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.