Visualization of Bottleneck Distances for Persistence Diagram

- Journal title : Korean Journal of Applied Statistics
- Volume 25, Issue 6, 2012, pp.1009-1018
- Publisher : The Korean Statistical Society
- DOI : 10.5351/KJAS.2012.25.6.1009

Title & Authors

Visualization of Bottleneck Distances for Persistence Diagram

Cho, Kyu-Dong; Lee, Eunjee; Seo, Taehee; Kim, Kwang-Rae; Koo, Ja-Yong;

Cho, Kyu-Dong; Lee, Eunjee; Seo, Taehee; Kim, Kwang-Rae; Koo, Ja-Yong;

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.

Keywords

Multidimensional scaling(MDS);persistent homology;persistence diagram;bottleneck distance;functional data;topology;

Language

Korean

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