Fixed Point Strategies in Data Science - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles IEEE Transactions on Signal Processing Year : 2021

Fixed Point Strategies in Data Science

Abstract

The goal of this paper is to promote the use of fixed point strategies in data science by showing that they provide a simplifying and unifying framework to model, analyze, and solve a great variety of problems. They are seen to constitute a natural environment to explain the behavior of advanced convex optimization methods as well as of recent nonlinear methods in data science which are formulated in terms of paradigms that go beyond minimization concepts and involve constructs such as Nash equilibria or monotone inclusions. We review the pertinent tools of fixed point theory and describe the main state-of-the-art algorithms for provenly convergent fixed point construction. We also incorporate additional ingredients such as stochasticity, block-implementations, and non-Euclidean metrics, which provide further enhancements. Applications to signal and image processing, machine learning, statistics, neural networks, and inverse problems are discussed.
Fichier principal
Vignette du fichier
sp14.pdf (780.92 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03495546 , version 1 (04-01-2022)

Identifiers

Cite

Patrick Combettes, Jean-Christophe Pesquet. Fixed Point Strategies in Data Science. IEEE Transactions on Signal Processing, 2021, 69, pp.3878-3905. ⟨10.1109/TSP.2021.3069677⟩. ⟨hal-03495546⟩
132 View
127 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More