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Proximity of persistence modules and their diagrams (2008)
| Content Provider | CiteSeerX |
|---|---|
| Author | Chazal, Frédéric Cohen-Steiner, David Glisse, Marc Guibas, Leonidas J. Oudot, Steve Y. |
| Abstract | Topological persistence has proven to be a key concept for the study of real-valued functions defined over topological spaces. Its validity relies on the fundamental property that the persistence diagrams of nearby functions are close. How-ever, existing stability results are restricted to the case of continuous functions defined over triangulable spaces. In this paper, we present new stability results that do not suffer from the above restrictions. Furthermore, by working at an algebraic level directly, we make it possible to compare the persistence diagrams of functions defined over different spaces, thus enabling a variety of new applications of the concept of persistence. Along the way, we extend the defini-tion of persistence diagram to a larger setting, introduce the notions of discretization of a persistence module and associ-ated pixelization map, define a proximity measure between persistence modules, and show how to interpolate between persistence modules, thereby lending a more analytic char-acter to this otherwise algebraic setting. We believe these new theoretical concepts and tools shed new light on the theory of persistence, in addition to simplifying proofs and enabling new applications. |
| File Format | |
| Language | English |
| Publisher Date | 2008-01-01 |
| Access Restriction | Open |
| Subject Keyword | Persistence Module Persistence Diagram New Application Stability Result Real-valued Function New Light Topological Persistence Nearby Function Triangulable Space Continuous Function New Stability Result Topological Space Key Concept Associ-ated Pixelization Map Analytic Char-acter New Theoretical Concept Proximity Measure Validity Relies Fundamental Property Different Space Algebraic Level |
| Content Type | Text |
| Resource Type | Technical Report |
