Stochastic Multidimensional Scaling

TL;DR

This paper introduces a scalable stochastic optimization algorithm for multidimensional scaling, enabling efficient network visualization and localization with provable convergence and applicability to large datasets.

Contribution

A novel linear-complexity stochastic MDS algorithm that is incremental, distributed, and provably convergent, improving scalability over traditional methods.

Findings

Algorithm is effective on synthetic datasets.

Algorithm performs well on real-world datasets.

Demonstrates scalability and convergence.

Abstract

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.