  This paper addresses the issue of building a part-based representation of a
dataset of images. More precisely, we look for a non-negative, sparse
decomposition of the images on a reduced set of atoms, in order to unveil a
morphological and interpretable structure of the data. Additionally, we want
this decomposition to be computed online for any new sample that is not part of
the initial dataset. Therefore, our solution relies on a sparse, non-negative
auto-encoder where the encoder is deep (for accuracy) and the decoder shallow
(for interpretability). This method compares favorably to the state-of-the-art
online methods on two datasets (MNIST and Fashion MNIST), according to
classical metrics and to a new one we introduce, based on the invariance of the
representation to morphological dilation.
