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.
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