English

Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization

Machine Learning 2022-06-13 v3 Functional Analysis

Abstract

A fuzzy theoretic analytical approach was recently introduced that leads to efficient and robust models while addressing automatically the typical issues associated to parametric deep models. However, a formal conceptualization of the fuzzy theoretic analytical deep models is still not available. This paper introduces using measure theoretic basis the notion of \emph{membership-mapping} for representing data points through attribute values (motivated by fuzzy theory). A property of the membership-mapping, that can be exploited for data representation learning, is of providing an interpolation on the given data points in the data space. An analytical approach to the variational learning of a membership-mappings based data representation model is considered.

Keywords

Cite

@article{arxiv.2104.07060,
  title  = {Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization},
  author = {Mohit Kumar and Bernhard A. Moser and Lukas Fischer and Bernhard Freudenthaler},
  journal= {arXiv preprint arXiv:2104.07060},
  year   = {2022}
}
R2 v1 2026-06-24T01:10:35.576Z