Distributed Continuous and Discrete Time Projection Neurodynamic Approaches for Sparse Recovery

You Zhao, Xiaofeng Liao, Xing He

Abstract:

Sparse representation acts as a fundamental data
science methodology for solving a wide range of problems in
machine learning and engineering. In this paper, we respectively
propose novel distributed continuous-time and discrete-time projection neurodynamic approaches for sparse recovery by seeking
the minimum l1-norm solution with the undetermined linear measurement Ax = b in two cases over undirected networks. The
proposed approaches only require the communication network to
be undirected and connected, without the notion of central processing node, and no node visit the entire matrix A, so some privacy
preserving efficiencies are guaranteed based on our approaches.
First, for the one case that the rows of A are distributed, we
propose a distributed continuous-time projection neurodynamic
approach based on the projection operators and prove the global
convergence and optimality of it. Then, a corresponding distributed
discrete-time projection neurodynamic algorithm with a fixed step
size is also presented, and the convergence and the scope of values
of the step size of it are also analyzed. Second, for another case that
the columns of A are distributed, a distributed continuous-time
projection neurodynamic approach based on the projection operators and its derivative feedback is proposed and its global convergence is rigorously analyzed. Immediately following, we discuss its
corresponding distributed discrete-time projection neurodynamic
algorithm with a discrete version of the differential feedback term.
Finally, the effectiveness and superiority of the proposed neurodynamic method are verified by the experiments of sparse signal and
image reconstruction.