Paper Info
Title
Sparse solution of nonnegative least squares problems with applications in the construction of probabilistic Boolean networks
Abstract
In this paper, we consider finding a sparse solution of nonnegative least squares problems with a linear equality constraint. We propose a projection-based gradient descent method for solving huge size constrained least squares problems. Traditional Newton-based methods require solving a linear system. However, when the matrix is huge, it is neither practical to store it nor possible to solve it in a reasonable time. We therefore propose a matrix-free iterative scheme for solving the minimizer of the captured problem. This iterative scheme can be explained as a projection-based gradient descent method. In each iteration, a projection operation is performed to ensure the solution is feasible. The projection operation is equivalent to a shrinkage operator, which can guarantee the sparseness of the solution obtained. We show that the objective function is decreasing. We then apply the proposed method to the inverse problem of constructing a probabilistic Boolean network. Numerical examples are then given to illustrate both the efficiency and effectiveness of our proposed method. Copyright (c) 2015 John Wiley & Sons, Ltd.
Year
DOI
Venue
2015
10.1002/nla.2001
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Keywords
Field
DocType
gradient decent method,least squares,projection,probabilistic Boolean networks (PBNs)
Least squares,Boolean network,Mathematical optimization,Gradient descent,Linear system,Matrix (mathematics),Algorithm,Operator (computer programming),Inverse problem,Probabilistic logic,Mathematics
Journal
Volume
Issue
ISSN
22.0
SP5.0
1070-5325
Citations 
PageRank 
References 
3
0.43
15
Authors
6
Name
Order
Citations
PageRank
You-Wei Wen135318.93
Man Wang230.43
Zhi-Ying Cao330.77
Xiaoqing Cheng4123.26
Wai-Ki Ching568378.66
Vassilios S. Vassiliadis618822.38