Universal multi-dimensional scaling

In this paper, we propose a unified algorithmic framework for solving many known variants of MDS. Our algorithm is a simple iterative scheme with guaranteed convergence, and is modular; by changing the internals of a single subroutine in the algorithm, we can switch cost functions and target spaces easily. In addition to the formal guarantees of convergence, our algorithms are accurate; in most cases, they converge to better quality solutions than existing methods in comparable time. Moreover, they have a small memory footprint and scale effectively for large data sets. We expect that this framework will be useful for a number of MDS variants that have not yet been studied. Our framework extends to embedding high-dimensional points lying on a sphere to points on a lower dimensional sphere, preserving geodesic distances. As a complement to this result, we also extend the Johnson-Lindenstrauss Lemma to this spherical setting, by showing that projecting to a random O((1/ 2 )log n)dimens...

• Type: Conference
• Year: 2010
• Where: KDD
• Authors: Arvind Agarwal, Jeff M. Phillips, Suresh Venkatasubramanian
• Keywords: Algorithms, Data Mining, Geodesic Distances, KDD 2010, Unified Algorithmic Framework