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Everything about Persistence module

A persistence module is a mathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological features of an object across a range of scale parameters. A persistence module often consists of a collection of homology groups corresponding to a filtration of topological spaces, and a collection of linear maps induced by the inclusions of the filtration. The concept of a persistence module was first introduced in 2005 as an application of graded modules over polynomial rings, thus importing well-developed algebraic ideas from classical commutative algebra theory to the setting of persistent homology. Since then, persistence modules have been one of the primary algebraic structures studied in the field of applied topology. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Persistence moduleA 5-minute orientation
  2. Skim a recent paper: Generalized persistence algorithm for decomposing multiparameter persistence modulesInfluential work since 2022
  3. Pick up a classic book: JavaScriptThe most-reprinted book on the subject
  4. Read the landmark paper: Spread and Persistence of Virulence and Antibiotic Resistance Genes: A Ride on the F Plasmid Conjugation ModuleCited 112 times
  5. Go sideways: Topological data analysisA closely related topic
  6. Go sideways: Persistence barcodeA closely related topic

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