Convergence and Rate Analysis of Neural Networks for Sparse Approximation

We present an analysis of the Locally Competitive Algorithm (LCA), which is a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few nonzero coefficients). This class of problems plays a significant role in...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	IEEE transaction on neural networks and learning systems Ročník 23; číslo 9; s. 1377 - 1389
Hlavní autoři:	Balavoine, A., Romberg, J., Rozell, C. J.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.09.2012 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Artificial intelligence Computer science; control theory; systems Computer Simulation Connectionism. Neural networks Convergence Dictionaries Exact sciences and technology Exponential convergence global stability Least squares approximation locally competitive algorithm Lyapunov function Lyapunov methods Models, Statistical Neural networks Neural Networks (Computer) nonsmooth objective Optimization Pattern Recognition, Automated - methods Sample Size sparse approximation Studies Theoretical computing Hopfield neural nets Exponential convergence Dictionaries Competitiveness Global optimum global stability locally competitive algorithm Network management Neural network Function approximation Competitive algorithms Convergence speed nonsmooth objective, sparse approximation Convergence rate Signal processing Sparse representation Objective function Numerical convergence Hopfield model Lyapunov function
ISSN:	2162-237X, 2162-2388, 2162-2388
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Popis
Shrnutí:	We present an analysis of the Locally Competitive Algorithm (LCA), which is a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few nonzero coefficients). This class of problems plays a significant role in both theories of neural coding and applications in signal processing. However, the LCA lacks analysis of its convergence properties, and previous results on neural networks for nonsmooth optimization do not apply to the specifics of the LCA architecture. We show that the LCA has desirable convergence properties, such as stability and global convergence to the optimum of the objective function when it is unique. Under some mild conditions, the support of the solution is also proven to be reached in finite time. Furthermore, some restrictions on the problem specifics allow us to characterize the convergence rate of the system by showing that the LCA converges exponentially fast with an analytically bounded convergence rate. We support our analysis with several illustrative simulations.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 (aurele.balavoine@gatech.edu; jrom@ece.gatech.edu; crozell@gatech.edu).
ISSN:	2162-237X 2162-2388 2162-2388
DOI:	10.1109/TNNLS.2012.2202400