A hybrid layout algorithm for sub-quadratic multidimensional scaling

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(N²) 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√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.