Fast Multidimensional Scaling using Vector Extrapolation

Multidimensional scaling (MDS) is a class of methods used to find a low-dimensional representation of a set of points given a matrix of pairwise distances between them. Problems of this kind arise in various applications, from dimensionality reduction of image manifolds to psychology and statistics. In many of these applications, efficient and accurate solution of an MDS problem is required. In this paper, we propose using vector extrapolation techniques to accelerate the numerical solution of MDS problems. Vector extrapolation is used to accelerate the convergence of fixed-point iterative algorithms. We review the problem of multidimensional scaling and vector extrapolation techniques, and show several examples of our accelerated solver for multidimensional scaling problems in various applications.