Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization

TL;DR

This paper introduces a measure theoretic framework for membership-mappings in data representation learning, providing a formal conceptualization and an analytical variational approach to improve robustness and efficiency in deep models.

Contribution

It formalizes membership-mappings using measure theory and develops an analytical variational learning approach for data representation, addressing gaps in fuzzy theoretic deep models.

Findings

Provides a measure theoretic foundation for membership-mappings

Develops an analytical variational learning method

Enhances robustness and efficiency of data representations

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.