Visualization of Bottleneck Distances for \linebreak Persistence DiagramVisualization of Bottleneck Distances for \linebreak Persistence Diagram
- Other Titles
- Visualization of Bottleneck Distances for \linebreak Persistence Diagram
- Authors
- 조규동; 이은지; Taehee Seo; 김광래; 구자용
- Issue Date
- 2012
- Publisher
- 한국통계학회
- Keywords
- Multidimensional scaling(MDS); persistent homology; persistence diagram; bottleneck distance; functional data; topology
- Citation
- 응용통계연구, v.25, no.6, pp.1009 - 1018
- Indexed
- KCI
- Journal Title
- 응용통계연구
- Volume
- 25
- Number
- 6
- Start Page
- 1009
- End Page
- 1018
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/109670
- ISSN
- 1225-066X
- 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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Collections - College of Political Science & Economics > Department of Statistics > 1. Journal Articles
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