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DD HDS ： A Method for Visualization and Exploration of High-Dimensional Data

Learn about DD-HDS, a nonlinear dimensionality reduction method designed for high-dimensional data visualization. This method incorporates a weighting of distances and ensures symmetry between the original and output spaces. Discover its advantages, disadvantages, and applications in visualization clustering.

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DD HDS ： A Method for Visualization and Exploration of High-Dimensional Data

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  1. DD HDS：A Method for Visualization and Exploration of High-Dimensional Data Author: Sylvain Lespinats, Michel Verleysen, Senior Member, IEEE, Alain Giron, and Bernard Fertil Reporter: Wen-Cheng Tsai 2007/11/28 TNN , 2007

  2. Outline • Motivation • Objective • Method • data-driven high-dimensional scaling(DD-HDS) • Experiments • Conclusions • Comments

  3. Motivation • High-dimensional data raise unusual problems of analysis, given that some properties of the space they live in cannot be extrpolated from our common experience. • Euclidean distance in high-dimensional space is much more difficult to discriminate between small and large distances in a relative way.

  4. Objective • We propose a nonlinear dimensionality reduction method(DD-HDS) specifically adapted to high-dimensional data. • It differs from existing methods in this way. • A weighting of distance . • Symmetric with respect to distance in the original and output space • Optimization of the method-specific objective function is performed by force-directed placement(FDP).

  5. Method ：DD-HDS 3D to 2D • Optimization of the method-specific objective function is performed by force-directed placement(FDP).

  6. Symmetric with respect to distance in the original and out put space

  7. Force-directed placement(FDP) • The level of stability may be measured by the total energy in the system given by

  8. Experiments –Earth Globe

  9. Experiments –Open Boxes

  10. Experiments-Open Boxes

  11. Conclusions • This paper presents DD-HDS, mapping method designed to take into account the specificities of high-dimensional data. • It introduces a specific • weighting of distances taking into account the concentration of measure phenomenon. • A symmetric handling of short distance in the original and output spaces, avoiding false neighbor representations while still alowing some necessary tears. • In DD-HDS, a single user-defined parameter allows fixing the compromise between local neighborhood preservation and global mapping.

  12. Comments • Advantages • … • Disadvantages • … • Application • Visualization clustering.

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