A hybrid layout algorithm for sub-quadratic multidimensional scaling

Abstract

Many clustering and layout techniques have been used for structuring and visualising complex data. This paper is inspired by a number of such contemporary techniques and presents a novel hybrid approach based upon stochastic sampling, interpolation and spring models. We use Chalmers' 1996 O(N/sup 2/) spring model as a benchmark when evaluating our technique, comparing layout quality and run times using data sets of synthetic and real data. Our algorithm runs in O(N/spl radic/N) and executes significantly faster than Chalmers' 1996 algorithm, whilst producing superior layouts. In reducing complexity and run time, we allow the visualisation of data sets of previously infeasible size. Our results indicate that our method is a solid foundation for interactive and visual exploration of data.