Analytic Organization of High Himensional observational Databases as a tool for learning and inference

Tuesday, September 27, 2011 - 4:30pm - 5:30pm
Keller 3-180
Ronald Coifman (Yale University)
We describe a mathematical framework for dimensional reduction, learning and organization of databases . The database could be a matrix of a linear transformation for which the goal is to reorganize the matrix so as to achieve compression and fast algorithms. Or the database could be a collection of documents and their vocabulary, an array of sensor measurements such as EEG , or financial a time series or segments of recorded music. If we view the database as a questionnaire , we organize the population into a contextual demographic diffusion geometry and the questions into a conceptual geometry, this is an iterative process in which each organization informs the other, with the goal of entropy reduction of the whole data base.

This organization being totally data agnostic applies to the other examples thereby generating automatically a data driven conceptual /contextual pairing.We will describe the basic underlying tools from Harmonic Analysis for measuring success in extracting structure , tools which enable functional regression prediction and basically signal processing methodologies.
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