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.<\/p>\n","protected":false},"excerpt":{"rendered":"
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 – […]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[36,11,89,3],"tags":[1787,1782,14,348,242,278,20,671,374,409,554,1064,253,1015,379,931,134],"class_list":["post-8326","post","type-post","status-publish","format-standard","hentry","category-algorithms","category-computer-science","category-nvidia-cuda","category-paper","tag-algorithms","tag-computer-science","tag-cuda","tag-data-mining","tag-mpi","tag-multidimensional-scaling","tag-nvidia","tag-nvidia-geforce-8500-gt","tag-nvidia-geforce-8800-ultra","tag-nvidia-geforce-9500-gt","tag-nvidia-geforce-9800-gt","tag-nvidia-geforce-gt-330-m","tag-nvidia-geforce-gtx-260","tag-nvidia-geforce-gtx-460","tag-nvidia-geforce-gtx-480","tag-tesla-m2050","tag-visualization"],"views":2943,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/8326","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8326"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/8326\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}