Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

A note on stochastic subgradient descent for persistence-based functionals: convergence and practical aspects

Mathieu Carriere 1 Frédéric Chazal 1 Marc Glisse 1 Yuichi Ike 2 Hariprasad Kannan
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : Solving optimization tasks based on functions and losses with a topological flavor is a very active and growing field of research in Topological Data Analysis, with plenty of applications in non-convex optimization, statistics and machine learning. All of these methods rely on the fact that most of the topological constructions are actually stratifiable and differentiable almost everywhere. However, the corresponding gradient and associated code is always anchored to a specific application and/or topological construction, and do not come with theoretical guarantees. In this article, we study the differentiability of a general functional associated with the most common topological construction, that is, the persistence map, and we prove a convergence result of stochastic subgradient descent for such a functional. This result encompasses all the constructions and applications for topological optimization in the literature, and comes with code that is easy to handle and mix with other non-topological constraints, and that can be used to reproduce the experiments described in the literature.
Complete list of metadatas

Cited literature [38 references]  Display  Hide  Download

https://hal.inria.fr/hal-02969305
Contributor : Mathieu Carrière <>
Submitted on : Monday, October 19, 2020 - 12:31:27 PM
Last modification on : Tuesday, October 20, 2020 - 3:37:24 AM

File

inverse_math.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02969305, version 1
  • ARXIV : 2010.08356

Collections

Citation

Mathieu Carriere, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hariprasad Kannan. A note on stochastic subgradient descent for persistence-based functionals: convergence and practical aspects. 2020. ⟨hal-02969305⟩

Share

Metrics

Record views

84

Files downloads

97