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Fodava Review Presentation

Fodava Review Presentation. Stanford Group G. Carlsson, L. Guibas. Mapper . Represents data by graphs rather than scatterplots or clusters Retains geometry, but is not too sensitive to it Geometric features yield interesting information about the data.

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Fodava Review Presentation

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  1. Fodava Review Presentation Stanford Group G. Carlsson, L. Guibas

  2. Mapper • Represents data by graphs rather than scatterplots or clusters • Retains geometry, but is not too sensitive to it • Geometric features yield interesting information about the data

  3. Mapper: Breast Cancer Example (Carlsson, Nicolau) t

  4. Mapper: RNA folding (Carlsson,Guibas, et al)

  5. Parametrization • How to get a tangible feel for features • Get maps to simpler spaces • Principal Components maps to linear spaces • Clustering maps to discrete spaces • Mapper maps to simplicial complexes • Could try to map to circles, trees, etc.

  6. Circular Coordinates • Homotopy classes of maps to circle are correspond to 1d cohomology • Hodge theory analogue gives a map (De Silva, Morozov, Vejdemo-Johansson)

  7. Circular Coordinates - Rotating Cube Example

  8. Heat Kernel Methods for Shape Analysis (Guibas et al) • Heat kernel attached to metric produces for each point of a shape a real value function on the real line. • Produces a faithful signature for the shape • Can be used to match shapes

  9. Heat Kernel Methods for Shape Analysis • Invariant under isometry • Finds features

  10. New Directions • Critical problem: compare shapes of data, find mappings • Related to Data Fusion • Need to develop “functorial” methods for study of data • Will make clear relationships among subsets of data, different data sets.

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