1. Tighter Bounds for Random Projections of Manifolds


    Ken Clarkson
    IBM Almaden

  2. Overview

  3. Dimensionality Reduction

  4. Random projection

  5. From one point to many

  6. Random projection : why?

  7. From many to infinite

  8. (What's a `d`-manifold?)

  9. (When is the input to a program infinite?)

  10. "All `d`-manifolds are not the same"

  11. Measures of manifold complexity

  12. Measures of manifold complexity, II

  13. Manifold JL

  14. Why is this an improvement or interesting?

  15. Areas of proof: the rest of the talk

  16. `epsilon`-nets

  17. `epsilon`-nets and measures

  18. Getting to infinite

    (Very similar to [AHY], inspired by [IN])
  19. From drafting to embedding:
    applying the theorem

  20. From drafting to embedding: long chords

    `epsilon`-nets for long chords:
  21. From drafting to embedding: short chords

  22. From drafting to embedding: short chords, II


  23. Short chords, tangents, reach


  24. Tangent vectors `approx` short chords : planar curves

  25. Tangent vectors `approx` short chords:
    low-torsion curves

  26. Concluding Remarks


    Thank you for your attention
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