Search results for "Persistent homology"
showing 4 items of 4 documents
European Congress of Mathematics Kraków, 2 – 7 July, 2012
2013
Persistent homology is a recent grandchild of homology that has found use in science and engineering as well as in mathematics. This paper surveys the method as well as the applications, neglecting completeness in favor of highlighting ideas and directions. 2010 Mathematics Subject Classification. Primary 55N99; Secondary 68W30.
Eksperimenti ar topoloģisko datu analīzi
2022
Maģistra darba mērķis ir iepazīstināt ar topoloģisko datu analīzi, kas ir pieeja datu kopu analīzei, izmantojot topoloģijas, kā matemātikas novirziena, metodes. Šī inovatīvā datu analīzes metode pasaulē pēdējos gados strauji attīstās un ar vien plašāk tiek pielietota, lai iegūtu informāciju no sarežģītiem, liela apjoma, daudzdimensionāliem datiem. Pašreiz nekur nav atrodams topoloģiskās datu analīzes apraksts un pielietojamība, latviešu valodā. Darbā tiek apskatīti divi dažādi uz topoloģiskās datu analīzes balstīti algoritmi - Mapper un ToMATo, kuru veiksmīgā izmantošanā noteicošais ir pareizu parametru izvēle. Darbā tiek pētītas un piedāvātas šo algoritmu parametru optimizācijas metodes un…
Convergence Rates for Persistence Diagram Estimation in Topological Data Analysis
2014
International audience; Computational topology has recently seen an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and that persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.
Optimal rates of convergence for persistence diagrams in Topological Data Analysis
2013
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.