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Membership-Mappings for Data Representation Learning: Measure Theoretic Conceptualization

2021; Springer Science+Business Media; Linguagem: Inglês

10.1007/978-3-030-87101-7_13

1865-0937

Mohit Kumar, Bernhard Moser, Lukas Fischer, Bernhard Freudenthaler,

Anomaly Detection Techniques and Applications

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 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.