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arXiv · 2104.07060

Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization

Mohit Kumar·Bernhard A. Moser·Lukas Fischer·Bernhard Freudenthaler
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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.

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Mohit Kumar, Bernhard A. Moser, Lukas Fischer, Bernhard Freudenthaler. 2021-04-14. Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization. https://arxiv.org/abs/2104.07060

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