Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization
This work addresses a theoretical gap in fuzzy-based deep learning, but it appears incremental as it builds on existing fuzzy approaches without clear application impact.
The paper tackles the lack of a formal conceptualization for fuzzy theoretic deep models by introducing membership-mappings based on measure theory for data representation learning, which provides interpolation on data points.
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.