1. Neighbourhood relation preservation (NRP) A rank-based data visualisation quality 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. By LeftSammon, using graph distances, k=20 Samples of high dimensional data (each image is 28*28=784 dimensions) 2 dimensional projection

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

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

7. Each method has its own criterion.

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

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

10. by Sammon's mappingby LeftSammon mapping Sammon vs LeftSammon mapping Assessing mapping quality by eye is usually difficult

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

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

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

14. Neighbourhood relation preservation (NRP)

15. Assessment to mappings of open box

16. Mappings of MNIST digits By CMDS By Isomap 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?