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Keywords = rank-deficient quadratic cost

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18 pages, 751 KiB  
Article
Aiding Dictionary Learning Through Multi-Parametric Sparse Representation
by Florin Stoican and Paul Irofti
Algorithms 2019, 12(7), 131; https://doi.org/10.3390/a12070131 - 28 Jun 2019
Cited by 4 | Viewed by 4451
Abstract
The 1 relaxations of the sparse and cosparse representation problems which appear in the dictionary learning procedure are usually solved repeatedly (varying only the parameter vector), thus making them well-suited to a multi-parametric interpretation. The associated constrained optimization problems differ only through [...] Read more.
The 1 relaxations of the sparse and cosparse representation problems which appear in the dictionary learning procedure are usually solved repeatedly (varying only the parameter vector), thus making them well-suited to a multi-parametric interpretation. The associated constrained optimization problems differ only through an affine term from one iteration to the next (i.e., the problem’s structure remains the same while only the current vector, which is to be (co)sparsely represented, changes). We exploit this fact by providing an explicit, piecewise affine with a polyhedral support, representation of the solution. Consequently, at runtime, the optimal solution (the (co)sparse representation) is obtained through a simple enumeration throughout the non-overlapping regions of the polyhedral partition and the application of an affine law. We show that, for a suitably large number of parameter instances, the explicit approach outperforms the classical implementation. Full article
(This article belongs to the Special Issue Dictionary Learning Algorithms and Applications)
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