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High Dimensionality

This resource explores advanced techniques for visualizing high-dimensional data, focusing on Chernoff Faces and Isomap. Chernoff Faces offer a unique method by representing multivariate data using facial features for intuitive interpretation. Isomap provides a global geometric framework for nonlinear dimensionality reduction, transforming high-dimensional data into two dimensions while preserving intrinsic geometry. The document discusses naive and faster spring models for optimizing point positioning, emphasizing efficiency through local neighborhood strategies. Suitable for researchers and enthusiasts in data visualization and dimensionality reduction fields.

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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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