The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Visualization of Bottleneck Distances for Persistence Diagram

  • Cho, Kyu-Dong (Department of Statistics, Korea University) ;
  • Lee, Eunjee (Statistics and Operations Research, University of North Carolina at Chapel Hill) ;
  • Seo, Taehee (Department of Statistics, Korea University) ;
  • Kim, Kwang-Rae (Institute for Mathematical Stochastics, Georg-August-University of Goettingen) ;
  • Koo, Ja-Yong (Department of Statistics, Korea University)
  • Received : 2012.08.30
  • Accepted : 2012.10.31
  • Published : 2012.12.31
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Abstract

Persistence homology (a type of methodology in computational algebraic topology) can be used to capture the topological characteristics of functional data. To visualize the characteristics, a persistence diagram is adopted by plotting baseline and the pairs that consist of local minimum and local maximum. We use the bottleneck distance to measure the topological distance between two different functions; in addition, this distance can be applied to multidimensional scaling(MDS) that visualizes the imaginary position based on the distance between functions. In this study, we use handwriting data (which has functional forms) to get persistence diagram and check differences between the observations by using bottleneck distance and the MDS.

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References

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