Tropical Sufficient Statistics for Persistent Homology.

摘要: We show that an embedding in Euclidean space based on tropical geometry generates stable sufficient statistics for barcodes. In topological data analysis, barcodes are multiscale summaries of algebraic characteristics capture the `shape' data; however, practice, they have complex structures make them difficult to use statistical settings. The sufficiency result presented this work allows classical probability distributions be assumed geometric representation This makes a variety parametric inference methods amenable barcodes, all while maintaining their initial interpretations. More specifically, we exponential family may assumed, and likelihood functions persistent homology constructed. conceptually demonstrate illustrate its utility dimensions 0 1 with concrete applications human immunodeficiency virus avian influenza data.