Dimensionality Reduction via Euclidean Distance Embeddings
2011 (English)Report (Other academic)
This report provides a mathematically thorough review and investigation of Metric Multidimensional scaling (MDS) through the analysis of Euclidean distances in input and output spaces. By combining a geometric approach with modern linear algebra and multivariate analysis, Metric MDS is viewed as a Euclidean distance embedding transformation that converts between coordinate and coordinate-free representations of data. In this work we link Mercer kernel functions, data in infinite-dimensional Hilbert space and coordinate-free distance metrics to a finite-dimensional Euclidean representation. We further set a foundation for a principled treatment of non-linear extensions of MDS as optimization programs on kernel matrices and Euclidean distances.
Place, publisher, year, edition, pages
Stockholm, Sweden: KTH Royal Institute of Technology, CAS/CVAP , 2011. , 20 p.
, TRITA-CSC-CV, 2011:2 CVAP320
Computer Vision and Robotics (Autonomous Systems)
IdentifiersURN: urn:nbn:se:kth:diva-40629OAI: oai:DiVA.org:kth-40629DiVA: diva2:441924
FunderICT - The Next Generation
QC 201110032011-10-032011-09-192011-10-26Bibliographically approved