Glimmer: Multilevel MDS on the GPU

Abstract

Abstract-We present Glimmer, a new multilevel algorithm for multidimensional scaling designed to exploit modern graphics processing unit (GPU) hardware. We also present GPU-SF, a parallel, force-based subsystem used by Glimmer. Glimmer organizes input into a hierarchy of levels and recursively applies GPU-SF to combine and refine the levels. The multilevel nature of the algorithm makes local minima less likely while the GPU parallelism improves speed of computation. We propose a robust termination condition for GPU-SF based on a filtered approximation of the normalized stress function. We demonstrate the benefits of Glimmer in terms of speed, normalized stress, and visual quality against several previous algorithms for a range of synthetic and real benchmark datasets. We also show that the performance of Glimmer on GPUs is substantially faster than a CPU implementation of the same algorithm.

LoCH: A neighborhood-based multidimensional projection technique for high-dimensional sparse spaces

“…More recent global techniques include Part-Linear Multidimensional Projection (PLMP) [15] and Glimmer [16]. Similarly to LMDS and Pekalska's approach, PLMP initially projects a small sample of instances on the transformed space, then it employs this information to compute a linear transformation that, applied to the original space, obtains the transformed space.…”

Multidimensional Scaling by Deterministic Annealing with Iterative Majorization Algorithm

“…Recently, Ingram et al introduced a multilevel algorithm called Glimmer [22] which is based on force-based MDS algorithm with restriction, relaxation, and interpolation operators. Glimmer shows less sensitivity to initial configurations than GPU-SF subsystem, which is used in Glimmer [22], due to the multilevel nature.…”

“…Glimmer shows less sensitivity to initial configurations than GPU-SF subsystem, which is used in Glimmer [22], due to the multilevel nature. In Glimmer's paper [22], however, SMA-COF algorithm shows better mapping quality than Glimmer. Also, the main purpose of Glimmer is to achieve speed up with less cost of quality degrade rather than mapping quality improvement.…”

Scattering Points in Parallel Coordinates

“…Ingram et al proposed a multi-level GPU MDS algorithm [23] based on a parallel force-based subsystem simulation. Their approach organizes datasets into a hierarchy of levels, and recursively constructs an MDS configuration.…”