A Local Block Coordinate Descent Algorithm for the CSC Model

2019 ◽  
Author(s):  
Ev Zisselman ◽  
Jeremias Sulam ◽  
Michael Elad
Keyword(s):  
Coordinate Descent ◽  
Block Coordinate Descent ◽  
Descent Algorithm ◽  
Coordinate Descent Algorithm ◽  
Local Block

scholarly journals Convergence of Slice-Based Block Coordinate Descent Algorithm for Convolutional Sparse Coding

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jing Li ◽  
Hui Yu ◽  
Xiao Wei ◽  
Jinjia Wang
Keyword(s):  
Sparse Coding ◽  
Convergence Theorem ◽  
Optimal Solution ◽  
Global Optimum ◽  
Coordinate Descent ◽  
Basis Pursuit ◽  
Block Coordinate Descent ◽  
Coordinate Descent Algorithm ◽  
Original Domain ◽  
Local Block

Convolutional sparse coding (CSC) models are becoming increasingly popular in the signal and image processing communities in recent years. Several research studies have addressed the basis pursuit (BP) problem of the CSC model, including the recently proposed local block coordinate descent (LoBCoD) algorithm. This algorithm adopts slice-based local processing ideas and splits the global sparse vector into local vector needles that are locally computed in the original domain to obtain the encoding. However, a convergence theorem for the LoBCoD algorithm has not been given previously. This paper presents a convergence theorem for the LoBCoD algorithm which proves that the LoBCoD algorithm will converge to its global optimum at a rate of O1/k. A slice-based multilayer local block coordinate descent (ML-LoBCoD) algorithm is proposed which is motivated by the multilayer basis pursuit (ML-BP) problem and the LoBCoD algorithm. We prove that the ML-LoBCoD algorithm is guaranteed to converge to the optimal solution at a rate O1/k. Preliminary numerical experiments demonstrate the better performance of the proposed ML-LoBCoD algorithm compared to the LoBCoD algorithm for the BP problem, and the loss function value is also lower for ML-LoBCoD than LoBCoD.

scholarly journals The Sparse Group Log Ridge for the Selection of Variable Groups

2021 ◽  
Vol 2078 (1) ◽  
pp. 012012
Author(s):  
Song Yao ◽  
Lipeng Cui ◽  
Sining Ma
Keyword(s):  
Artificial Intelligence ◽  
Group Structure ◽  
Coordinate Descent ◽  
Block Coordinate Descent ◽  
Descent Algorithm ◽  
Mm Algorithm ◽  
Sparse Model ◽  
Coordinate Descent Algorithm ◽  
Variables Selection ◽  
Selection Of

Abstract In recent years, the sparse model is a research hotspot in the field of artificial intelligence. Since the Lasso model ignores the group structure among variables, and can only achieve the selection of scattered variables. Besides, Group Lasso can only select groups of variables. To address this problem, the Sparse Group Log Ridge model is proposed, which can select both groups of variables and variables in one group. Then the MM algorithm combined with the block coordinate descent algorithm can be used for solving. Finally, the advantages of the model in terms of variables selection and prediction are shown through the experiment.

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