Enhancing multidimensional scaling through a distributed algorithm

Classic multidimensional scaling (MDS) and scaling by majorizing a complex function (SMACOF) are well-known centralized algorithms that are used to solve MDS problem. In this paper, we present a distributed algorithm for solving MDS problem. Estimations of coordinates are performed concurrently under the assumption that each item knows only its own position and its distances from its neighbors and their approximated present locations. The update process is done by calculating the average of the current coordinate of each object and its projections on the solution spaces allocated to it by its neighbors. We apply the method to the problem of sensor localization and obtain numerical results that demonstrate the efficacy of our suggested strategy.