  Multidimensional scaling (MDS) is a popular dimensionality reduction
techniques that has been widely used for network visualization and cooperative
localization. However, the traditional stress minimization formulation of MDS
necessitates the use of batch optimization algorithms that are not scalable to
large-sized problems. This paper considers an alternative stochastic stress
minimization framework that is amenable to incremental and distributed
solutions. A novel linear-complexity stochastic optimization algorithm is
proposed that is provably convergent and simple to implement. The applicability
of the proposed algorithm to localization and visualization tasks is also
expounded. Extensive tests on synthetic and real datasets demonstrate the
efficacy of the proposed algorithm.
