high performance computing on graphics processing units: hgpu.org

Multidimensional scaling (MDS) is a very popular and reliable method used in feature extraction and visualization of multidimensional data. The role of MDS is to reconstruct the topology of an original N-dimensional feature space consisting of M feature vectors in target 2-D (3-D) Euclidean space. It can be achieved by minimization of the error – "stress" function – F(||D-d||), where D and d are the MxM dissimilarity matrices in the original and in the target spaces, respectively. However, the stress function is in general a multimodal and multidimensional function for which the complexity of finding global minimum increases exponentially with the number of data. We employ here a robust heuristics based on discrete particle method enabling interactive visualization of data for various types of stress functions. Nevertheless, due to at least O(M^2) memory and time complexity, the method becomes computationally demanding when applied for interactive visualization of data sets involving M~10^4. We present here efficient parallel algorithms developed for various small and pre-medium computer architectures from single and multi-core processors to GPU and multiprocessor MPI clusters. The timings obtained show that the computational efficiency of CUDA implementation of MDS on a PC equipped with a strong GPU board (Tesla M2050 or GeForce 480) is two times greater than its MPI equivalent run on 10 nodes (10x 2xIntel Xeon X5670 = 120 threads) of a professional multiprocessor cluster (HP SL390). We show also that the hybridized two-level MPI/CUDA implementation run on a small cluster of GPU nodes can additionally provide a linear speed-up.