  This study 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. The study outlines an analytical
approach to the variational learning of a membership-mappings based data
representation model. An alternative idea of deep autoencoder, referred to as
Bregman Divergence Based Conditionally Deep Autoencoder (that consists of
layers such that each layer learns data representation at certain abstraction
level through a membership-mappings based autoencoder), is presented.
Experiments are provided to demonstrate the competitive performance of the
proposed framework in classifying high-dimensional feature vectors and in
rendering robustness to the classification.
