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High Dimensionality

High Dimensionality. Chernoff Faces. http://kspark.kaist.ac.kr/Human%20Engineering.files/Chernoff/Chernoff%20Faces.htm. Parallel coordinates. Dimensionality Reduction. Isomap: 4096 D to 2D [Tenenbaum 00]. [ Courtesy of Tamara Munzner ].

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High Dimensionality

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  1. High Dimensionality

  2. Chernoff Faces

  3. http://kspark.kaist.ac.kr/Human%20Engineering.files/Chernoff/Chernoff%20Faces.htmhttp://kspark.kaist.ac.kr/Human%20Engineering.files/Chernoff/Chernoff%20Faces.htm

  4. Parallel coordinates

  5. Dimensionality Reduction Isomap: 4096 D to 2D [Tenenbaum 00] [Courtesy of Tamara Munzner] [A Global Geometric Framework for Nonlinear Dimensionality Reduction. Tenenbaum, de Silva and Langford. Science 290 (5500): 2319-2323, 22 December 2000, isomap.stanford.edu]

  6. Naive Spring Model • repeat for all points • compute spring force to all other points • difference between high dim, low dim distance • move to better location using computed forces • compute distances between all points • O(n2) iteration, O(n3) algorithm [Courtesy of Tamara Munzner]

  7. Faster Spring Model [Chalmers 96] • compare distances only with a few points • maintain small local neighborhood set [Courtesy of Tamara Munzner]

  8. Faster Spring Model [Chalmers 96] • compare distances only with a few points • maintain small local neighborhood set • each time pick some randoms, swap in if closer [Courtesy of Tamara Munzner]

  9. Faster Spring Model [Chalmers 96] • compare distances only with a few points • maintain small local neighborhood set • each time pick some randoms, swap in if closer [Courtesy of Tamara Munzner]

  10. Faster Spring Model [Chalmers 96] • compare distances only with a few points • maintain small local neighborhood set • each time pick some randoms, swap in if closer • small constant: 6 locals, 3 randoms typical • O(n) iteration, O(n2) algorithm [Courtesy of Tamara Munzner]

  11. Dimensional Stacking

  12. [Matt Ward et al.]

  13. Pixel-oriented techniques [Keim and Kriegel, VisDB]

  14. [Yang et al. InfoVis 2003]

  15. [Yang et al. InfoVis 2003]

  16. [Yang et al. InfoVis 2003]

  17. [Yang et al. InfoVis 2003]

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