Stochastic Multidimensional Scaling
This work addresses the problem of scaling MDS for large-sized problems in network visualization and cooperative localization, offering an incremental and distributed solution.
The paper tackled the scalability issue of traditional multidimensional scaling (MDS) by proposing a stochastic stress minimization framework, resulting in a linear-complexity algorithm that is provably convergent and effective in tests on synthetic and real datasets.
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.