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Sparse solution of nonnegative least squares problems with applications in the construction of probabilistic Boolean networks
Author(s) -
Wen YouWei,
Wang Man,
Cao Zhiying,
Cheng Xiaoqing,
Ching WaiKi,
Vassiliadis Vassilios S.
Publication year - 2015
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2001
Subject(s) - mathematics , gradient descent , projection (relational algebra) , iterative method , constraint (computer aided design) , mathematical optimization , least squares function approximation , probabilistic logic , algorithm , matrix (chemical analysis) , non linear least squares , computer science , estimation theory , artificial neural network , artificial intelligence , statistics , materials science , geometry , estimator , composite material
Summary 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 © 2015 John Wiley & Sons, Ltd.