Data-Dependent Geometries and Structures: Analyses and Algorithms for Machine Learning

Data-Dependent Geometries and Structures : Analyses and Algorithms for Machine Learning Page 1 Data-Dependent Geometries and Structures : Analyses and Algorithms for Machine Learning Mark Herbster, Guy Lever, John Shawe-Taylor University College London m.herbster@cs.ucl.ac.uk g.lever@cs.ucl.ac.uk jst@cs.ucl.ac.uk Claudio Gentile, Fabio Vitale Universita’ dell’Insubria, Varese claudio.gentile@uninsubria.it, fabiovdk@yahoo.com Nello Cristianini University of Bristol nello.cristianini@gmail.com 29th March 2012 Page 2 Data Dependent Geometry What is a “data-dependent geometry”? Standard paradigm A dataset is sampled from a space with a given geometry the “distances” between particular points is independent of the sample Data-dependent paradigm A dataset is sampled from a space with an unknown geometry Hence the “distances” between particular points is dependent on the sample …