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Jigang Sun PhD studies finished in July 2011 PhD Supervi s or : Colin Fyfe, Malcolm Crowe

Neighbourhood relation preservation (NRP) A rank-based data visualisation quality assessment criterion. Jigang Sun PhD studies finished in July 2011 PhD Supervi s or : Colin Fyfe, Malcolm Crowe University of the West of Scotland. outline. Multidimensional Scaling (MDS);

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Jigang Sun PhD studies finished in July 2011 PhD Supervi s or : Colin Fyfe, Malcolm Crowe

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  1. Neighbourhood relation preservation (NRP)A rank-based data visualisationquality assessment criterion Jigang Sun PhD studies finished in July 2011 PhD Supervisor: Colin Fyfe, Malcolm Crowe University of the West of Scotland

  2. outline • Multidimensional Scaling (MDS); • The need for a common quality measure for data visualisation; • Local continuity meta-criterion (LCMC); • Definition of neighbourhood relation preservation (NRP); • Illustration of LCMC and NRP on mappings of data sets created by different methods;

  3. Multidimensional Scaling (MDS) A group of information visualisation methods that projects data points from high dimensional data space to low, typically two dimensional, latent space in which the structure of the original data set can be identified by eye. For example…

  4. Samples of high dimensional data (each image is 28*28=784 dimensions) 2 dimensional projection By LeftSammon, using graph distances, k=20

  5. Various methods • The classical MDS, the stress function to be minimised is defined to be • SammonMapping (1969) • Each method has its own criterion

  6. Various methods Instead of we use base function to create LeftSammon mapping My insight: 1. The above can be performed very efficiently. 2. The higher order Taylor series terms are better for analysis.

  7. Various methods • Each method has its own criterion.

  8. Mappings of open box Mappings can be assessed by eye By Sammon’s mapping By LeftSammon mapping

  9. Mappings of open box By Isomap By CMDS By LeftExp By RightExp

  10. SammonvsLeftSammon mapping by Sammon's mapping by LeftSammon mapping • Assessing mapping quality by eye is usually difficult

  11. Local continuity meta-criterion (LCMC) Problem: loose constraints

  12. Rank based quality measures • Rank is discrete; distance is continuous • Traditional rank is used in trustworthiness and continuity (T&C ) • p is mapped perfectly since rank of p does not change • Problem 1: change of intermediate points is not considered

  13. Rank based quality measures Problem 2: angle constraint is not considered

  14. Neighbourhood relation preservation (NRP) • Given and the difference in angle piq in data space and output space is less than ), we say that a neighbourhood relation of p over q with respect to i, , is preserved. We denote this as )=1; otherwise )=0; • Φ(i,k)=, t=1.3 • NRP(k)=1/N

  15. Assessment to mappings of open box

  16. Mappings of MNIST digits By Isomap By CMDS By LeftExp By RightExp

  17. Assessment of mappings of digits

  18. Conclusions • Multidimensional Scaling (MDS); • List of objective function of some MDS methods; • The need for a common quality measure for data visualisation; • Local continuity meta-criterion (LCMC); • Definition of Neighbourhood relation preservation (NRP); • Comparison of LCMC and NRP on mappings of data sets created by different methods; Thank you! Any questions?

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