6533b86dfe1ef96bd12c953b

RESEARCH PRODUCT

Optimal rates of convergence for persistence diagrams in Topological Data Analysis

Frédéric ChazalMarc GlisseCatherine LabruèreBertrand Michel

subject

Computational Geometry (cs.CG)FOS: Computer and information sciences[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT][STAT.TH] Statistics [stat]/Statistics Theory [stat.TH]Topological Data analysis Persistent homology minimax convergence rates geometric complexes metric spacesGeometric Topology (math.GT)Mathematics - Statistics TheoryStatistics Theory (math.ST)[INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG][STAT.TH]Statistics [stat]/Statistics Theory [stat.TH][INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG][ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH][ INFO.INFO-LG ] Computer Science [cs]/Machine Learning [cs.LG]Machine Learning (cs.LG)Computer Science - LearningMathematics - Geometric Topology[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG][INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG][MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: Mathematics[ INFO.INFO-CG ] Computer Science [cs]/Computational Geometry [cs.CG]Computer Science - Computational Geometry[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]

description

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.

yearjournalcountryeditionlanguage
2013-05-27
http://arxiv.org/abs/1305.6239