Title :
The atomic norm formulation of OSCAR regularization with application to the Frank-Wolfe algorithm
Author :
Zeng, Xuan ; Figueiredo, Mario A. T.
Author_Institution :
Inst. de Telecomun., Inst. Super. Tecnico, Lisbon, Portugal
Abstract :
This paper proposes atomic norm formulation of octagonal shrinkage and clustering algorithm for regression (OSCAR) regularization. The OSCAR regularizer can be reformulated using a decreasing weighted sorted ℓ1 (DWSL1) norm (which is shown to be convex). We also show how, by exploiting an atomic norm formulation, the Ivanov regularization scheme involving the OSCAR regularizer can be handled using the Frank-Wolfe (also known as conditional gradient) method.
Keywords :
compressed sensing; gradient methods; pattern clustering; regression analysis; DWSL1 norm; Frank-Wolfe method; Ivanov regularization scheme; OSCAR regularization; atomic norm formulation; conditional gradient method; decreasing weighted sorted ℓ1 norm; octagonal shrinkage and clustering algorithm for regression; Algorithm design and analysis; Bismuth; Clustering algorithms; Convex functions; Gradient methods; Signal processing algorithms; Vectors; Frank-Wolfe algorithm; Group sparsity; Ivanov regularization; atomic norm; conditional gradient method;
Conference_Titel :
Signal Processing Conference (EUSIPCO), 2014 Proceedings of the 22nd European
Conference_Location :
Lisbon
