches. We present several illustrative applications of the MSTO in the context of Group LASSO penalized estimation. |
| Databáze: | OpenAIRE |
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