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Dual geometries of high-dimensional data sets

This month we have Sarah Constantin presenting "Dual geometries of high-dimensional data sets".

Abstract:

When a dataset consists of many samples, each consisting of many features (for example, a database of questionnaire responses) there are two complementary ways to organize the structure of the dataset: similar samples are those whose features are similar, and related features are those which are shared between similar samples.  An iterative procedure, alternating between these dual geometries, simultaneously clusters both features and samples, in a robust fashion.  This method can compress, denoise, and organize large, high-dimensional datasets.  Relatedly, there's a duality between the geometry of a surface and the geometry of the Laplacian eigenfunctions on that surface, though there are many open problems surrounding the nature of that relationship.  This talk will be based on past work by Dr. Ronald Coifman and my in-progress research.

Bio:

Sarah Constantin is a PhD student in mathematics at Yale University.  Her research interests are in harmonic analysis with applications to machine learning.  She's published in Communications of Pure and Applied Analysis and presented at several conferences.  She received her BA from Princeton in 2010.

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  • archisman r.

    Missed the talk by a mile. But does this have any direct connection to diffusion wavelet type ideas? For example are the basis functions diffusion wavelets on the occurrance matrix?

    September 12, 2012

  • Pete S.

    Unfortunately, we had some issues with the audio this time. But it's posted here for anyone who's interested: http://dl.dropbox.com/u/11139096/g33ktalk%20mp3/Machine%20Learning_Dual%20_Geom.mp3

    August 22, 2012

  • John Z.

    Can not find audio there.

    August 19, 2012

    • drew b.

      it's there - http://g33ktalk.com/i...­ you'll see PODCAST halfway down on the left-hand side of the page and a play button - click the play button. try another browser (chrome, etc.) if not working properly in your browser of choice.

      August 19, 2012

  • cz_d

    Keep the good talks coming. Enjoyed it very much.

    August 18, 2012

  • A former member
    A former member

    Interesting ideas and I would be curious to see the results of more comprehensive research on the theory.

    August 17, 2012

  • Nick G.

    Awesome, Thank you Sarah :).

    August 17, 2012

  • Huascar

    No empirical validation or proof of the concept (compression, gene expression ... does it really work?). Totally derailed in analytical geometry. Poor presentation.

    August 17, 2012

  • A former member
    A former member

    How long do these usually last?

    August 14, 2012

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