Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization
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.
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}
}